Department of

# Mathematics

Seminar Calendar
for events the year of Friday, February 26, 2021.

.
events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2021          February 2021            March 2021
Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa   Su Mo Tu We Th Fr Sa
1  2       1  2  3  4  5  6       1  2  3  4  5  6
3  4  5  6  7  8  9    7  8  9 10 11 12 13    7  8  9 10 11 12 13
10 11 12 13 14 15 16   14 15 16 17 18 19 20   14 15 16 17 18 19 20
17 18 19 20 21 22 23   21 22 23 24 25 26 27   21 22 23 24 25 26 27
24 25 26 27 28 29 30   28                     28 29 30 31
31


Thursday, January 7, 2021

3:00 pm in Zoom,Thursday, January 7, 2021

#### On the shifted Littlewood-Richardson coefficients and Littlewood-Richardson coefficients

###### Khanh Nguyen Duc   [email] (Université de Lyon)

Abstract: We give a new interpretation of the shifted Littlewood-Richardson coefficients $f_{\lambda\mu}^\nu$ ($\lambda,\mu,\nu$ are strict partitions). The coefficients $g_{\lambda\mu}$ which appear in the decomposition of Schur $Q$-function $Q_\lambda$ into the sum of Schur functions $Q_\lambda = 2^{l(\lambda)}\sum\limits_{\mu}g_{\lambda\mu}s_\mu$ can be considered as a special case of $f_{\lambda\mu}^\nu$ (here $\lambda$ is a strict partition of length $l(\lambda)$). We also give another description for $g_{\lambda\mu}$ as the cardinal of a subset of a set that counts Littlewood-Richardson coefficients $c_{\mu^t\mu}^{\tilde{\lambda}}$. This new point of view allows us to establish connections between $g_{\lambda\mu}$ and $c_{\mu^t \mu}^{\tilde{\lambda}}$. More precisely, we prove that $g_{\lambda\mu}=g_{\lambda\mu^t}$, and $g_{\lambda\mu} \leq c_{\mu^t\mu}^{\tilde{\lambda}}$. We conjecture that $g_{\lambda\mu}^2 \leq c^{\tilde{\lambda}}_{\mu^t\mu}$ and formulate some conjectures on our combinatorial models which would imply this inequality if it is valid. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Thursday, January 14, 2021

3:00 pm in Zoom,Thursday, January 14, 2021

#### A crystal for stable Grothendieck polynomials

###### Jianping Pan   [email] (UC Davis)

Abstract: We construct a type A crystal, which we call the $\star$-crystal, whose character is the stable Grothendieck polynomials for fully-commutative permutations. This crystal is a K-theoretic generalization of Morse-Schilling crystal on decreasing factorizations. Using the residue map, we showed that this crystal intertwines with the crystal on set-valued tableaux given by Monical, Pechenik and Scrimshaw. We also proved that this crystal is isomorphic to that of pairs of semistandard Young tableaux using a newly defined insertion called the $\star$ -insertion. The insertion offers a combinatorial interpretation to the Schur positivity of the stable Grothendieck polynomials for fully-commutative permutations. Furthermore, the $\star$ -insertion has interesting properties in relation to row Hecke insertion and the uncrowding algorithm. This is joint work with Jennifer Morse and Anne Schilling. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Wednesday, January 20, 2021

10:00 am in Online,Wednesday, January 20, 2021

#### Introduction to Integrability

###### Michael Gekhtman (Notre Dame)

Abstract: I will review the basic notions of the theory of integrable systems, including Poisson structures, integrals of motion and Lax pairs. I will use the Toda lattice as the main example to illustrate how the same mechanical system can have different geometric incarnations.

Thursday, January 21, 2021

3:00 pm in Zoom,Thursday, January 21, 2021

#### The e-positivity of chromatic symmetric functions

###### Stephanie van Willigenburg   [email] (University of British Columbia)

Abstract: The chromatic polynomial was generalized to the chromatic symmetric function by Stanley in his seminal 1995 paper. This function is currently experiencing a flourishing renaissance, in particular the study of the positivity of chromatic symmetric functions when expanded into the basis of elementary symmetric functions, that is, e-positivity. In this talk we approach the question of e-positivity from various angles. Most pertinently we resolve the 1995 statement of Stanley that no known graph exists that is not contractible to the claw, and whose chromatic symmetric function is not e-positive. This is joint work with Soojin Cho, Samantha Dahlberg, Angele Foley and Adrian She, and no prior knowledge is assumed. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Friday, January 22, 2021

4:00 pm in Zoom,Friday, January 22, 2021

#### Department Town Hall Meeting

###### Department of Mathematics (Illinois Math)

Monday, January 25, 2021

3:00 pm in Zoom,Monday, January 25, 2021

#### Organisational meeting

###### Sai (UIUC)

Abstract: This is the organisational meeting for the graduate student homotopy theory seminar. Please email vb8 at illinois dot edu for the zoom details.

Tuesday, January 26, 2021

11:00 am in Via Zoom,Tuesday, January 26, 2021

#### Models of Lubin-Tate spectra via Real bordism theory

###### XiaoLin "Danny" Shi (University of Chicago)

Abstract: In this talk, we will present Real-oriented models of Lubin-Tate theories at p=2 and arbitrary heights. For these models, we give explicit formulas for the action of certain finite subgroups of the Morava stabilizer groups on the coefficient rings. This is an input necessary for future computations. The construction utilizes equivariant formal group laws associated with the norms of the Real bordism theory. As a consequence, we will describe how we can use these models to prove periodicity theorems for Lubin-Tate theories and set up an inductive approach to prove differentials in their slice spectral sequences. This talk is based on several joint projects with Agnès Beaudry, Jeremy Hahn, Mike Hill, Guchuan Li, Lennart Meier, Guozhen Wang, Zhouli Xu, and Mingcong Zeng.

2:00 pm in Zoom,Tuesday, January 26, 2021

#### Coding Theory and Sidon Sequences

###### Zoltan Furedi (Renyi Institute for Mathematics)

Abstract: A sequence ${a_1, a_2,\dots, a_k}$ of integers is called a $B_2$ sequence if all the sums $a_i + a_j$, $1 \leq i \leq j \leq k$, are different. Let $F_2(n)$ be the maximum number of elements that can be selected from the set ${1,2,\dots,n}$ so as to form a $B_2$ sequence. Among others we give a new elementary proof for the result of Erdos and Turan (1941) that $F_2(n)= \sqrt{n} + O(n^{1/4})$.

Thursday, January 28, 2021

3:00 pm in Zoom,Thursday, January 28, 2021

#### On the Okounkov-Olshanski formula for standard tableaux of skew shapes

###### Alejandro H. Morales   [email] (University of Massachusetts Amherst)

Abstract: The classical hook length formula counts the number of standard tableaux of straight shapes. In 1996, Okounkov and Olshanski found a positive formula for the number of standard Young tableaux of a skew shape. We prove various properties of this formula, including three determinantal formulas for the number of nonzero terms, an equivalence between the Okounkov-Olshanski formula and another skew tableaux formula involving Knutson-Tao puzzles, and two q-analogues for reverse plane partitions, which complements work by Stanley and Chen for semistandard tableaux. We also give applications and several reformulations of the formula, including two in terms of the excited diagrams appearing in a more recent skew tableaux formula by Naruse. This is joint work with Daniel Zhu. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Friday, January 29, 2021

4:00 pm in Zoom,Friday, January 29, 2021

#### Organizaitonal Meeting

###### Brannon (UIUC)

Abstract: We will be having our first organizational meeting. Please email basilio3(at)illinois(dot)edu for the Zoom information.

4:00 pm in Zoom,Friday, January 29, 2021

#### The Mathematics Behind Two Puzzles

###### Jared Bronski (UIUC)

Abstract: I plan to talk about two puzzles with very elegant mathematical solutions. I would encourage you to think about (but not Google!) these puzzles, particularly the easier version of the first puzzle, before the talk. All of them can be found in the attachment below. We'll also need volunteers for a demonstration on Friday, so if you'd like to help please email undergradseminar@math.illinois.edu. For Zoom info, please email undergradseminar@math.illinois.edu

Monday, February 1, 2021

3:00 pm in Zoom,Monday, February 1, 2021

#### Thom spectra via rigid spaces

###### Heyi Zhu (UIUC)

Abstract: The classical definition of the space $GL_1(R)$ of units, given a ring spectrum $R$, does not play well with more modern models of spectra. In this talk, we will introduce Ando-Blumberg-Gepner-Hopkins-Rezk's Thom spectra functor, which builds upon a construction of $GL_1(R)$ as an $A_{\infty}$-space. If time permits, we will also briefly look at their $E_{\infty}$-version. Please email vb8 at illinois dot edu for the zoom details.

Tuesday, February 2, 2021

11:00 am in Zoom,Tuesday, February 2, 2021

#### Redshift in algebraic K-theory

###### Jeremy Hahn (MIT)

Abstract: I will describe work, joint with Dylan Wilson, about the redshifting properties of algebraic K-theory. I will focus on concrete examples, sketching proofs at the prime 2 that K(ko) has chromatic height 2 and K(tmf) has chromatic height 3.

For Zoom info, please email vesna@illinois.edu

2:00 pm in Zoom,Tuesday, February 2, 2021

#### Acyclic graphs with at least 2L + 1 vertices are L-recognizable

###### Dara Zirlin (UIUC)

Abstract: The $(n-L)$-deck of an $n$-vertex graph is the multiset of subgraphs obtained from it by deleting $L$ vertices. A family of $n$-vertex graphs is $L$-recognizable if every graph having the same $(n-L)$-deck as a graph in the family is also in the family. We prove that the family of $n$-vertex graphs having no cycles is $L$-recognizable when $n\geq 2L+1$ (except when $(n,L)=(5,2)$). It is already known that this fails when $n=2L$ and when $(n,L)=(5,2)$.

This is joint work with Alexandr V. Kostochka, Mina Nahvi, and Douglas B. West.

Wednesday, February 3, 2021

10:00 am in Zoom,Wednesday, February 3, 2021

#### Introduction to Integrability, part 2

###### Michael Gekhtman (Notre Dame)

Abstract: I will review the basic notions of the theory of integrable systems, including Poisson structures, integrals of motion and Lax pairs. I will use the Toda lattice as the main example to illustrate how the same mechanical system can have different geometric incarnations.

Thursday, February 4, 2021

4:00 pm in Zoom,Thursday, February 4, 2021

#### The 1/3-2/3 Conjecture for Coxeter groups

###### Yibo Gao   [email] (Massachusetts Institute of Technology )

Abstract: The 1/3-2/3 Conjecture, originally formulated in 1968, is one of the best-known open problems in the theory of posets, stating that the balance constant of any non-total order is at least 1/3. By reinterpreting balance constants of posets in terms of convex subsets of the symmetric group, we extend the study of balance constants to convex subsets C of any Coxeter group. Remarkably, we conjecture that the lower bound of 1/3 still applies in any finite Coxeter group, with new and interesting equality cases appearing. We generalize several of the main results towards the 1/3-2/3 Conjecture to this new setting: we prove our conjecture when C is a weak order interval below a fully commutative element in any acyclic Coxeter group (a generalization of the case of width-two posets), we give a uniform lower bound for balance constants in all finite Weyl groups using a new generalization of order polytopes to this context, and we introduce generalized semiorders for which we resolve the conjecture. We hope this new perspective may shed light on the proper level of generality in which to consider the 1/3-2/3 Conjecture, and therefore on which methods are likely to be successful in resolving it. This is joint work with Christian Gaetz. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Friday, February 5, 2021

4:00 pm in Zoom,Friday, February 5, 2021

#### Satisfiability: Why some problems are easy, while others are hard

###### Vaibhav Karve (UIUC)

Abstract: I will introduce a 50-year-old problem called Boolean Satisfiability (or simply SAT) and I will explain why we should care about it. We will explore how an abstract-looking problem can end up being connected to circuits, airline scheduling, Rubiks cubes, chess, video games, and travelling salesmen. I will explain how small SAT are easy and how big SAT can be hard -- and how we quantify the hardness of a problem. By the end of the talk, we will have learned some computer science as well.

4:30 pm in Zoom,Friday, February 5, 2021

#### Department Town Hall Meeting

###### Department of Mathematics (Illinois Math)

Monday, February 8, 2021

3:00 pm in Zoom,Monday, February 8, 2021

#### Spectral sequences and deformations of homotopy theories I

###### William Balderrama (UIUC)

Abstract: One of the oldest problems in stable homotopy theory is simple: just compute the stable homotopy groups of spheres. This turns out to be difficult, and a complete answer may never be known, but the computations continue. A recent technique being applied to great success can be summarized as: don't just compute the stable homotopy groups of the sphere spectrum, also compute the stable homotopy groups of other sphere spectra. These other sphere spectra include, for example, those arising in motivic and equivariant contexts, and can be thought of as deformations of the classical sphere spectrum. The homotopy theories they live in can then be thought of as deformations of classical stable homotopy theory. There are a few methods for building these deformations; the goal of this sequence of two talks is to describe the concrete approach to this deformation story using filtered objects. Please email vb8 at illinois dot edu for the zoom details.

Tuesday, February 9, 2021

2:00 pm in Zoom,Tuesday, February 9, 2021

#### Maximum Number of Almost Similar Triangles in the Plane

###### Felix Clemen (UIUC)

Abstract: A triangle $T'$ is $\epsilon$-similar to another triangle $T$ if their angles pairwise differ by at most $\epsilon$. Given a triangle $T$, $\epsilon>0$ and a natural number $n$, Bárány and Füredi asked to determine the maximum number of triangles being $\epsilon$-similar to $T$ in a planar point set of size $n$. We determine this quantity for almost all triangles $T$ and sufficiently small $\epsilon$. Exploring connections to hypergraph Turán problems, we use flag algebras and stability techniques for the proof. This is joint work with József Balogh and Bernard Lidický.

Thursday, February 11, 2021

3:00 pm in Zoom,Thursday, February 11, 2021

#### Doing Schubert calculus with Bumpless Pipe Dreams

###### Daoji Huang   [email] (Brown University)

Abstract: Bumpless pipe dreams were introduced by Lam, Lee, and Shimozono in the context of back stable Schubert calculus. Like ordinary pipe dreams, they compute Schubert and double Schubert polynomials. In this talk, I will give a bijective proof of Monk's rule for Schubert polynomials, and show that the proof extends easily to the proof of Monk's rule for double Schubert polynomials. As an application, I will explain how to biject bumpless pipe dreams and ordinary pipe dreams using the transition and co-transition formulas, which are specializations of Monk's rule. If time permits I will also briefly discuss and share some work in progress on how bumpless pipe dreams can be used to compute products of certain Schubert polynomials in generalizations of the Littlewood-Richardson rule for Schur polynomials. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Friday, February 12, 2021

2:00 pm in Contact for zoom link,Friday, February 12, 2021

#### The Largest Sum-free Subsets of Integers and its Generalization

###### Shukun Wu (UIUC Math)

Abstract: An old conjecture in additive combinatorics asks: what is the largest sum-free subset of any set of N positive integers? Here the word "largest" should be understood in terms of cardinality. For example, the largest sum-free subset of the first N positive integers has cardinality [(N+1)/2], which is the number of odd integers smaller than N, as well as the number of integers that lie in the interval [N/2,N]. In this talk, I will discuss a special case of the sum-free conjecture and the analogous conjecture on (k,l)-sum-free sets. This is a joint work with Yifan Jing

4:00 pm in Zoom,Friday, February 12, 2021

#### Geometry of Knots

###### Brannon Basilio (UIUC)

Abstract: In this talk, we give an introduction to the geometry of knots. We first start with an example of how to decompose a knot complement into ideal tetrahedron and the conditions needed in order to obtain a hyperbolic structure on the tetrahedron. We then talk briefly of recent work in knot theory that uses this decomposition to obtain bounds on the hyperbolic volume of the knot complement. For Zoom information, please email basilio3 (at) illinois (dot) edu.

Monday, February 15, 2021

3:00 pm in Zoom,Monday, February 15, 2021

#### Spectral sequences and deformations of homotopy theories II

###### William Balderrama (UIUC)

Abstract: One of the oldest problems in stable homotopy theory is simple: just compute the stable homotopy groups of spheres. This turns out to be difficult, and a complete answer may never be known, but the computations continue. A recent technique being applied to great success can be summarized as: don't just compute the stable homotopy groups of the sphere spectrum, also compute the stable homotopy groups of other sphere spectra. These other sphere spectra include, for example, those arising in motivic and equivariant contexts, and can be thought of as deformations of the classical sphere spectrum. The homotopy theories they live in can then be thought of as deformations of classical stable homotopy theory. There are a few methods for building these deformations; the goal of this sequence of two talks is to describe the concrete approach to this deformation story using filtered objects. Please email vb8 at illinois dot edu for the zoom details.

5:00 pm in Altgeld Hall,Monday, February 15, 2021

#### organizational meeting

Abstract: Material in folder see you at https://illinois.zoom.us/j/87333719853?pwd=bFdWSkdqeEt1M3djNmVEU2Jvb3JzUT09 Meeting ID: 873 3371 9853 Password: 982399

Tuesday, February 16, 2021

11:00 am in Zoom,Tuesday, February 16, 2021

#### Understanding accessible infinity-categories

###### Charles Rezk   [email] (UICU)

Abstract: Lurie introduced the very important notion of "accessible infinity-category", a generalization of the more classical notion of "accessible category". These are (infinity-)categories which are produced from two pieces of data: a small (infinity-)category and a "regular cardinal". The goal of this talk is to give an introduction to some of the ideas surrounding these, and to put them in a broader context.

Email vesna@illinois.edu for zoom info.

11:00 am in Zoom,Tuesday, February 16, 2021

#### Landau-Siegel zeros and central values of L-functions

###### Kyle Pratt (Oxford)

Abstract: Researchers have tried for many years to eliminate the possibility of Landau-Siegel zeros---certain exceptional counterexamples to the Generalized Riemann Hypothesis. Often one thinks of these zeros as being a severe nuisance, but there are many situations in which their existence allows one to prove spectacular, though illusory, results. I will review some of this history and some of these results. In the latter portion of the talk I will discuss recent work, joint with H. M. Bui and Alexandru Zaharescu, in which we show that the existence of Landau-Siegel zeros has implications for the behavior of $L$-functions at the central point.

2:00 pm in Zoom,Tuesday, February 16, 2021

#### A proof of the Erdős–Faber–Lovász conjecture

###### Abhishek Methuku (University of Birmingham)

Abstract: The celebrated Erdős–Faber–Lovász conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on $n$ vertices is at most $n$. In this talk, I will sketch a proof of this conjecture for every large n.

Joint work with D. Kang, T. Kelly, D. Kühn and D. Osthus.

Wednesday, February 17, 2021

6:30 pm in Zoom,Wednesday, February 17, 2021

#### To Be Announced

###### Jennifer Gillespie (President-elect, Society of Actuaries)

Thursday, February 18, 2021

2:00 pm in Zoom,Thursday, February 18, 2021

#### Interlacing methods in extremal combinatorics

###### Hao Huang (Emory University)

Abstract: Extremal Combinatorics studies how large or how small a collection of finite objects could be, if it must satisfy certain restrictions. In this talk, we will discuss how eigenvalue interlacing lead to various interesting results in Extremal Combinatorics, including the Erdos-Ko-Rado Theorem and its degree version, an isodiametric inequality for discrete cubes, and the resolution of a thirty-year-old open problem in Theoretical Computer Science, the Sensitivity Conjecture. A number of open problems will be discussed during this talk.

3:00 pm in Zoom,Thursday, February 18, 2021

#### Determinantal ideals, pipe dreams, and non-intersecting lattice paths

###### Li Li   [email] (Oakland University)

Abstract: Determinantal ideals are ideals generated by minors of a variable matrix. They play an important role in both commutative algebra and algebraic geometry. A combinatorial approach to study a determinantal ideal is to apply Groebner degeneration to get a squarefree monomial ideal, and study the corresponding simplicial complex instead. Through this approach, some invariants such as Hilbert polynomials of the ideals can be expressed in terms of pipe dreams and non-intersecting lattice paths. In this talk, I will report recent work on double determinantal ideals, and in particular the combinatorial objects that play the role of non-intersecting lattice paths. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Friday, February 19, 2021

2:00 pm in Contact for zoom link,Friday, February 19, 2021

#### Expanding Thurston Maps and Visual Spheres

###### Stathis Chrontsios (UIUC Math)

Abstract: Complex Dynamics study iterations of entire functions and/or rational maps. While doing so in the latter case, the properties of the Riemann sphere are being used (e.g. conformal structure). In this talk, the protagonists will be Thurston maps, generalizations of rational maps that are defined on topological spheres. Connections with their complex analytic counterparts will be discussed, as well as questions from a metric-analytic point of view about visual spheres, the metric spaces the dynamics of these maps induce.

4:30 pm in Zoom,Friday, February 19, 2021

#### Department Town Hall Meeting

###### Department of Mathematics (Illinois Math)

Monday, February 22, 2021

3:00 pm in zoom,Monday, February 22, 2021

#### Symplectic fillings and cobordisms of lens spaces

###### John Etnyre (Georgia Tech)

Abstract: Tight contact structures on lens space break into two types: universally tight and virtually overtwisted. In 2008, Lisca classified all symplectically fillable contact structures of universally tight contact structures on lens spaces. There have been several partial results for the larger class of virtually overstated contact structures on lens spaces, most notably Plamenevskaya and Van Horn-Morris classification of symplectic fillings of all tight contact structures on L(p,1). In this talk I will discuss joint work with Agniva Ray that classifies all minimal symplectic fillings of all tight contact structures on lens spaces. If time permits we will also discuss some interesting cobordisms between them and related open problems.

3:00 pm in Zoom,Monday, February 22, 2021

#### Structure of the Motivic Stable Homotopy Category

###### Brian Shin (UIUC)

Abstract: In classical homotopy theory, a first step in understanding the stable homotopy category is understanding the zeroth stable stem $\pi_0 \mathbf{S}$. The fact that this is the ring of integers leads to the idea that we may be able to study things "one prime at a time". In this expository talk, I'll talk about the analogous story in the setting of motivic homotopy theory. After reviewing basics of the motivic story, we'll see how knowledge of the motivic zeroth stable stem can be used to better understand the motivic stable homotopy category. Please email vb8 at illinois dot edu for the zoom details.

5:00 pm in Altgeld Hall,Monday, February 22, 2021

#### Subriemanian Geodesic Flow

Abstract: We will discuss a paper by Grong and Molina for subriemanian flow in totally geodesic Riemaninan submesions https://illinois.zoom.us/j/87333719853?pwd=bFdWSkdqeEt1M3djNmVEU2Jvb3JzUT09

Tuesday, February 23, 2021

11:00 am in Zoom,Tuesday, February 23, 2021

#### The Borel C_2-equivariant K(1)-local sphere

###### William Balderrama (UIUC)

Abstract: I'll talk about the structure of the Borel C_2-equivariant K(1)-local sphere. This captures Im J-type phenomena in C_2-equivariant and R-motivic stable stems, and gives a concise approach to understanding the K(1)-localizations of stunted projective spaces.

1:00 pm in Altgeld Hall,Tuesday, February 23, 2021

#### Poisson manifolds of strong compact type over 2-tori

###### Luka Zwann (UICU)

2:00 pm in Zoom,Tuesday, February 23, 2021

#### The Feasible Region of Hypergraphs

###### Dhruv Mubayi (University of Illinois, Chicago)

Abstract: Many extremal hypergraph problems seek to maximize the number of edges subject to some local constraints. We aim to gain a more detailed understanding of such problems by studying the maximum subject to an additional global constraint, namely the size of the shadow. Put differently, we seek the pairs $(x,y)$ in the unit square such that there are $F$-free hypergraphs whose shadow density approaches $x$ and edge density approaches $y$. I will give some general results about the shape of this "feasible region" and also extend and improve some classical Turan-type results for particular choices of $F$. This is joint work with Xizhi Liu.

For Zoom information, please email Sean at SEnglish (at) illinois (dot) edu.

3:00 pm in Zoom,Tuesday, February 23, 2021

#### The Peterson Isomorphism and Quantum Cohomology of the Grassmannian

###### Elizabeth Milićević   [email] (Haverford College)

Abstract: The Peterson isomorphism directly relates the homology of the affine Grassmannian to the quantum cohomology of any finite flag variety. In the case of a partial flag, Peterson’s map is only a surjection, and one needs to quotient by a suitable ideal to map isomorphically onto the quantum cohomology. In this talk, we first provide an exposition of this parabolic Peterson isomorphism in the case of the Grassmannian. We then relate the Peterson isomorphism via Postnikov’s strange duality to several quantum-to-affine correspondences on the k-Schur functions representing the homology of the affine Grassmannian. This talk includes joint work with J. Cookmeyer, as well as L. Chen and J. Morse. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Thursday, February 25, 2021

3:00 pm in Zoom,Thursday, February 25, 2021

#### Equivariant quantum Pieri rule on cylindric shapes

###### Kaisa Taipale   [email] (University of Minnesota and C.H. Robinson)

Abstract: The equivariant quantum cohomology of Grassmannians is an amazing place to study the collision of a number of combinatorial and algebro-geometric phenomena. In this talk, I will introduce an equivariant quantum Pieri rule for Grassmannians (https://arxiv.org/pdf/2010.15395.pdf) that uses the machinery of cylindric shapes in novel ways: it is computationally elegant, requires no recursion, and puts in reach the solutions to a number of additional combinatorial problems. While emphasizing the natural geometric structure of the Grassmannian that this rule illuminates, I’ll also tell the story of this problem, which started with collaboration and conjecture at IAS and continued through periods of both dormancy and deep discussion, as well as the career changes of several of the collaborators. This is joint work with Elizabeth Milićević, Dorian Ehrlich, and Anna Bertiger. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Friday, February 26, 2021

2:00 pm in Contact for zoom link,Friday, February 26, 2021

#### Minimizing Eigenvalues of the Laplacian

###### Scott Harman (UIUC Math)

Abstract: pectral theory is concerned with studying the eigenvalues of partial differential operators. The most canonical example is the second order Laplacian . In this talk, we are concerned mostly with minimizing eigenvalues of the Laplacian on a bounded domain with and has zero boundary condition. To phrase it another way, what shape of domain will yield the smallest frequencies? We will give a brief overview of spectral theory, a proof of the Faber-Krahn inequality which states the ball minimizes the first eigenvalue, and conjectures for higher eigenvalues and the shape of the domain in the limiting case.

4:00 pm in Zoom,Friday, February 26, 2021

#### A Length and an Area Walk Into a Bar Complex

###### Cameron Rudd (UIUC)

Abstract: I will discuss some occurrences of lengths and area in geometry. Please contact basilio3 (at) illinois (dot) edu for Zoom information.

Monday, March 1, 2021

3:00 pm in Zoom,Monday, March 1, 2021

#### Generalized Gauge Theory: Where Logic Meets Homotopy Theory

###### Joseph Rennie (UIUC)

Abstract: Higher categories admit a notion of internal groupoids which Nikolaus et. al have shown yield a nice theory of principle bundles in any higher topos. An example of the practical use of this can be seen work of Freed-Hopkins where they define a higher topos of “generalized spaces” which then admits a universal bundle with connection. In an attempt to extend the results of Nikolaus to more kinds of categories, we inevitably end up working with the same kinds of structures as logicians. Namely, with pretoposes and logical functors, as opposed to the more homotopy theoretic grothendieck toposes and geometric morphisms. The goal of this talk will be to demystify this deep connection between model theory (in the logician’s sense) and homotopy theory. This talk will mostly operate at a conceptual level to more insightfully navigate the fact that many results that we want don’t yet have analogs proven in the higher-categorical setting, and the fact that the lower setting doesn’t quite have as nice of a picture. I assume no background in logic, and a vague awareness of the use (conceptually) of toposes in homotopy theory. Please email vb8 at illinois dot edu for the zoom details.

3:00 pm in zoom,Monday, March 1, 2021

#### Poisson manifolds of strong compact type over 2-tori

###### Luka Zwann (UIUC)

Abstract: An integrable Poisson manifold is said to be of strong compact type if the source 1-connected groupoid integrating it is compact. A trivial class of such manifolds is that of compact symplectic manifolds with finite fundamental group, but beyond that finding examples is difficult. The first non-trivial example was given by D. Martínez Torres in 2014. The construction there is inspired by D. Kotschick’s construction of a free symplectic circle action with contractible orbits. In this talk I will go over the original construction, recalling the relevant results on Poisson manifolds of compact types as well as the geometry of the moduli spaces of K3 surfaces, and then modify the construction to obtain more examples. In the end, we will have for every strongly integral affine 2-torus (i.e. integral affine 2-torus with integral translational part) a Poisson manifold of strong compact type having said torus as its leaf space.

5:00 pm in Altgeld Hall,Monday, March 1, 2021

#### Subriemanian Geodesic Flow

Abstract: Part 2 subriemanian geometry https://illinois.zoom.us/j/87333719853?pwd=bFdWSkdqeEt1M3djNmVEU2Jvb3JzUT09

Tuesday, March 2, 2021

11:00 am in Zoom,Tuesday, March 2, 2021

#### On the Liouville function at polynomial arguments

###### Joni Teravainen (Oxford)

Abstract: Let $\lambda$ be the Liouville function and $P(x)$ any polynomial that is not a square. An open problem formulated by Chowla and others asks to show that the sequence $\lambda(P(n))$ changes sign infinitely often. We present a solution to this problem for new classes of polynomials $P$, including any product of linear factors or any product of quadratic factors of a certain type. The proofs also establish some nontrivial cancellation in Chowla and Elliott type correlation averages.

2:00 pm in Zoom,Tuesday, March 2, 2021

#### Sparse random graphs with overlapping community structure

###### Sam Petti (Harvard University)

Abstract: In this talk we introduce two different random graph models that produce sparse graphs with overlapping community structure and discuss community detection in each context. The Random Overlapping Community (ROC) model produces a sparse graph by constructing many Erdos Renyi random graphs (communities) on small randomly selected subsets of vertices. By varying the size and density of these communities, ROC graphs can be tuned to exhibit a wide range normalized of closed walk count vectors, including those of hypercubes. This is joint work with Santosh Vempala. In the second half of the talk, we introduce the Community Configuration Model (CCM), a variant of the configuration model in which half-edges are assigned colors and pair according to a matching rule on the colors. The model is a generalization of models in the statistical physics literature and is a natural finite analog for classes of graphexes. We describe a hypothesis testing algorithm that determines whether a graph came from a community configuration model or a traditional configuration model. This is joint work with Christian Borgs, Jennifer Chayes, Souvik Dhara, and Subhabrata Sen.

Thursday, March 4, 2021

3:00 pm in Zoom,Thursday, March 4, 2021

#### Uncrowding Algorithm for Hook-Valued Tableaux

###### Wencin Poh (UC Davis)

Abstract: Whereas set-valued tableaux are the combinatorial objects associated to stable (Grassmann) Grothendieck polynomials, hook-valued tableaux are associated to stable canonical Grothendieck polynomials. We define a novel uncrowding algorithm for hook-valued tableaux. The algorithm “uncrowds” the entries in the arm of the hooks and yields a set-valued tableau and a column-flagged increasing tableau. This uncrowding algorithm intertwines with the crystal operators on hook-valued tableaux. We also provide an alternative uncrowding algorithm that “uncrowds” the entries in the leg instead of the arm of the hooks. As an application, we obtain various expansions of the canonical Grothendieck polynomials.

Friday, March 5, 2021

2:00 pm in Contact for zoom link,Friday, March 5, 2021

#### $L^{2}$ decoupling: An Introduction and Applications

###### Ryan McConnell (UIUC Math)

Abstract: Suppose one wants to decompose a function on into parts that have disjoint Fourier supports. Due to linearity of the Fourier transform, the sum of these parts must be the original function. Suppose, however, that you wish to understand how the norms of these parts relates to the norm of the original function. While this task isn’t so straight forward, Bourgain and Demeter (2015) were able to resolve a conjecture related to this: the $L^{2}$ Decoupling Conjecture.In this talk we will introduce the conjecture, provide applications of it to both PDEs and Number Theory, prove an earlier result of Bourgain for a smaller range of admissible exponents, and (time permitting) comment on how to adapt the ideas presented to prove the full result.

4:00 pm in Zoom,Friday, March 5, 2021

#### To (Conformal) Infinity and Beyond!

Abstract: In this talk I'll describe a few geometric and analytic questions in the context of asymptotically hyperbolic spaces: manifolds which look like hyperbolic space at infinity. I'll do my best to gesture at which of these questions were inspired by conjectures of physicists (such as the AdS-CFT correspondence), while remaining firmly in the context of well-defined mathematical objects. At the end I'll discuss how the geometry of the hyperbolic space inside of Minkowski space can be used to prove theorems on such asymptotically hyperbolic spaces. Email basilio3 (at) illinois (dot) edu for Zoom details.

Monday, March 8, 2021

3:00 pm in zoom,Monday, March 8, 2021

#### Symplectic geometry of Anosov flows in dimension 3 and bi-contact topology

###### Surena Hozoori (Georgia Tech)

Abstract: We give a purely contact and symplectic geometric characterization of Anosov flows in dimension 3 and set up a framework to use tools from contact and symplectic geometry and topology in the study of questions about Anosov dynamics. If time permits, we will discuss a characterization of Anosovity based on Reeb flows and its consequences.

4:00 pm in Zoom,Monday, March 8, 2021

#### International Women's Day Social Hour

Abstract: March 8th is International Women's Day, and AWM is celebrating by hosting a social hour. Everyone in the department is welcome to join us, and we encourage everyone to use this time to check in with the women of the department about our research, our teaching, our accomplishments, and our lives. We hope to see you there!

Tuesday, March 9, 2021

10:00 am in Zoom,Tuesday, March 9, 2021

#### Open problems in additive combinatorics

###### Ben Green (Oxford University)

Abstract: There will be discussion on some open problems, the audience is encouraged to look some in advance.

11:00 am in Zoom,Tuesday, March 9, 2021

#### Cyclotomic Galois extensions in the chromatic homotopy

###### Tomer Schlank (Hebrew University)

Abstract: The chromatic approach to stable homotopy theory is "divide and conquer". That is, questions about spectra are studied through various localizations that isolate pure height phenomena and then are put back together. For each height n, there are two main candidates for pure height localization. The first is the generally more accessible K(n)-localization and the second is the closely related T(n)-localization. It is an open problem whether the two families of localizations coincide. One of the main reasons that the K(n)-local category is more amenable to computations is the existence of well understood Galois extensions of the K(n)-local sphere. In the talk, I will present a generalization, based on ambidexterity, of the classical theory of cyclotomic extensions, suitable for producing non-trivial Galois extensions in the T(n)-local and K(n)-local context. This construction gives a new family of Galois extensions of the T(n)-local sphere and allows to lift the well known maximal abelian extension of the K(n)-local sphere to the T(n)-local world. I will then describe some applications, including the study of the T(n)-local Picard group, a chromatic version of the Kummer theory, and interaction with algebraic K-theory. This is a joint project with Shachar Carmeli and Lior Yanovski.

for Zoom info, please email vesna@illinois.edu

2:00 pm in Zoom,Tuesday, March 9, 2021

#### Ramsey numbers of Sparse Digraphs

###### Xiaoyu He (Stanford University)

Abstract: The Ramsey number $r(H)$ of a digraph $H$ is the minimum $N$ such that every $N$-vertex tournament contains $H$ as a subgraph. Note that $r(H)$ only exists if $H$ has no oriented cycle, so we will assume H is acyclic. In 1934, Rédei showed that every tournament has a Hamiltonian path, which implies $r(H)=n$ when $H$ is the oriented path on $n$ vertices. For which other $n$-vertex digraphs $H$ is it true that $r(H) = O(n)$?

A famous result of Lee, proving a conjecture of Burr and Erdős, says that any sparse undirected graph has Ramsey number linear in $n$. It is natural to ask whether the analogous statement also holds for digraphs, and surprisingly we show that it is false. For any $C > 1$, we construct a family of bounded-degree digraphs $H$ with $r(H) > n^C$. In the other direction, we prove linear and nearly-linear upper bounds for $r(H)$ for several natural families of bounded-degree digraphs, including random digraphs and digraphs of bounded height.

Joint work with Jacob Fox and Yuval Wigderson.

6:00 pm in Zoom | Register at http://bit.ly/MathWithoutBorders,Tuesday, March 9, 2021

#### Opening remarks

###### Various speakers (see abstract) (Various)

Abstract: Opening remarks for the Kyushu-Illinois Strategic Partnership Colloquia Series, "Mathematics Without Borders – Applied and Applicable," featuring Susan Martinis, vice chancellor for research and innovation, Stephen G. Sligar Professor of Molecular and Cellular Biology, Illinois; Reitumetse Mabokela, vice provost for international affairs and global strategies, professor of higher education, Illinois; Yoshio Hisaeda, executive vice president for research, professor of applied chemistry, Kyushu; Toshiyuki Kono, executive vice president for international affairs, professor of law, Kyushu.

Register at https://zoom.us/webinar/register/WN_tddbR8ciTHKKji-QCvbjkA

6:10 pm in Zoom | Register at http://bit.ly/MathWithoutBorders,Tuesday, March 9, 2021

#### “Water Waves: breaking, peaking and disintegration”

###### Vera Mikyoung Hur (University of Illinois Urbana-Champaign, Department of Mathematics)

Abstract: Water waves describe the situation where water lies below a body of air and are acted upon by gravity. Describing what we may see or feel at the beach or in a boat, they are a perfect specimen of applied mathematics. They encompass wide-ranging wave phenomena, from whitecapping to tsunamis and to rogue waves. The interface between the water and the air is free, and poses profound and subtle difficulties for rigorous analysis, numerical computation and modeling. I will discuss some recent developments and future research directions, particularly, a rich variety of wave phenomena in rotational flows, and their instability, and also statistical and machine learning approaches to rogue waves.

Register at https://zoom.us/webinar/register/WN_tddbR8ciTHKKji-QCvbjkA

7:20 pm in Zoom | Register at http://bit.ly/MathWithoutBorders,Tuesday, March 9, 2021

#### “Visual Design Analysis with Machine Learning”

###### Seiichi Uchida, professor (Faculty of Information Science and Electrical Engineering, Kyushu University )

Abstract: Visual designs are image data, such as fonts, logos, and typographies, and often carefully created for showing specific impressions. In this talk, several on-going attempts of visual design analysis at my lab will be introduced. For the trials, we employ various machine learning techniques to deal with the complex relationships between image appearance and impression.

Wednesday, March 10, 2021

3:00 pm in Zoom,Wednesday, March 10, 2021

#### Preparing Pre-Service Math Educators for Teaching Emerging Bilinguals

###### Tasha Austin (Rutgers)

Abstract: Many teacher educators have redoubled efforts to be as precise and impactful as ever with instruction with the recent challenges of remote instruction and pandemic inequities. Preparing pre-service teachers to instruct emerging bilingual populations remains a critical undertaking as we identify high-leverage considerations that will yield the best results for our multilingual learners in general education settings. Among these considerations are acknowledging the legislative and theoretical precedents to centering the specific strengths and needs of these populations. For math educators in particular, practical considerations include valuing community, inquiry, and representation in the learning environment as well as discipline-specific language demands and scaffolding. In this session I will speak to the specific courses I teach in seven-week iterations which span the theoretical and practical steps for preparing pre-service math educators to teach emerging bilinguals.

Tasha Austin is a doctoral student and lecturer in Language Education at the Rutgers Graduate School of Education and the Teacher Education Special Interest Group Representative for NJTESOL-NJBE. As founder of Premise LLC, she supports schools with innovative and humanizing pedagogies. Her research uses critical race theory and Black feminist epistemologies to qualitatively examine language, identity and power, and the ways in which anti-Blackness emerges in language education and language teacher preparation.

6:00 pm in Zoom | Register at http://bit.ly/MathWithoutBorders,Wednesday, March 10, 2021

#### “Structure-preserving discretization of differential calculus and geometry”

###### Anil Hirani, associate professor (University of Illinois Urbana-Champaign, Department of Mathematics)

Abstract: Two important aspects of the structure of differential calculus are the chain and product rules. On manifolds, chain rule generalizes to the exterior derivative commuting with pullback by smooth maps. The product rule generalizes to a rule for the exterior derivative of wedge product of differential forms. These properties, especially the product rule, may be used as one of the defining properties for a covariant derivative in differential geometry. What if one is developing calculus and geometry for non-smooth spaces. One such application is the development of a discrete exterior calculus and discrete differential geometry for simplicial complexes (e.g. triangle meshes and tetrahedral meshes). What should play the role of the smooth maps, the exterior derivative, the wedge product and the covariant derivative so that we can speak of the above structural properties of calculus and geometry in this discrete setting? I will use examples to describe such a discrete calculus and geometry we have been developing. This will be a survey of some old ideas and some new developments. The newer developments are joint work with Mark Schubel (Apple Inc.) and Daniel Berwick-Evans (UIUC).

6:55 pm in Zoom | Register at http://bit.ly/MathWithoutBorders,Wednesday, March 10, 2021

#### “Geometry of Kaleidocycles”

###### Shizuo Kaji, professor (Institute of Mathematics for Industry, Kyushu University )

Abstract: Kaleidocycles are Origami models of flexible polyhedra which exhibit an intriguing turning-around motion (have a look at the pictures at https://github.com/shizuo-kaji/Kaleidocycle). The study of Kaleidocycles involves kaleidoscopic aspects and lies at the intersection of geometry, topology, and integrable systems (and mechanics). In this talk, we discuss two "incarnations" of them. (1) The states of a Kaleidocyce form a real-algebraic variety defined by a system of quadratic equations. In particular, the degree-of-freedom of its motion corresponds to the dimension of the variety. Using this formulation, we introduce a special family of Kaleidocycles, which we call the Mobius Kaleidocycles, having a single-degree-of-freedom (joint work with J. Schoenke at OIST). (2) A Kaleidocycle can be viewed as a discrete space curve with a constant torsion. Its motion corresponds to a deformation of the curve. Through this correspondence, we describe particular motions of Kaleidocycles using semi-discrete integrable systems (joint work with K. Kajiwara and H. Park at Kyushu University).

8:50 pm in Zoom | Register at http://bit.ly/MathWithoutBorders,Wednesday, March 10, 2021

#### Closing Remarks

###### Yuliy Baryshnikov, professor (University of Illinois Urbana-Champaign, Department of Mathematics)

Abstract: Closing remarks for the two-day workshop, Kyushu-Illinois Strategic Partnership Colloquia Series, "Mathematics Without Borders – Applied and Applicable."

Thursday, March 11, 2021

3:00 pm in Zoom,Thursday, March 11, 2021

#### Newell-Littlewood numbers

###### Shiliang Gao   [email] (University of Illinois at Urbana-Champaign)

Abstract: The Newell-Littlewood numbers are defined in terms of their celebrated cousins, the Littlewood-Richardson coefficients. Both arise as tensor product multiplicities for a classical Lie group. They are the structure coefficients of the K. Koike-I. Terada basis of the ring of symmetric functions. Recent work of H. Hahn studies them, motivated by R. Langlands' beyond endoscopy proposal; we address her work with a simple characterization of detection of Weyl modules. This motivates further study of the combinatorics of the numbers. We consider analogues of ideas of J. De Loera-T. McAllister, H. Derksen-J. Weyman, S. Fomin-W. Fulton-C.-K. Li-Y.-T. Poon, W. Fulton, R. King-C. Tollu-F. Toumazet, M. Kleber, A. Klyachko, A. Knutson-T. Tao, T. Lam-A. Postnikov-P. Pylyavskyy, K. Mulmuley-H. Narayanan-M. Sohoni, H. Narayanan, A. Okounkov, J. Stembridge, and H. Weyl. This is joint work with Gidon Orelowitz and Alexander Yong. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Friday, March 12, 2021

2:00 pm in Contact for zoom link,Friday, March 12, 2021

#### Circle Packings and a discrete Riemann Mapping Theorem

###### Kesav Krishnan (UIUC Math)

Abstract: I will introduce Circle Packings as defined by Thurston, and describe how they provide a discrete analogue of complex analysis and conformal maps. I will also introduce the discrete analogue of the Riemann Mapping Theorem, and if time permits I will talk about how discrete complex function theory plays a crucial role in certain 2-dimensional models in probability theory.

4:00 pm in Zoom,Friday, March 12, 2021

#### Department Town Hall Meeting

###### Department of Mathematics (Illinois Math)

Abstract: Department chair Jeremy Tyson will provide a building project update, including a tour through the building plans for both Altgeld and Illini Halls. This same content will also be presented at a special building project update meeting on March 15 at noon.

4:00 pm in Zoom,Friday, March 12, 2021

#### Primes represented by binary quadratic forms

###### Olivia Beckwith   [email] (UIUC Math)

Abstract: Let Q(x,y) = ax^2 + bxy + cy^2, where a, b, and c are integers. Which prime numbers are of the form Q(x,y), for some integers x and y? This classical number theory question is connected to rich areas of math, including algebraic number theory, class field theory, and modular functions. This talk will introduce one of the fundamental elements of this theory: the group structure on equivalence classes of binary quadratic forms of a fixed discriminant.

For zoom info, please email drthoma2@illinois.edu

Monday, March 15, 2021

12:00 pm in Zoom (http://bit.ly/AH-IH0315),Monday, March 15, 2021

#### Altgeld & Illini Halls building project update

###### Department of Mathematics (Illinois Math)

Abstract: Department chair Jeremy Tyson will provide a building project update, including a tour through the building plans for both Altgeld and Illini Halls. This same content will be shared at the department's town hall meeting on March 12 at 4 p.m. Please note: You will need to authenticate with Zoom (either through Zoom Illinois or Zoom.us) to enter the meeting.

3:00 pm in Zoom,Monday, March 15, 2021

#### Equivariant motivic orientations

###### Tsutomu Okano (UIUC)

Abstract: For a finite abelian group A, I will introduce the notion of oriented spectra in A-equivariant motivic homotopy theory. Orientation yields a theory of Chern classes which can be used to compute the cohomology of Grassmannians. As an application, we obtain the equivariant motivic analogue of the Snaith theorem. Please email vb8 at illinois dot edu for the zoom details.

3:00 pm in zoom,Monday, March 15, 2021

#### Stacky Hamiltonian actions and symplectic reduction

###### Reyer Sjamaar (Cornell)

Abstract: Extending work of Lerman and Malkin, we introduce the notion of a Hamiltonian action of an étale Lie group stack on an étale symplectic stack and establish versions of some basic theorems of symplectic geometry in this context, such as the Kirwan convexity theorem and the Mayer-Marsden-Weinstein symplectic reduction theorem. This is joint work with Benjamin Hoffman.

5:00 pm in Altgeld Hall,Monday, March 15, 2021

#### Seemingly injective von Neumann algebras

###### Timur Oikhberg

Abstract: We study Pisier's paper on a property which looks like injectivity, but holds for free group factors. https://illinois.zoom.us/j/87333719853?pwd=bFdWSkdqeEt1M3djNmVEU2Jvb3JzUT09

Tuesday, March 16, 2021

11:00 am in Zoom,Tuesday, March 16, 2021

#### An asymptotic local-global principle for integral Kleinian sphere packings

###### Edna Jones (Rutgers University)

Abstract: We will discuss an asymptotic local-global principle for certain integral Kleinian sphere packings. Examples of Kleinian sphere packings include Apollonian circle packings and Soddy sphere packings. Sometimes each sphere in a Kleinian sphere packing has a bend (1/radius) that is an integer. When all the bends are integral, which integers appear as bends? For certain Kleinian sphere packings, we expect that every sufficiently large integer locally represented as a bend of the packing is a bend of the packing. We will discuss ongoing work towards proving this for certain Kleinian sphere packings. This work uses the circle method, quadratic forms, spectral theory, and expander graphs.

For Zoom info, please email obeck@illinois.edu

2:00 pm in Zoom,Tuesday, March 16, 2021

#### Expressing graphs as symmetric differences of cliques of the complete graph

###### Puck Romback (University of Vermont)

Abstract: Any finite simple graph $G = (V,E)$ can be represented by a collection $\mathcal{C}$ of subsets of $V$ such that $uv\in E$ if and only if $u$ and $v$ appear together in an odd number of sets in $\mathcal{C}$. We are interested in the minimum cardinality of such a collection. In this talk, we will discuss properties of this invariant and its close connection to the minimum rank problem. This talk will be accessible to students. Joint work with Calum Buchanan and Christopher Purcell.

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, March 16, 2021

#### Solution to Enflo's problem

###### Paata Ivanishvili (North Carolina State University)

Abstract: Pick any finite number of points in a Hilbert space. If they coincide with vertices of a parallelepiped then the sum of the squares of the lengths of its sides equals the sum of the squares of the lengths of the diagonals (parallelogram law). If the points are in a general position then we can define sides and diagonals by labeling these points via vertices of the discrete cube {0,1}^n. In this case the sum of the squares of diagonals is bounded by the sum of the squares of its sides no matter how you label the points and what n you choose. In a general Banach space we do not have parallelogram law. Back in 1978 Enflo asked: in an arbitrary Banach space if the sum of the squares of diagonals is bounded by the sum of the squares of its sides for all parallelepipeds (up to a universal constant), does the same estimate hold for any finite number of points (not necessarily vertices of the parallelepiped)? In the joint work with Ramon van Handel and Sasha Volberg we positively resolve Enflo's problem. Banach spaces satisfying the inequality with parallelepipeds are called of type 2 (Rademacher type 2), and Banach spaces satisfying the inequality for all points are called of Enflo type 2. In particular, we show that Rademacher type and Enflo type coincide.

Friday, March 19, 2021

2:00 pm in Contact for zoom link,Friday, March 19, 2021

#### The descriptive complexity of classes of Banach lattices

###### Mary Angelica Gramcko-Tursi (UIUC Math)

Abstract: The descriptive complexity of a class of spaces gives us an initial sense of how "nice" the class is. When a set is not "nice," this fact can also be used to derive results related to the existence of universal spaces. In this talk, we present some examples of Borel and non-Borel classes of Banach lattices and some related results derived from their descriptive complexity. We also show areas where the descriptive complexity results on Banach lattices compare and contrast with previously done analogous work on Banach spaces.

4:00 pm in Zoom,Friday, March 19, 2021

#### Free products of Abelian groups in Mod(S)

###### Chris Loa (UIUC)

Abstract: In 2002, Farb and Mosher introduced a notion of convex cocompactness for mapping class groups. The original notion of convex cocompactness comes from Kleinian groups, where it is a special case of geometric finiteness. In recent work Dowdall, Durham, Leininger, and Sisto have introduced a notion of “parabolic” geometric finiteness for mapping class groups. Examples include convex cocompact groups (as one would hope) and finitely generated Veech groups by work of Tang. In this talk we’ll construct a new family of examples of parabolically geometrically finite groups and show why they are undistorted in Mod(S). Please email basilio3 (at) illinois (dot) edu for Zoom information.

4:00 pm in Zoom,Friday, March 19, 2021

###### AJ Hildebrand   [email] (UIUC Math)

Abstract: If one makes a list of the areas of all 200 countries in the world, one finds that around 30 percent of those numbers begin with the digit 1, around 17 percent begin with the digit 2, while only around 5 percent begin with the digit 9. Similar frequencies of first digits have been observed in all sorts of real world data—from populations of cities to heights of tallest buildings to numbers in tax returns and numbers of Twitter followers. This near-universal phenomenon is called Benford's Law. In the first part of this talk I will give an overview of Benford's Law and its applications and explain the math behind it. In the second part I will focus on Benford's Law for mathematical sequences such as the powers of 2. I will describe an undergraduate research project that started out back in 2015 as an IGL project, then turned into a multi-year research adventure full of surprises and unexpected twists, and ended up being the most fun, rewarding, and interesting undergraduate research project I have ever supervised.

For zoom info, email drthoma2@illinois.edu

Monday, March 22, 2021

3:00 pm in Zoom,Monday, March 22, 2021

#### An introduction to Milnor conjecture

###### Timmy Feng (UIUC)

Abstract: Milnor conjecture (1970 by J.Milnor) states that the Milnor K-theory (mod 2) and the Galois/etale cohomology of a field (char not 2) in mod 2 coefficient are equivalent. In 1996, V.Voevodsky proved Milnor conjecture by using new theories and techniques including motivic cohomology, splitting varieties and cohomology operations. Bloch-Kato conjecture, which generalizes Milnor conjecture to mod l coefficients, was also proved in the following years. In the talk, I will start from the Milnor K-theory and its relation with the quadratic forms. I will also introduce the motivic cohomology and the higher dimensional analogues of Hilbert’s Theorem 90. Then, if time allowed, I’ll talk about the strategy of Voevodsky’s proof on mod 2 Milnor conjecture. Please email vb8 at illinois dot edu for the zoom details.

3:00 pm in zoom,Monday, March 22, 2021

#### Immersed Floer cohomology, mean curvature flow, and Lagrangian surgery

###### Joseph Palmer (UIUC)

Abstract: We study the behavior of (immersed) Floer cohomology under coupled mean curvature and Kähler-Ricci flow. Given an unobstructed immersed Lagrangian we prove (under some conditions) a lower bound on the time for which the immersed Floer cohomology is invariant under the flow, as long as the flow exists. Furthermore, in some cases when the Lagrangian becomes obstructed we show how performing a Lagrangian surgery allows the flow to be continued in such a way that the Floer cohomology instead remains unobstructed and is invariant. This surgery prevents certain geometric singularities in the mean curvature flow before they can form. This is partially motivated by a conjecture of Joyce. This work is joint with Chris Woodward, see arxiv.org/abs/1804.06799 and arxiv.org/abs/1903.01943.

5:00 pm in Altgeld Hall,Monday, March 22, 2021

#### Seemingly injective von Neumann algebras

Abstract: Paet 2 https://illinois.zoom.us/j/87333719853?pwd=bFdWSkdqeEt1M3djNmVEU2Jvb3JzUT09

Tuesday, March 23, 2021

11:00 am in Zoom (contact Olivia Beckwith at obeck@illinois.edu for details),Tuesday, March 23, 2021

#### Modular zeros in the character table of the symmetric group

###### Sarah Peluse (Princeton)

Abstract: In 2017, Miller conjectured, based on computational evidence, that for any fixed prime $p$ the density of entries in the character table of $S_n$ that are divisible by $p$ goes to $1$ as $n$ goes to infinity. I’ll describe a proof of this conjecture, which is joint work with K. Soundararajan. I will also discuss the (still open) problem of determining the asymptotic density of zeros in the character table of $S_n$, where it is not even clear from computational data what one should expect.

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, March 23, 2021

#### Phylogenomics: Inverting Random Trees

###### Sebastien Roch (University of Wisconsin-Madison)

Abstract: Phylogenomic analysis, in particular the estimation of species phylogenies from genome-scale data, is a common step in modern evolutionary studies. This estimation is complicated by the fact that genes evolve under biological processes that produce discordant trees. Such processes include horizontal gene transfer (HGT), incomplete lineage sorting (ILS), and gene duplication and loss (GDL), all of which can be modeled using specialized random tree distributions. I will survey some recent results regarding the analysis of these probabilistic models. Specifically their identifiability, or "invertibility," will be discussed as well as the asymptotic properties of species tree estimation methods (time permitting). Based on joint works with Max Bacharach, Brandon Legried, Erin Molloy, Elchanan Mossel, Allan Sly, Tandy Warnow, Shuqi Yu.

2:00 pm in Zoom,Tuesday, March 23, 2021

#### Extremal results for convex geometric hypergraphs

###### Jacques Verstraete (University of California, San Diego)

Abstract: A convex geometric hypergraph or cgh is a hypergraph whose vertex set comprises the vertices of a convex polygon in the plane. The extremal problem consists in determining, given an $r$-uniform cgh $F$, the maximum number of edges $\mbox{ex}(n,F)$ in an $r$-uniform cgh on $n$ vertices that does not contain $F$. In the case of graphs, this problem has a rich history with applications to a variety of problems in combinatorial geometry. In this talk, we survey some of the known results for convex geometric graphs, and determine tight bounds for the extremal function for most configurations consisting of a pair of triangles, using a variety of different methods. For instance, we show that the maximum number of triangles that can be formed amongst $n \geq 3$ points in the plane so that any two of the triangles share an interior point is $n(n - 1)(n + 1)/24$ if $n$ is odd and $n(n - 2)(n + 2)/24$ if $n$ is even. Our results generalize old work of Kupitz, Perles, Capoyleas-Pach, Brass, Brass-Karolyi-Valtr and recent work of Aronov-Dujmovic-Morin-Ooms-da Silveira, and answer recent questions of Frankl, Holmsen and Kupavskii.

Joint work with Z. Furedi, T. Jiang, A. Kostochka, D. Mubayi and J. O'Neill.

Friday, March 26, 2021

4:00 pm in Zoom,Friday, March 26, 2021

#### An introduction to CAT(0) cube complexes

###### Marissa Miller (UIUC)

Abstract: In this talk, I will introduce the notion of a CAT(k) metric spaces, which are spaces that have geometry comparable to complete simply connected surfaces of constant curvature k. We will specifically focus on CAT(0) spaces and will explore CAT(0) cube complexes in some detail, looking at various examples of these complexes and their relationships to questions in geometric group theory. Please email basilio3 (at) illinois (dot) edu for Zoom details.

4:00 pm in Zoom,Friday, March 26, 2021

#### To Be Announced

###### Eliot Kaplan   [email] (UIUC Math)

Abstract: TBA

4:30 pm in Zoom,Friday, March 26, 2021

#### Department Town Hall Meeting

###### Department of Mathematics (Illinois Math)

Saturday, March 27, 2021

9:00 am in Online (Cvent),Saturday, March 27, 2021

#### Actuarial Innovations to Emerging Risks 9am-4pm

###### See schedule

Abstract: The Risk Analytics Symposium will be an all-day event presented on March 27, 2021 through Cvent, a user-friendly platform that facilitates a seamless virtual experience. Emerging trends in actuarial science, data science, and InsureTech will be presented by accomplished actuarial researchers and experienced consultants. There will be opportunities available to build professional relationships with leaders working to apply the statistics and business concepts we learn about in our classes.

Registration information and previews of our expert speakers will be updated on the Actuarial Science Club page: https://www.ascuiuc.com/2021.

Monday, March 29, 2021

3:00 pm in Zoom,Monday, March 29, 2021

#### The Telescope Conjecture

###### Liz Tatum (UIUC)

Abstract: In his 1984 paper “Localization with Respect to Certain Periodic Homotopy Theories”, Ravenel made seven major conjectures about homotopy theory. While the rest of these conjectures were quickly proven and are an important part of the framework for chromatic homotopy theory, the telescope conjecture remains open. Roughly, the telescope conjecture claims that: “finite localization and smashing localization in the stable homotopy category are the same”. In this talk, we’ll discuss localization in the stable homotopy category and various ways to state the telescope conjecture. Time permitting, we’ll briefly discuss a generalization of this conjecture to other categories. Please email vb8 at illinois dot edu for the zoom details.

5:00 pm in Altgeld Hall,Monday, March 29, 2021

#### Seemingly injective von Neumann algebras

###### Timur Oikhberg

Abstract: Part 3 https://illinois.zoom.us/j/87333719853?pwd=bFdWSkdqeEt1M3djNmVEU2Jvb3JzUT09

Tuesday, March 30, 2021

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, March 30, 2021

#### Exponential concentration of overlap, free energy, and replica symmetry breaking for inhomogeneous Sherrington-Kirkpatrick Spin glass

###### Qiang Wu (UIUC)

Abstract: Multi-species Sherrington-Kirkpatrick Spin glass model, as an inhomogeneous generalization of classical SK model, was first introduced by Barra etal in 2015, later Panchenko set up the Parisi formula to compute limiting free energy at all temperatures. However, all those results can only hold when the disorder variance matrix is positive semi-definite. For the indefinite MSK model, nearly nothing rigorous is known, physicists conjectured that this model has some intrinsic difference with the positive definite case. In this talk, we will discuss some fluctuation results for the general MSK model in replica symmetric regime. First, A unified argument for the exponential concentration of overlap will be presented, and this concentration result further enables one to prove a CLT of free energy. Besides that, we also introduce a new species-wise cavity approach to study the fluctuation of overlap vectors, and this approach does not require positive definite assumption. The fluctuation results also suggest the phase boundary (known as AT line) of replica symmetry and replica symmetry breaking for general MSK model, we will conclude with an explicit form of conjectured AT equation.

2:00 pm in Zoom,Tuesday, March 30, 2021

#### Lower Bounds for Generalized Ramsey Numbers Through Color Energy Graphs

###### Sean English (UIUC)

Abstract: Let the generalized Ramsey number $f(n,p,q)$ denote the least integer $c$ such that $K_n$ can be edge-colored with $c$ colors such that every set of $p$ vertices spans a clique with at least $q$ colors. in this talk, we will discuss the method of color energy graphs, which borrows some ideas from the concept of additive energy used in additive combinatorics to find new lower bounds on generalized Ramsey numbers, and the connections between generalized Ramsey numbers and other interesting problems in extremal combinatorics.

Joint work with Jozsef Balogh, Emily Heath and Robert A. Krueger.

Wednesday, March 31, 2021

3:00 pm in Zoom (Email na17 [AT] illinois [DOT] edu for details),Wednesday, March 31, 2021

#### Panel: Life after UIUC

###### Panel

Abstract: Are you curious about what some of our graduates do once they leave UIUC? If so, then this panel is for you! The panel will consist of 5 amazing mathematicians. They will answer questions like: When did you start looking for jobs? How much time did you dedicate to it? What if I’m in pure mathematics and want an industry job? What if I prefer to teach? What if I don’t know what I want to do yet? How different is the postdoc life from the graduate life? How has COVID impacted your job? What if I don’t find a job in time? How did you tackle the moving process? Even if you are at the start or end of your journey, this panel can be beneficial for you.

Thursday, April 1, 2021

11:00 am in zoom,Thursday, April 1, 2021

#### On subRiemannian geodesics and billiard trajectories

###### Alvaro del Pino (Universiteit Utrecht)

Abstract: SubRiemannian Geometry studies triples consisting of a smooth manifold, a subbundle of the tangent bundle (a "tangent distribution"), and a metric along the distribution. Such a triple can be regarded as a degenerate limit of Riemannian manifolds, where the directions not in the distribution have been infinitely penalised. In such a setup, which is the framework in which Geometric Control Theory is phrased, a central question is to study the properties of the minimising curves. In many ways, this resembles the usual theory of geodesics in Riemannian Geometry, but various exotic behaviours appear. The underlying reason behind these behaviours is that, upon dualising, the subRiemannian metric becomes a degenerate Hamiltonian with fibrewise non-compact level sets. I will review the basic theory behind this setup, particularly the cotangent formulation, which goes back to work of Pontryagin. I aim to give a (very biased) overview of the area, emphasising various results about global topological properties of subRiemannian geodesics, as well as some intriguing open questions. If time allows, I will comment on recent work, joint with L. Dahinden, in which we study the subRiemannian billiard flow, which is the natural generalisation to manifolds with boundary.

3:00 pm in Zoom,Thursday, April 1, 2021

#### Minimal elements in the limit weak order

###### Christian Gaetz   [email] (Massachusetts Institute of Technology)

Abstract: The limit weak order on an affine Weyl group was introduced by Lam and Pylyavskyy in their study of total positivity for loop groups. They showed that in the case of the affine symmetric group the minimal elements of this poset coincide with the infinite fully commutative reduced words and with infinite powers of Coxeter elements. We answer several open problems raised there by classifying minimal elements in all affine types and relating these elements to the classes of fully commutative and Coxeter elements. Interestingly, the infinite fully commutative elements correspond to the minuscule and cominuscule nodes of the Dynkin diagram, while the infinite Coxeter elements correspond to a single node, which we call the heavy node, in all affine types other than type A. No background on Weyl groups will be assumed. This talk is based on joint work with Yibo Gao. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Friday, April 2, 2021

2:00 pm in Contact for zoom link,Friday, April 2, 2021

#### Understanding Cyclicity in Spaces of Analytic Functions

###### Jeet Sampat (Washington University St. Louis)

Abstract: TBA

4:00 pm in Zoom,Friday, April 2, 2021

#### Oriented Cohomology Theories

###### Tsutomu Okano (UIUC)

Abstract: I will discuss oriented cohomology theories in both topological and algebro-geometric settings. They naturally come equipped with useful tools such as Thom isomorphisms, Chern classes and Gysin maps. I will give a sketch of the Thom-Pontrjagin construction, from which it follows that complex cobordism is the universal (complex) oriented cohomology theory. For Zoom details, please email basilio3 (at) illinois (dot) edu.

4:00 pm in Zoom,Friday, April 2, 2021

#### Mathematics, big data, and mobility

###### Prof. Richard Sowers   [email] (UIUC Math)

Abstract: We look at some mobility data from New York city from a mathematical perspective. We use several recent techniques from big data to identify patterns. Our interests will be traffic accidents, matrix decompositions, and the topology of congestion. The goal of the talk will be to understand how mathematics can help us understand some properties of complex human behavior.

Monday, April 5, 2021

3:00 pm in Zoom,Monday, April 5, 2021

#### Equivariant BPQ and Bicategorical Enrichment

###### Samuel Hsu (UIUC)

Abstract: Following the work of Guillou, May, Merling, and Osorno, we give a (very) broad overview of the (2-)algebraic input that goes into their proof of the multiplicative equivariant Barratt-Priddy-Quillen theorem. Although it is not explicitly invoked, an underlying point we wish to make is the presence of bicategorical enrichment over the 2-category of categories internal to G-spaces when G is a finite group, where bicategorical enrichment is meant in the sense of e.g. Garner--Shulman, Franco, or Lack. This also opens up a pathway to concepts like enriched analogues of bicategorical concepts, less celebrated structures such as double multi or poly categories, and other devices which are related to the usual celebrities in formal category theory, which we might discuss existing or hoped applications for, time permitting. This talk is intended to be accessible with hardly any knowledge of homotopy theory. Please email vb8 at illinois dot edu for the zoom details.

Tuesday, April 6, 2021

11:00 am in Zoom,Tuesday, April 6, 2021

#### A multiplicative theory of motivic infinite loop series

###### Brian Shin (UIUC)

Abstract: From a spectrum $E$ one can extract its infinite loop space $\Omega^\infty E = X$. The space $X$ comes with a rich structure. For example, since $X$ is a loop space, we know $\pi_0 X$ comes with a group structure. Better yet, since $X$ is a double loop space, we know $\pi_0 X$ is in fact an abelian group. How much structure does this space $X$ possess? In 1974 Segal gave the following answer to this question: the structure of an infinite loop space is exactly the structure of a grouplike $E_\infty$ monoid. In fact, this identification respects multiplicative structures. In this talk, I'd like to discuss the analogue of this story in the setting of motivic homotopy theory. In particular we'll see that the motivic story, while similar to the classical one, has a couple interesting twists.

For Zoom info, please email vesna@illinois.edu

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, April 6, 2021

#### Modified log-Sobolev inequalities, Beckner inequalities and moment estimates

Abstract: I will present recent results concerning the equivalence between the modified log-Sobolev inequality and a family of Beckner type inequalities with constants uniformly separated from zero. Next I will discuss moment estimates which can be derived from such inequalities, generalizing previous results due to Aida and Stroock, based on a stronger log-Sobolev inequality due to Federbush and Gross. If time permits I will present examples to moment estimates for certain Cauchy type measures, for invariant measures of Glauber dynamics and on the Poisson path space. Based on joint work with B. Polaczyk and M. Strzelecki.

2:00 pm in Zoom,Tuesday, April 6, 2021

#### Size of Sidon sets revisited

###### Jozsef Balogh (UIUC)

Abstract: Earlier in this semester, Zoltan Furedi gave a talk, where he presented a proof for the best known upper bound on sizes of Sidon subsets of $\{1,\dots,n\}$. In this talk we repeat his proof, and explore the differences from other proofs of the same bound.

The talk is based on discussions with Zoltan Furedi and Souktik Roy.

Thursday, April 8, 2021

11:00 am in zoom,Thursday, April 8, 2021

#### Deformations of symplectic foliations

###### Marco Zambon (KU Leuven)

Abstract: Symplectic foliations and regular Poisson structures are the same thing. Taking the latter point of view, we exhibit an algebraic structure that governs the deformations of symplectic foliations, i.e. which allows to describe the space of symplectic foliations nearby a given one. Using this, we will address the question of when it is possible to prolong a first order deformation to a smooth path of symplectic foliations. We will be especially interested in the relation to the underlying foliation. This is joint work in progress with Stephane Geudens and Alfonso Tortorella.

3:00 pm in Zoom,Thursday, April 8, 2021

#### Recent advances in analysis of implicit bias of gradient descent on deep networks

###### Matus Telgarsky (UIUC)

Abstract: The purpose of this talk is to highlight three recent directions in the study of implicit bias, a promising approach to developing a tight generalization theory for deep networks interwoven with optimization. The first direction is a warm-up with purely linear predictors: here, the implicit bias perspective gives the fastest known hard-margin SVM solver! The second direction is on the early training phase with shallow networks: here, implicit bias leads to good training and testing error, with not just narrow networks but also arbitrarily large ones. The talk concludes with deep networks, providing a variety of structural lemmas that capture foundational aspects of how weights evolve for any width and sufficiently large amounts of training. This is joint work with Ziwei Ji.

To register: https://berkeley.zoom.us/webinar/register/WN_iEXcldw1QPOuUofhS0WT4g

Friday, April 9, 2021

4:00 pm in Zoom,Friday, April 9, 2021

#### The Yamabe Problem

###### Xinran Yu (UIUC)

Abstract: In a two-dimensional case, the fact that every Riemann surface has a metric with constant Gaussian curvature leads to a successful classification of Riemann surfaces. Generalizing this property to higher dimensions could be an interesting problem to consider. Thus we seek a conformal metric on a compact Riemannian manifold with constant scalar curvature. The Yamabe problem was solved in the 1980s, due to Yamabe, Trudinger, Aubin, and Schoen. Their solution to the Yamabe problem uses the techniques of calculus of variation and elliptic regularity of the Laplacian. The proof introduces a conformal invariant, so-called the Yamabe invariant, which shifts the focus from an analysis point of view to understanding a geometric invariant. The solution is separated nicely into two cases, regarding the dimension and flatness of a given Riemannian manifold. For Zoom details, please email basilio3 (at) illinois (dot) edu.

4:00 pm in Zoom,Friday, April 9, 2021

#### To Be Announced

###### Prof. Reuven Hodges   [email] (UIUC Math)

Abstract: TBA

4:30 pm in Zoom,Friday, April 9, 2021

#### Department Town Hall Meeting

###### Department of Mathematics (Illinois Math)

Tuesday, April 13, 2021

11:00 am in Zoom,Tuesday, April 13, 2021

#### Bombieri-Vinogradov type theorems for primes with a missing digit

###### Kunjakanan Nath (U. Montreal math)

Abstract: One of the fundamental questions in number theory is to find primes in any subset of the natural numbers. In general, it's a difficult question and leads to open problems like the twin prime conjecture, Landau's problem and many more. Recently, Maynard considered the set of natural numbers with a missing digit and showed that it contains infinitely many primes whenever the base b ≥ 10. In fact, he has established the right order of the upper and the lower bounds when the base b = 10 and an asymptotic formula whenever b is large (say 2 × 10⁶). In this talk, we will consider the distribution of primes with a missing digit in arithmetic progressions for base b large enough. In particular, we will show an analog of the Bombieri-Vinogradov type theorems for primes with a missing digit for large base b. The proof relies on the circle method, which in turn is based on the Fourier structure of the digital set and the Fourier transform of primes over arithmetic progressions on an average. Finally, we will give its application to count the primes of the form p = 1 + m² + n² with a missing digit for a large base.

2:00 pm in Zoom,Tuesday, April 13, 2021

#### Hexagon-Free Planar Graphs

###### Ervin Gyori (Renyi Institute for Mathematics)

Abstract: In this talk, we concentrate on determining the maximum number of edges in a hexagon-free planar graphs and we would like to show the nature of these problems (difficulties, necessary results and conjectures). Let $\mathrm{ex}_\mathcal{P}(n, H)$ denote the maximum number of edges in an $n$-vertex planar graph which does not contain $H$ as a subgraph. Dowden obtained exact results for $\mathrm{ex}_\mathcal{P}(n, C_4)$ and $\mathrm{ex}_\mathcal{P}(n, C_5)$, but the case of longer cycles remained open. Later on, Y. Lan, et al. proved that $\mathrm{ex}_\mathcal{P}(n, C_6)\leq \frac{18(n−2)}7$. In this talk I plan to sketch the proof of the tight result $\mathrm{ex}_\mathcal{P}(n, C_6)\leq \frac{5}2n-7$, for all $n\geq 18$, and show infinitely many examples when it is tight. Based on them, we raise a conjecture on $\mathrm{ex}_\mathcal{P}(n, C_k)$, for $k\geq 7$.

Joint work with Debarun Ghosh (CEU), Ryan R. Martin (Iowa State Univ.), Addisu Paulos (CEU), Chuanqi Xiao(CEU)

Wednesday, April 14, 2021

3:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Wednesday, April 14, 2021

#### Random Graph Matching with Improved Noise Robustness

###### Konstantin Tikhomirov (Georgia Institute of Technology)

Abstract: Graph matching, also known as network alignment, refers to finding a bijection between the vertex sets of two given graphs so as to maximally align their edges. This fundamental computational problem arises frequently in multiple fields such as computer vision and biology. In this work we will discuss a new algorithm for exact matching of correlated Erdos-Renyi graphs. Based on joint work with Cheng Mao and Mark Rudelson.

Thursday, April 15, 2021

2:00 pm in Zoom,Thursday, April 15, 2021

#### Flat Littlewood polynomials exist

###### Robert Morris (IMPA, Brazil)

Friday, April 16, 2021

4:00 pm in Altgeld Hall,Friday, April 16, 2021

#### To Be Announced

###### Prof. Joey Palmer   [email] (UIUC Math)

Abstract: TBA

Tuesday, April 20, 2021

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, April 20, 2021

#### To Be Announced

###### Firas Rassoul-Agha (University of Utah)

Thursday, April 22, 2021

3:00 pm in Zoom,Thursday, April 22, 2021

#### To Be Announced

###### Li Ying   [email] (University of Notre Dame)

Abstract: To Be Announced

Friday, April 23, 2021

4:30 pm in Zoom,Friday, April 23, 2021

#### Department Town Hall Meeting

###### Department of Mathematics (Illinois Math)

Tuesday, April 27, 2021

1:00 pm in Zoom (email Philipp Hieronymi),Tuesday, April 27, 2021

#### To Be Announced

###### Eion Blanchard (Illinois)

Abstract: TBA

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, April 27, 2021

#### To Be Announced

###### Wenqing Hu (Missouri University of Science and Technology)

4:00 pm in Zoom,Tuesday, April 27, 2021

#### Compositions as Trans-Scalar Identity

###### Gualtiero Piccinini (University of Missouri, St. Louis)

Abstract: We define mereologically invariant composition as the relation between a whole object and its parts when the object retains the same parts during a time interval. We argue that mereologically invariant composition is identity between a whole and its parts taken collectively. Our reason is that parts and wholes are equivalent measurements of a portion of reality at different scales in the precise sense employed by measurement theory. The purpose of these scales is the numerical representation of primitive relations between quantities of objects. To show this, we prove representation and uniqueness theorems for composition. Thus, mereologically invariant composition is trans-scalar identity.

Zoom Info: Please email Kay Kirkpatrick (kkirkpat@illinois.edu).

Thursday, April 29, 2021

3:00 pm in Zoom,Thursday, April 29, 2021

#### To Be Announced

###### Wai Ling Yee   [email] (University of Windsor)

Abstract: To Be Announced

Tuesday, May 4, 2021

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, May 4, 2021

#### To Be Announced

###### Jeremy Hoskins (University of Chicago)

Thursday, May 6, 2021

3:00 pm in Zoom,Thursday, May 6, 2021

#### To Be Announced

###### Alexander Garver   [email] (Carleton College)

Abstract: To Be Announced

Friday, May 7, 2021

4:30 pm in Zoom,Friday, May 7, 2021

#### Department Town Hall Meeting

###### Department of Mathematics (Illinois Math)

Friday, May 21, 2021

4:30 pm in Zoom,Friday, May 21, 2021

#### Department Town Hall Meeting

###### Department of Mathematics (Illinois Math)

Friday, June 4, 2021

4:30 pm in Zoom,Friday, June 4, 2021