Department of

Mathematics


Seminar Calendar
for events the week of Friday, September 22, 2017.

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More information on this calendar program is available.
Questions regarding events or the calendar should be directed to Tori Corkery.
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Monday, September 18, 2017

3:00 pm in 243 Altgeld Hall,Monday, September 18, 2017

Non-associative local Lie groupoids

Daan Michiels (UIUC)

Abstract: Historically, local Lie groups were studied before Lie groups. Surprisingly, not every local Lie group can be embedded into a Lie group, and a theorem by Mal'cev shows that the obstructions to such embeddings can be understood in terms of the associativity of the local Lie group. In this talk, I will explain Mal'cev's theorem and show how it generalizes to the groupoid setting. Then, I will point out an intimate connection between this result, and the theory of integrability of Lie algebroids.

3:00 pm in 141 Altgeld Hall,Monday, September 18, 2017

Framed Cobordism and Stable Homotopy Groups

Brian Shin   [email] (UIUC)

Abstract: I will introduce the notion of framed cobordism describe its connection to the homotopy groups of spheres. Using this connection, I will calculate several of these groups using geometry.

4:00 pm in 245 Altgeld Hall,Monday, September 18, 2017

From Brownian motion to Levy processes

Renming Song   [email] (Department of Mathematics, University of Illinois at Urbana-Champaign)

Abstract: In this talk, I will briefly introduce Brownian motion and Levy processes, and their connections to analysis and PDE's.

Tuesday, September 19, 2017

1:00 pm in 345 Altgeld Hall,Tuesday, September 19, 2017

No seminar

2:00 pm in 347 Altgeld Hall,Tuesday, September 19, 2017

Derivative formula for Mean-field SDEs with jumps

Yulin Song (Nanjing University and University of Illinois)

Abstract: By using Malliavin calculus for jump processes, we study the Bismut type derivative formula for Mean-field stochastic differential equations driven by L\'evy processes. Both of the derivatives with respect to a fixed initial value $x\in R^d$ and the ones with respect to an initial distribution are considered.

3:00 pm in 241 Altgeld Hall,Tuesday, September 19, 2017

Ramsey numbers of 2-interval chromatic ordered graphs

Dana Neidinger (Illinois Math)

Abstract: An ordered $G$ is a graph together with a specified linear ordering on the vertices, and its interval chromatic number is the minimum number of independent sets consisting of consecutive vertices that are needed to partition the vertex set. The $t$-color Ramsey number $R_t(G)$ of an ordered graph $G$ is the minimum number of vertices of an ordered complete graph such that every edge-coloring by $t$ colors contains a copy of $G$ in some color $i$, where the copy of $G$ preserves the original ordering on $G$. We obtain lower bounds linear in the number of vertices for the ordered Ramsey numbers of certain classes of 2-ichromatic ordered graphs using the methodology of Balko, Cibulka, Král, and Kynčl. We also determine the exact value of the $t$-color Ramsey number for two families of 2-ichromatic ordered graphs. We prove a linear upper bound for a class of 2-ichromatic ordered graphs.

3:00 pm in 243 Altgeld Hall,Tuesday, September 19, 2017

Character values, combinatorics, and some p-adic representations of finite groups

Michael Geline (Northern Illinois University)

Abstract: There are many questions which remain open from Brauer's modular representation theory of finite groups, and little agreement exists over the extent to which they ought to ultimately depend on the classification of finite simple groups. In studying a classification-free approach to one such question, involving lattices over the p-adics, I was led to an elementary combinatorial problem which is interesting in its own right and somewhat amenable to analysis by means of character values. I will present this problem, the original conjecture of Brauer which gave rise to it, and my own progress in the area. If it is necessary to mention algebraic geometry, there is something of a long-shot analogy between the character values and the Weil conjectures.

Wednesday, September 20, 2017

3:00 pm in 343 Altgeld Hall,Wednesday, September 20, 2017

Symmetric group representations and Z

Anshul Adve (UIUC)

Abstract: We discuss implications of the following statement about the representation theory of symmetric groups: every integer appears infinitely often as an irreducible character evaluation, and every nonnegative integer appears infinitely often as a Littlewood-Richardson coefficient and as a Kronecker coefficient. This is joint work with A. Yong.

4:00 pm in Altgeld Hall 141,Wednesday, September 20, 2017

Higgs bundle and related "physics"

Lutian Zhao (Illinois Math)

Abstract: Higgs bundle was a math term introduced by Nigel Hitchin as a rough analogue of Higgs boson in standard model of physics. It turns out that it is deeply rooted in the N=4 super Yang-Mills world, where Kapustin and Witten realize the geometric Langlands correspondence as a special case of S-duality. In this talk. I'll introduce the history and notion of the Higgs bundle, and try to talk about some of the idea in their "proof". No knowledge of physics is assumed.

4:00 pm in 245 Altgeld Hall,Wednesday, September 20, 2017

Rehumanizing Mathematics: A Vision for the Future

Dr. Rochelle Gutierrez   [email] (Illinois, Department of Curriculum and Instruction)

Abstract: In this session, Dr. Gutiérrez will reorient the audience away from a long established "equity" standpoint towards reframing the goal as rehumanizing mathematics. In particular, she will highlight 1) what may constitute dehumanizing practices/experiences in mathematics classrooms and 2) what can be done so that students and teachers are provided with both windows and mirrors onto the world and ways of relating to each other with dignity through mathematics. Specific examples of what one might look for in a rehumanized mathematics classroom will be provided.

Thursday, September 21, 2017

11:00 am in 241 Altgeld Hall,Thursday, September 21, 2017

4-Shadows in q-Series: Gupta, Kimberling, the Garden of Eden and the OEIS.

George Andrews (Penn State )

Abstract: This talk is devoted to discussing the implications of a very elementary technique for proving mod 4 congruences in the theory of partitions. It starts with a tribute to the late Hans Raj Gupta and leads in unexpected ways to partitions investigated by Clark Kimberling, to Bulgarian Solitaire, and to Garden of Eden partitions. Each surprise busts forth from the OEIS

12:00 pm in Altgeld Hall 243,Thursday, September 21, 2017

Pair correlation in Apollonian circle packings

Xin Zhang (University of Illinois at Urbana-Champaign)

Abstract: Consider four mutually tangent circles, one containing the other three. An Apollonian circle packing is formed when the remaining curvilinear triangular regions are recursively filled with tangent circles. The extensive study of this object in the last fifteen years has led to many beautiful theorems in number theory, graph theory, and homogeneous dynamics. In this talk I will discuss a new type of problems, which concern the fine scale structure of Apollonian circle packings. In particular, I will show that the limiting pair correlation of circles exists. A critical tool we use is an extended version of a theorem of Mohammadi-Oh on the equidistribution of expanding horospheres in infinite volume hyperbolic spaces. This work is motivated by an IGL project that I mentored in Spring 2017.

12:30 pm in 276 Loomis,Thursday, September 21, 2017

Soft particles in Effective Field Theories

Henriette Elvang (University of Michigan)

Abstract: I will discuss the approach to study quantum field theories using the soft limits of massless particles. In particular, I will present modifications to classic soft theorems for photons and gravitons that arise from higher-dimension operators in effective field theories; these can be interpreted as the corrections from loops of massive particles. Finally I will discuss on-going work on using soft limits to examine the landscape of effective field theories with enhanced symmetry.

4:00 pm in 245 Altgeld Hall,Thursday, September 21, 2017

The Man Who Knew Infinity: the Movie, the Man, and the Mathematics

George Andrews (Penn State)

Abstract: In the spring of 2016, the motion picture, The Man Who Knew Infinity, was released. It is now available on DVD. The movie tells the life story of the Indian genius, Ramanujan. In this talk, I hope to start with the trailer from the movie. Then I shall provide a brief discussion of Ramanujan's life with a glimpse of the mathematics contained in his celebrated Lost Notebook (of which Bruce Berndt and I have just concluded preparing the fifth and final volume explicating the many assertion therein). The bulk of the talk will consider the path from the Rogers-Ramanujan identities to current open problems and how computer algebra assists in their study.

Friday, September 22, 2017

12:00 pm in 243 Altgeld Hall,Friday, September 22, 2017

Measurable Differentiable Structures and Nonbeddability into RNP spaces

Chris Gartland (UIUC)

Abstract: In 1999, Cheeger proved that doubling metric measure spaces admitting a Poincare inequality carry a 'measurable differentiable structure' with respect to which Lipschitz functions could be differentiated almost everywhere. A major consequence of this theorem is that if such a space were to biLipschitz embed into a finite dimensional normed space (or as was later proved, any RNP space), a generic point would have all of its tangent cones biLipschitz equivalent to some finite dimensional normed space. We'll outline the proof of this consequence and discuss its application to Carnot groups and inverse limits of graphs.

1:00 pm in 141 Altgeld Hall,Friday, September 22, 2017

Travis Nell

Abstract: We continue reading Simon's "A guide to NIP Theories", chapter 7.

4:00 pm in 241 Altgeld Hall,Friday, September 22, 2017

Spectral Gaps, Dynamic Maps, Groups convex and co-compact

Hadrian Quan (UIUC)

Abstract: What do limit sets of group actions, solutions of the linear wave equation, and zeta functions all have in common? They’ll all appear in this talk in surprising ways. By the end of the talk I hope to convince you that their relation is more than surface-deep. This will be an introductory talk, with lots of pictures and examples and little assumed beyond knowledge of the fundamental group of a surface.

4:00 pm in 345 Altgeld Hall,Friday, September 22, 2017

Constructing Analyzable Types in Differentially Closed Fields with Logarithmic Derivatives

Ruizhang Jin (U Waterloo Math)

Abstract: We generalize the well-known fact that the equation $\delta(\log \delta x) = 0$ is analyzable in but not internal to the constants. We use the logarithmic derivative as a building block to construct analyzable types with a unique analysis of minimal length (up to interalgebraicity). We also look for criteria for a given definable set such that its pre-image under the logarithmic derivative is analyzable in but not internal to the constants.