MSCS Seminar Calendar
Monday October 6, 2025

Equivariant birational geometry of Fano threefolds
Zhijia Zhang (NYU)
3:00 PM in 636 SEO
The notion of G-varieties was introduced by Manin when he studied rationality problems of surfaces. Broadly speaking, a G-variety is a variety X carrying an action of a group G. The group can act via automorphisms of X or via Galois actions if the base field is non-closed. There are close connections, as well as drastic differences between these two types of actions from the perspective of birational geometry. In this talk, I will explore these similarities and differences with a focus on equivariant unirationality of Fano threefolds. This is joint work with Yuri Tschinkel and Ivan Cheltsov.

The number of induced subgraphs
Dhruv Mubayi (UIC)
3:00 PM in 1227 SEO
We consider the following general question that encompasses some of the most celebrated theorems in Combinatorics.
Given a small graph H and a large graph G with density x, what is the possible number of induced subgraphs of G that are isomorphic to H.
A complete answer is known only in the case when H is a clique or a two edge star (and their complements). We will discuss some general theory around this problem and then focus on some specific H. This is joint work with Xizhi Liu and Christian Reiher.

Integral equations for linear flexural-gravity waves
Jeremy Hoskins (University of Chicago)
4:00 PM in 636 SEO
Flexural waves, the propagation of waves in thin elastic sheets, arise in a number of contexts, and, particularly, in the study of ice shelves. In the frequency domain, they are commonly modeled as a fourth order PDE in two dimensions with clamped plate, free plate, or supported plate boundary conditions. Here, we review existing approaches for solving boundary value problems of this type, and discuss some limitations. Building on this, for the supported plate and free plate problems, we propose novel representations which ultimately reduce the problems to second kind integral equations. Moreover, the resulting integral equations are amenable to standard high order discretization approaches and fast algorithms. Several numerical examples will be presented which illustrate the properties of these integral equations. Finally, generalizations to other wave phenomena will be discussed.
Tuesday October 7, 2025

Topic Seminar: Forking
Scott Mutchnik (UIC)
2:00 PM in 427 SEO
We will have a research seminar this semester on forking, broadly construed, particularly in the setting of unstable first-order theories.
Graduate students are particularly encouraged to attend.
We will show that the stability of the forking relation, a global variant of the stable forking conjecture, is equivalent for supersimple countably categorical theories to the stable forking conjecture. We then discuss the simple Kim-forking conjecture in NSOP_1 theories, and prove cases of this conjecture from joint work with Baldwin and Freitag, including an infinite-variable global variant in a general NSOP_1 theory, a finite-variable global variant in the case of finite F_Mb, and the full conclusion of the simple Kim-forking conjecture, given enough indices, for forking with realizations of an isolated type with the definable Morley property. All three of these results use a strong version of Kim’s lemma in NSOP_1 theories, due to Kaplan and Ramsey, which says that all Kim-independent Morley sequences exhibit Kim-dividing.
Wednesday October 8, 2025

Double exponential mixing in analytic dynamics
Ekaterina Shchetka (University of Michigan)
3:00 PM in 636 SEO
In dynamics, the speed of mixing depends on the chaos of the map and the regularity of the observables. Notably, two classical linear models—the Bernoulli doubling map and the CAT map—exhibit double exponential mixing for analytic observables. Are linear maps the only ones with this property? In dimension one, we provide a full classification for maps from the space of finite Blaschke products acting on the circle (as well as for free semigroup actions generated by a finite collection of such maps). In higher dimensions, we identify a necessary condition for double exponential mixing and present several families of examples and non-examples. Key ideas of the proof involve the Koopman precomposition operator on spaces of hyperfunctions (elements of the dual space of analytic functions), which turns out to be non-self-adjoint, compact, and quasinilpotent, with spectrum reduced to zero.
The talk is accessible to all; no background knowledge is required.

Is O-minimal Topology too Tame?
John E. Solak (UIC)
4:00 PM in 427 SEO
In this talk, I will provide an introduction to o-minimal theories and some of the Geometry and Topology available to those who study them. The introduction will be based heavily on portions from Lou Van den Dries’ book, Tame Topology and O-minimal Structures, as well as Ronnie’s reading course from last Fall. After the introduction, I will discuss the definitions of dimension and Euler characteristic in the o-minimal setting, and then survey some of their applications while bringing to light small personal concerns over the intuitiveness of these measurements.
Thursday October 9, 2025
Monday October 13, 2025

Self-similar singularities in fluids and related equations
Jiajie Chen (U Chicago)
4:00 PM in 636 SEO
In this talk, we will present recent developments in constructing self-similar singularities in the compressible Euler equations and the nonlinear wave equation, associated with implosion. Our approach combines ODE techniques, weighted energy estimates, compact perturbation methods, and soft functional analysis arguments.
Tuesday October 14, 2025

Zarankiewicz’s Problem and Model Theory
Aris Papadopoulos (University of Maryland)
3:00 PM in 636 SEO
A shower thought that anyone interested in graph theory must have had at some point in their lives is the following: `How “sparse" must a given bipartite graph be, if I know that it has no “dense” subgraphs?’. This curiosity definitely crossed the mind of Polish mathematician K. Zarankiewicz, who asked a version of this question formally in 1951. In the years that followed, many central figures in the development of extremal combinatorics contemplated this problem, giving various kinds of answers. Some of these will be surveyed in the first part of my talk.
So far so good, but this is a logic seminar and the title says the words “Model Theory"… In the second part of my talk, I will discuss how the celebrated Szemerédi-Trotter theorem gave a starting point to the study of Zarankiewicz’s problem in “geometric” contexts, and how the language of model theory has been able to capture exactly what these contexts are. I will then ramble about improvements to the classical answers to Zarankiewicz’s problem, when we restrict our attention to semilinear/semibounded o-minimal structures, Presburger arithmetic, and various kinds of Hrushovski constructions.
The new results that will appear in the talk have been obtained jointly with Pantelis Eleftheriou.
Wednesday October 15, 2025
Friday October 17, 2025

Higher arity Vapnik–Chervonenkis theory and PAC learning
Artem Chernikov (Maryland)
3:00 PM in 636 SEO
Finite VC-dimension, a combinatorial property of families of sets, was discovered simultaneously in the 70's by Vapnik and Chervonenkis in probabilistic learning theory, and by Shelah in model theory (where it is called NIP). It plays an important role in several areas including machine learning, combinatorics, mathematical logic, functional analysis and topological dynamics. A higher arity generalization of VC-dimension for families of sets in n-fold product spaces (i.e. a bound on the sizes of n-dimensional boxes that can be shattered) is implicit in Shelah's work on n-dependent theories in model theory. Following some preliminary work in Chernikov, Palacin, Takeuchi '14, in Chernikov, Towsner '20 we developed aspects of higher-arity VC-theory, including a generalization of Haussler's packing lemma for families of sets (and real-valued functions) of bounded VC_n-dimension. Probably Approximately Correct (PAC) learning is a classical framework for mathematical analysis of machine learning, and PAC learnability is famously characterized by finite VC dimension. Generalizing this, we demonstrate that finite VC_n dimension characterizes higher arity PAC learning (PAC_n learning) in n-fold product spaces with respect to product measures introduced by Kobayashi, Kuriyama and Takeuchi '15. Joint work with Henry Towsner.
Monday October 20, 2025
Wednesday October 22, 2025
Monday October 27, 2025
Wednesday October 29, 2025

Dynamical Commensurator Groups
Steve Hurder (UIC)
3:00 PM in 636 SEO
We introduce the dynamical commensurator group for a generalized odometer action, that is for minimal equicontinuous group actions on Cantor sets. We show there is a map from the pointed mapping class group of a solenoidal manifold (ie a weak solenoid) to a dynamical commensurator group, and give conditions for when this map is either surjective or an isomorphism. Odden proved that this map is an isomorphism for the mapping class of the universal hyperbolic solenoid; Bering and Studenmund proved that the mapping class group of a universal solenoid over a compact K(G,1) manifold maps onto the commensurator group of G. We extend the results of both of these papers to arbitrary solenoidal manifolds. This work is joint with Olga Lukina.
Wednesday November 5, 2025
Monday November 10, 2025

Local inequalities for cA_k singularities
Erik Paemurru (Bulgarian Academy of Sciences)
3:00 PM in 636 SEO
We generalize an intersection-theoretic local inequality
of Fulton–Lazarsfeld to weighted blowups. Using this together with the
classification of 3-dimensional divisorial contractions, we prove
nonrationality of many families of terminal Fano 3-folds. This is a
joint work with Igor Krylov and Takuzo Okada.
Wednesday November 12, 2025
Friday November 14, 2025
Monday November 17, 2025
Wednesday November 19, 2025
Wednesday November 26, 2025
Wednesday December 3, 2025