Department of

# Mathematics

Seminar Calendar
for events the week of Friday, February 15, 2019.

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events for the
events containing

Questions regarding events or the calendar should be directed to Tori Corkery.
     January 2019          February 2019            March 2019
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Monday, February 11, 2019

3:00 pm in 243 Altgeld Hall,Monday, February 11, 2019

#### Rigidity of Lie groupoids and foliations

###### Rui Loja Fernandes (UIUC)

Abstract: I will discuss a result stating that a compact, Hausdorff, Lie groupoid is rigid. i.e., has no non-trivial deformations. As an application of this result, it follows that a compact, Hausdorff foliation is rigid if and only if the generic leaf has trivial 1st cohomology. This is closely related to old stability results for foliations due to Epstein, Rosenberg and Hamilton. This talk is based on joint work with Matias del Hoyo.

5:00 pm in 241 Altgeld Hall,Monday, February 11, 2019

#### Introduction to differential and Riemannian geometry part II

Tuesday, February 12, 2019

1:00 pm in 345 Altgeld Hall,Tuesday, February 12, 2019

#### The Open Graph Dichotomy and the second level of the Borel hierarchy

###### Raphaël Carroy (Gödel Research Center for Math. Logic at Univ. of Vienna)

Abstract: I will explain how variants of the open graph dichotomy can be used to obtain various descriptive-set-theoretical dichotomies at the second level of the Borel hierarchy. This shows how to generalise these dichotomies from analytic metric spaces to separable metric spaces by working under the axiom of determinacy. If time allows it, I will also discuss some connections between cardinal invariants and the chromatic number of the graphs at stake.

2:00 pm in 243 Altgeld Hall,Tuesday, February 12, 2019

#### On the number of edges in C_5-free 3-uniform hypergraphs

###### Dara Zirlin (Illinois Math)

Abstract: In a 3-uniform hypergraph, a Berge 5-cycle is formed by five distinct edges $e_1,\dots e_5$ and five distinct vertices $v_1,\dots, v_5$, such that $v_i,v_{i+1}\in e_i$, where indices count modulo 5.

In 2007, Bollobás and Györi gave upper bounds on the number of triangles in a $C_5$-free graph, and on the number of edges in a 3-uniform hypergraph containing no Berge 5-cycles.
We improve their second bound. This is joint work with Alexandr Kostochka.

4:00 pm in Altgeld Hall,Tuesday, February 12, 2019

#### No Seminar Today

Abstract: To encourage faculty members of the seminar to join the 4pm departmental discussion in 245 of the math building design we won't have a seminar today. It will resume next week at the usual time and location.

4:00 pm in 245 Altgeld Hall,Tuesday, February 12, 2019

#### Altgeld-Illini Renovation/Building Project Feedback Session

Abstract: The department's Altgeld-Illini Renovation Committee seeks input from every member of the department to help us develop a clear vision of what we want in the new building and the renovations.

Wednesday, February 13, 2019

3:00 pm in 341 Altgeld Hall,Wednesday, February 13, 2019

#### Introduction to well and even better quasi-orders

###### Raphaël Carroy (Gödel Research Center for Math. Logic, Univ. of Vienna)

Abstract: Well-quasi-orders, or wqos, generalize well-orders in the context of partial orders. They appear naturally in various domains of mathematics, and have been frequently rediscovered. I'll briefly explain why, and what we can do with them. I'll then talk about their limitations and why it's hard to prove that non-trivial quasi-orders are wqo. I will also show how trying to fix these problems leads to the definition of a smaller class of quasi-orders: better-quasi-orders, or bqos. If time allows, I'll get a bit into bqo theory.

3:00 pm in 243 Altgeld Hall,Wednesday, February 13, 2019

#### To Be Announced

###### Chen Chen (University of Chicago, Geophysical Sciences)

3:00 pm in 2 Illini Hall,Wednesday, February 13, 2019

#### Equivariant Cohomology

###### Ciaran O'Neill (Illinois Math)

Abstract: I’ll define equivariant cohomology and give some basic examples. Then I’ll go into more detail for the case of a torus action on projective space.

Thursday, February 14, 2019

12:00 pm in 243 Altgeld Hall,Thursday, February 14, 2019

#### Spectral Rigidity of q-differential Metrics

###### Marissa Loving (UIUC Math)

Abstract: When geometric structures on surfaces are determined by the lengths of curves, it is natural to ask which curves’ lengths do we really need to know? It is a classical result of Fricke that a hyperbolic metric on a surface is determined by its marked simple length spectrum. More recently, Duchin–Leininger–Rafi proved that a flat metric induced by a unit-norm quadratic differential is also determined by its marked simple length spectrum. In this talk, I will describe a generalization of the notion of simple curves to that of q-simple curves, for any positive integer q, and show that the lengths of q-simple curves suffice to determine a non-positively curved Euclidean cone metric induced by a q-differential metric.

2:00 pm in 347 Altgeld Hall,Thursday, February 14, 2019

#### An Introduction to Dyson Brownian Motion and Universality (Part 2)

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

Abstract: We will discuss the connections of Dyson Brownian Motion and the Totally Asymmetric Simple Exclusion Process (TASEP). This will be the first glimpse of the Kardar Parisi Zhang Universality class.

3:00 pm in 347 Altgeld Hall,Thursday, February 14, 2019

#### Quiver varieties and root multiplicities for symmetric Kac-Moody algebras

###### Peter Tingley   [email] (Loyola University, Chicago)

Abstract: We discuss combinatorial upper bounds on dimensions of certain imaginary root spaces for symmetric Kac-Moody algebras. These come from a realization of the infinity crystal using quiver varieties. The framework is quite general, but we only work out specifics for one special case. We conjecture that our bound is quite tight, and give both computational evidence and heuristic justification for this conjecture, but unfortunately not a proof.

Friday, February 15, 2019

2:00 pm in 141 Altgeld Hall,Friday, February 15, 2019

#### Convex geometry and the Mahler conjecture

###### Derek Kielty (Illinois Math)

Abstract: In this talk we will give an introduction to convex geometry and discuss the Mahler conjecture. This conjecture asserts that the product of the volume of a centrally symmetric convex set and the volume of its dual is minimized on a certain family of polytopes. We will also discuss a PDE analog of this conjecture.

3:00 pm in 341 Altgeld Hall ,Friday, February 15, 2019

#### Note the time and room change!"The complexity of topological group isomorphism" by A. Kechris, A. Nies, and K. Tent (Part 2)

###### Jenna Zomback (UIUC)

Abstract: This will be the second talk of the series on the paper in the title [arXiv link], which deals with the classification of some natural classes of non-Archimedean groups (= closed subgroups of S) up to topological group isomorphism. It gives a general criterion for a class of non-Archimedean groups to show that the topological group isomorphism on it is Borel-classifiable by countable structures. This criterion is satisfied by the classes of profinite groups, locally compact non-Archimedean groups, and oligomorphic groups. In this talk, we will fill in some proofs left out last time and prove this general criterion.

4:00 pm in Altgeld Hall 145 ,Friday, February 15, 2019

#### Laplacian Operator and Hyperbolic Geometry

###### Xiaolong Han (Illinois Math)

Abstract: The Laplacian operator acting on functions on a Riemannian manifold is an analytic operator invariant under isometry of the manifold. Its spectrum encodes much geometric information of the manifold. In this talk, I will start with some basic properties of Laplacian operator and hyperbolic geometry. Then I will talk about how these two interact with each other. Time permitting, I will talk about some of my recent works. No background on Laplacian operator or hyperbolic geometry is assumed.

4:00 pm in 241 Altgeld Hall,Friday, February 15, 2019

#### How to Give a Good Math Talk

###### uAWM, MATRIX, & IGL Outreach   [email] (UIUC Math)

Abstract: We will be having a workshop for undergraduates wishing to present and give a talk in the Undergraduate Seminar this semester (and in the future). We'll go through all the basics of giving an interesting talk as well as some details that can really make a presentation stand out.

4:00 pm in 245 Altgeld Hall,Friday, February 15, 2019

#### Harry Potter's Cloak Via Transformation Optics

###### Gunther Uhlmann (University of Washington)

Abstract: Can we make objects invisible? This has been a subject of human fascination for millennia in Greek mythology, movies, science fiction, etc. including the legend of Perseus versus Medusa and the more recent Star Trek and Harry Potter. In the last fifteen years or so there have been several scientific proposals to achieve invisibility. We will introduce in a non-technical fashion one of them, the so-called "transformation optics" which has received a lot of attention in the scientific community.