Department of

# Mathematics

Seminar Calendar
for events the week of Monday, October 26, 2020.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
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Sunday, October 25, 2020

10:00 am in Zoom,Sunday, October 25, 2020

#### Diameters of Graphs of Reduced Words of Permutations

###### Samantha Dahlberg   [email] (Arizona State University)

Abstract: It is a classical result that any permutation in the symmetric group can be generated by a sequence of adjacent transpositions. The sequences of minimal length are called reduced words. The graphs of these reduced words, with edges determined by relations in the underlying Coxeter group, have been well studied. Recently, the diameter has been calculated for the longest permutation $n\ldots 21$ by Reiner and Roichman as well as Assaf. In this talk we present our results on diameters for certain classes or permutations. We also make progress on conjectured bounds of the diameter by Reiner and Roichman, which are based on the underlying hyperplane arrangement. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Monday, October 26, 2020

11:00 am in zoom,Monday, October 26, 2020

#### Real forms and Hamiltonian dynamics

###### Marine Fontaine (University of Antwerp)

Abstract: We present a theory of real forms for holomorphic Hamiltonian systems which behaves well under integrability: given a real analytic integrable system, one can (under some assumptions) complexify the system and obtain other real integrable systems on different real forms. These systems are dynamically different but they do share the same complexification. As an example, we explain how we can apply this theory and use hyperkähler geometry to find a compact integrable real form of the spherical pendulum on S2 x S2. This is based on joint work with P. Arathoon.

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Monday, October 26, 2020

#### An introduction to random walks in random environments

###### Jonathon Peterson (Purdue University)

Abstract: I will give an introduction to the model of random walks in random environments, paying particular attention to the one-dimensional case. I will give sketches of proofs for some of the basic results, including criteria for recurrence/transience, limiting velocity, and a central limit theorem.

3:00 pm in Zoom,Monday, October 26, 2020

#### Introduction to simplicial sets

###### Haoyuan Li (UIUC)

Abstract: This is an introduction to simplicial sets. I will first talk about the definition of simplicial sets and also some examples of simplicial sets. Then I will introduce the Kan complex and some of its properties. If time permits, I will talk a little bit about the homotopy groups of Kan complex. Please email vb8 at illinois dot edu for the zoom details.

5:00 pmMonday, October 26, 2020

#### Recovery

###### Marius Junge (UIUC Math)

Abstract: We will talk about Petz recovery maps, and new developments. Please email mjunge@illinois.edu for details.

Tuesday, October 27, 2020

11:00 am in via Zoom (email vesna@illinois.edu for link),Tuesday, October 27, 2020

#### Decomposition of topological Azumaya algebras

###### Niny Arcila Maya (University of British Columbia)

Abstract: Let $\mathcal{A}$ be a topological Azumaya algebra of degree $mn$ over a CW complex $X$. We give conditions for the positive integers $m$ and $n$, and the space $X$ so that $\mathcal{A}$ can be decomposed as the tensor product of topological Azumaya algebras of degrees $m$ and $n$. Then we prove that if $m$<$n$ and the dimension of $X$ is higher than $2m+1$, $\mathcal{A}$ has no such decomposition. Please email vesna@illinois.edu for Zoom link.

11:00 am in Zoom,Tuesday, October 27, 2020

#### Distribution of reduced quadratic irrationals arising from even and of backward CF expansions

###### Maria Siskaki (UIUC Math)

Abstract: : The reduced quadratic irrationals (RQIs) coming from the regular continued Fraction (CF) expansion, when ordered by their length, are known to be uniformly distributed with respect to the Gauss probability measure. In this talk I will present the corresponding result for the RQIs arising from the even and backwards CF expansions, where the invariant measure is infinite. I will also be mentioning their connection with the Pell equation. This is joint work with F. Boca.

2:00 pm in Zoom,Tuesday, October 27, 2020

#### Universality of random polynomials

###### Oanh Nguyen (UIUC)

Abstract: Consider polynomials whose coefficients are 1 or -1. How many real roots do such polynomials typically have? This is one of the basic questions that we study in the field of random polynomials. In this talk, we will discuss the history and recent progress in the field. We will also discuss several current lines of research and intriguing open problems.

Contact Sean at SEnglish (at) illinois (dot) edu for Zoom information.

2:00 pm in Zoom Meeting (email daesungk@illinois.edu for info),Tuesday, October 27, 2020

#### Quantitative quenched CLTs for one-dimensional random walks in random environments

###### Jonathon Peterson (Purdue University)

Abstract: The Berry-Esseen estimates give quantitative error estimates on the CLT for sums of i.i.d. random variables, and the polynomial decay rate for the error depends on moment bounds of the i.i.d. random variables with the optimal $1/\sqrt{n}$ rate of convergence obtained under a third moment assumption. In this talk we will prove quantitative error bounds for quenched CLTs of both the position and hitting times of one dimensional random walks in random environments (RWRE). For the quantitative CLTs for the hitting times we prove that our rates our optimal. This talk is based on joint works with Sungwon Ahn.

8:00 pm in via Zoom (please email wfchong@illinois.edu),Tuesday, October 27, 2020

#### Cyber: How risky is it, really?

###### Chad Spensky (Founder and CEO, Allthenticate)

Wednesday, October 28, 2020

3:00 pm in Zoom (email na17@illinois.edu for Zoom link),Wednesday, October 28, 2020

#### Intersecting identities and the worldview

###### Joycelyn Landrum-Brown (Office of Inclusion and Intercultural Relations, UIUC)

Abstract: This workshop is based on a model developed and expanded upon by Dr. Landrum-Brown that uses the concept of worldview to help individuals develop understanding about the ways their social identities and their intersection (race/ethnicity, gender, social class, disability/ability statuses, etc.) influence individuals' lived experiences in the world. This model has two parts, the first part makes clear societal or group worldviews. The second part explores the personal worldviews of individuals. This interactive workshop helps participants understand the ways their multiple social identities intersect to create their unique lived experiences in today’s society. Within the model the interaction of both parts are explored to reveal how the interaction between one’s personal worldview and the society’s worldview provide a dynamic framework for understanding cross-cultural interpersonal and intergroup relations. Dr Landrum-Brown currently oversees the Intergroup Dialogue Courses offered through Educational Psychology and the OIIR. In addition, she has been teaching a Gen Ed course titled Exploring Cultural Diversity since Fall 2000. She has been working in the area of diversity & inclusion education and facilitation training for the last 39 years, including facilitating numerous workshops on a variety of Social Justice Education topics. She has also worked in this capacity through her private consulting firm, Landrum-Brown & Associates. She has published and co-authored several book chapters and articles in peer-reviewed journals. She is most interested in diversity and inclusion and social justice issues as they relate to preventive mental health.

Thursday, October 29, 2020

3:00 pm in Zoom,Thursday, October 29, 2020

#### Cyclic symmetry loci in Grassmannians

###### Chris Fraser   [email] (University of Minnesota)

Abstract: The Grassmannian admits an automorphism of finite order, the cyclic shift map. This map has finitely many fixed points, which were described by Steven Karp in a recent paper. We study the fixed-point set of any iterate of the cyclic shift map. These cyclic symmetry loci are typically positive-dimensional spaces. We give a simple geometric description of these loci, and of their totally nonnegative part.  We  describe an atlas of generalized cluster algebra charts on cyclic symmetry loci, whose clusters are efficient total positivity tests. These cluster algebras have connections with higher Teichmuller theory and with the category of representations of quantum affine algebras at roots of unity. Please email Colleen at cer2 (at) illinois (dot) edu for the Zoom ID and password.

Friday, October 30, 2020

1:00 pm in Zoom,Friday, October 30, 2020

#### Permutable Quasiregular maps

###### Athanasios Tsantaris   [email] (University of Nottingham - Math)

Abstract: Do commuting holomorphic maps have the same Julia set? This question was first asked by Fatou and Julia around 1920 in their attempts to classify commuting rational maps. For rational maps the answer is affirmative but for transcendental entire maps the question is still open. In this talk we will first discuss the progress to the problem for transcendental entire maps over the years and then we shall describe generalizations of those results in the setting of quasiregular maps which are higher dimensional analogues of holomorphic maps.

4:00 pm in Zoom (email ruiyuan at illinois for info),Friday, October 30, 2020

#### What generic automorphisms of the random poset look like

###### Dakota Thor Ihli (UIUC Math)

Abstract: The Fraïssé limit of the class of finite posets, also called the random poset, admits generic automorphisms — that is, its automorphism group admits a comeagre conjugacy class. This result, due to D. Kuske and J. Truss, was proven without explicitly describing the automorphisms in question. Here we give a new, concrete description of the generic automorphisms, and we discuss the tools-and-tricks involved.