Date/Time : 19 Aug 2025 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : York Ye, National University of Singapore

Configuration spaces of flags can be used to describe many algebraic varieties appearing in representation theory, such as double Bruhat cells and surface character varieties. In this talk, I will discuss the relationship between configuration spaces and cluster algebras. Then I will introduce my joint work with Huanchen Bao on the upper cluster structure of Kac-Moody Richardson varieties and explain some of the new techniques.

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Date/Time : 13 Aug 2025 17:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Kenny Gill, La Salle University

A countable structure S is indivisible if it satisfies a pigeonhole principle: for any bounded coloring of any presentation of S, there is a monochromatic induced substructure isomorphic to S. This naturally gives rise to an instance-solution problem Ind(S) which outputs such a substructure given a presentation and coloring. We seek to understand both (1) the computational difficulty of solving Ind(S) for various specific S; and (2) how properties of S can translate to properties of Ind(S) and vice versa. This talk will survey what is known about both (1) and (2), highlighting some of the many open problems in the area. In particular, we propose several notions of uniform embeddability of one structure in another which allow one to obtain desirable properties of Ind(S) for large classes of S. This is in part ongoing joint work with Damir Dzhafarov and Reed Solomon.

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Date/Time : 13 Aug 2025 16:30
Venue : S17 #04-04 (SR3)
Speaker : Liu Wenjie, Harbin Institute of Technology

In this talk, we introduce a new theoretical framework built upon fractional spaces for optimal error estimates of Chebyshev/Legendre polynomial approximations to functions with limited regularity. It naturally arises from exact representations of orthogonal polynomial expansion coefficients. Here, the essential pieces of the puzzle for the error analysis include (i) fractional integration by parts (under the weakest possible conditions); (ii) generalised Gegenbauer functions of fractional degree (GGF-Fs): a new family of special functions with notable fractional calculus properties, and (iii) asymptotic formulas or uniform upper bounds of GGF-Fs. Finally we introduce the hypothesis of Babuska and Hakula. The talk is based on joint work with Li-Lian Wang, Huiyuan Li, Boying Wu and Ruiyi Xie.

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Date/Time : 12 Aug 2025 14:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Matias Delgadino, University of Texas at Austin

We prove sharp estimates for the mean-field limit of weakly interacting diffusions with repulsive logarithmic interaction in arbitrary dimension. More precisely, we show that the associated partition function is uniformly bounded in the number of particles N for an arbitrary bounded base measure. Combined with the modulated free energy method, this amounts to a logarithmic improvement in N of the current best available closeness estimates in the literature. Our arguments are inspired by and borrow ideas from Nelson’s classical construction of the \Phi^4_2 Euclidean quantum field theory.

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Date/Time : 08 Aug 2025 10:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Timo Sprekeler, Texas A&M University

We begin by discussing the finite element approximation of stationary Fokker–Planck–Kolmogorov (FPK) equations subject to periodic boundary conditions in two settings: one with weakly differentiable coefficients, and one with merely essentially bounded measurable coefficients under a Cordes-type condition. These problems arise as governing equations for the invariant measure in the homogenization of nondivergence-form equations with large drifts. We then suggest and rigorously analyze an approximation scheme for the effective diffusion matrix in both settings, based on the finite element scheme for stationary FPK problems developed in the first part. This talk includes joint work with Endre Süli (University of Oxford) and Zhiwen Zhang (The University of Hong Kong).

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Date/Time : 30 Jul 2025 14:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Sang-hyun Kim, Korea Institute for Advanced Study

Two groups are elementarily equivalent if they have the same sets of true first order group theoretic sentences. We prove that for two real numbers r,s ≥ 1, and for two smooth closed manifolds M and N, the C^r diffeomorphism group of M is elementarily equivalent to the C^s diffeomorphism group of N if and only if r=s and M is diffeomorphic to N. In the case of r=s=0, we can even weaken the hypothesis so that the manifolds are only assumed to be compact, dropping the smoothability or closedness hypotheses. This strengthens (1) Whittaker’s theorem (1963) on the C^0 case, and (2) Takens–Filipkiewicz theorems (1982) on C^p case with an integer p. Joint work with Thomas Koberda (UVa) and Javier de la Nuez-Gonzalez (KIAS)

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Date/Time : 29 Jul 2025 14:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Vilas Sreenivasan Winstein, University of California, Berkeley

Independent sets have long been studied as a model for gases in statistical mechanics, and Sapozhenko’s famous graph container method was developed to understand their quantity in the hypercube, where they correspond to error-detecting codes. When removing edges at random (i.e. percolating the hypercube), the number of independent sets in the resulting graph becomes the partition function of a disordered system, akin to popular models like spin glasses. I will discuss a new probabilistic framework which establishes sharp distributional characterizations of this partition function and the underlying disordered system, settling several open problems and explaining various phase transitions observed in this model. This is joint work with Mriganka Basu Roy Chowdhury and Shirshendu Ganguly.

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Date/Time : 28 Jul 2025 16:00
Venue : S17 #04-04 (SR3)
Speaker : Vilas Winstein , University of California, Berkeley

This is part 2 of a two-talk series. We will discuss some recent results on the limiting Gaussian nature of fluctuations of various observables under exponential random graph models; in particular, we obtain quantitative error bounds via Stein’s method. A key novelty is that our results apply in the low-temperature parameter regime which has previously been unexplored and requires new methods. These include the application of novel concentration inequalities derived from carefully analyzing the mixing behavior of relevant Markov chains.

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Date/Time : 25 Jul 2025 16:00
Venue : S17 #05-12 (Seminar Room 4)
Speaker : Vilas Winstein , University of California, Berkeley

This is part 1 of a two-talk series. We will introduce exponential random graph models, which are exponential tilts of Erdős–Rényi models by functions which increase or decrease the number of certain small subgraphs (e.g. triangles). We will also discuss relevant tools for studying these modelThis is part 1 of a two-talk series. We will introduce exponential random graph models, which are exponential tilts of Erdős–Rényi models by functions which increase or decrease the number of certain small subgraphs (e.g. triangles). We will also discuss relevant tools for studying these models, such as large deviations principles, mixing results, and concentration inequalities.s, such as large deviations principles, mixing results, and concentration inequalities.

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