Department of

# Mathematics

Seminar Calendar
for events the day of Tuesday, September 25, 2018.

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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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Tuesday, September 25, 2018

11:00 am in 345 Altgeld Hall,Tuesday, September 25, 2018

#### $A_n$ spaces in homotopy type theory

###### Egbert Rijke (UIUC)

Abstract: We will propose a definition of $A_n$ spacesin homotopy type theory.

12:00 pm in 243 Altgeld Hall,Tuesday, September 25, 2018

#### Normal generators for mapping class groups are abundant

###### Justin Lanier (Georgia Tech Math)

Abstract: For mapping class groups of surfaces, we provide a number of simple criteria that ensure that a mapping class is a normal generator, with normal closure equal to the whole group. We then apply these criteria to show that every nontrivial periodic mapping class that is not a hyperelliptic involution is a normal generator whenever genus is at least 3. We also show that every pseudo-Anosov mapping class with stretch factor less than √2 is a normal generator. Showing that pseudo-Anosov normal generators exist at all answers a question of Darren Long from 1986. In addition to discussing these results on normal generators, we will describe several ways in which they can be leveraged to answer other questions about mapping class groups. This is joint work with Dan Margalit.

1:00 pm in 243 Altgeld Hall,Tuesday, September 25, 2018

#### Evolutionary dynamics of non-Hodgkin’s lymphoma CAR T cell therapy and extinction-event times in diffusive public goods games

###### Greg Kimmel (Moffitt Cancer Institute)

Abstract: Non-Hodgkin Lymphoma (NHL) is the most common hematologic malignancy in the United States with an estimated 72,000 new cases (4.3% of all cancer cases) and 20,000 deaths (3.4% of all cancer deaths) in 2017; the median 5-year survival rate is 71%. There exist patients that develop refractory disease. These patients have a median overall survival of less than seven months. Chimeric antigen receptor (CAR) T-cell therapy for refractory NHL relies on expansion of engineered T- cells that specifically target tumor cells expressing CD19. Here we combine mathematical modeling with statistical data-analysis based on recent results of clinical studies of CAR T-cell dynamics in individual patients. We find that the success of therapy may depend on dynamic regulation of inflammatory cytokines in the tumor microenvironment, as well as on specific properties of the heterogeneous CAR T-cell population. Relative abundances of juvenile and effector T cells are key factors that drive the duration of treatment response, and the tumor-killing rate of this CD19-specific immunotherapy.

1:00 pm in 345 Altgeld Hall,Tuesday, September 25, 2018

#### Pseudofinite groups, arithmetic regularity, and additive combinatorics

###### Gabe Conant (University of Notre Dame)

Abstract: I will report on joint work with Pillay and Terry on arithmetic regularity (a group theoretic analogue of Szemerédi regularity for graphs) for sets of bounded VC-dimension in finite groups, which is proved using a local version generic compact domination for NIP formulas in pseudofinite groups. I will then present more recent work on nonabelian versions of certain "inverse theorems" from additive combinatorics, which are proved using pseudofinite model theory, and can be used to give alternate proofs of NIP arithmetic regularity for certain classes of finite groups.

2:00 pm in 243 Altgeld Hall,Tuesday, September 25, 2018

#### Generalized Turán problems for graphs and hypergraphs

###### Ruth Luo (Illinois Math)

Abstract: We will talk about a generalization of the Turán problem for hypergraphs: given a graph $F$, what is the maximum number of hyperedges an $r$-uniform $n$-vertex Berge $F$-free hypergraph can have? In particular, we will discuss tools used to reduce the hypergraph problem to problems for graphs. Finally, I will present some recent results for graphs without long Berge cycles. This is joint work with (different subsets of) Zoltan Furedi and Alexandr Kostochka.

2:00 pm in 345 Altgeld Hall,Tuesday, September 25, 2018

#### Mean Field Analysis of Neural Networks in Machine Learning

###### Justin Sirignano (Illinois ISE)

Abstract: Neural network models in machine learning have revolutionized fields such as image, text, and speech recognition. There's also growing interest in using neural networks for applications in science, engineering, medicine, and finance. Despite their immense success in practice, there is limited mathematical understanding of neural networks. We mathematically study neural networks in the asymptotic regime of simultaneously (A) large network sizes and (B) large numbers of stochastic gradient descent training iterations. We rigorously prove that the neural network satisfies a Law of Large Numbers (LLN) and a Central Limit Theorem (CLT). The LLN is the solution of a nonlinear partial differential equation while the CLT satisfies a stochastic partial differential equation.

3:00 pm in 243 Altgeld Hall,Tuesday, September 25, 2018

#### Kasteleyn Operators from Mirror Symmetry

###### Eric Zaslow (Northwestern University)

Abstract: Kenyon-Okounkov-Sheffied showed that the statistical properties of dimer configurations on bipartite graphs on a two-torus are determined by a spectral curve. Goncharov-Kenyon showed how edge weights of the graph define a cluster integrable system. I will show how both of these results follow from sheaf quantization in the context of homological mirror symmetry (HMS): the spaces involved are moduli spaces of objects in two categories related by HMS. This talk is based on joint work with David Treumann and Harold Williams.