Date/Time : 29 Apr 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Juncheng Wei, The Chinese University of Hong Kong

In 2023, one year before his death, H. Brezis posted 28 open questions which he described as “challenging and difficult”. In this talk I will give complete answer to the first open question—Problem 1.1 on Brezis-Nirenberg problem on three dimensional unit ball, and the seventh open question—Problem 3.1 on harmonic map equation on disk.

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Date/Time : 30 Mar 2026 10:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Luis Vega, University of the Basque Country (UPV/EHU), Spain

I’ll present some recent work about the connection of vortex filaments/tubes that move according to Navier Stokes Equation and the binormal curvature flow of curves in 3d. This is a joint work with Marco A. Fontelos and Mikel Ispizua.

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Date/Time : 20 Mar 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Lucas Mason-Brown, University of Texas at Austin

Let G be a reductive group defined over a local field F. The local Langlands conjecture suggests a correspondence between (certain) infinite-dimensional irreducible G(F)-representations and (certain) finite-dimensional representations of the absolute Galois group \Gamma_F of F. If E/F is a field extension, then there is an inclusion \Gamma_F \subset \Gamma_E, and hence a natural map (restriction) from \Gamma_E-representations to \Gamma_F-representations. Composing with the (conjectural) Langlands correspondences for G(E) and G(F), we obtain a (conjectural) map, called `base change’ from G(F)-representations to G(E)-representations. In this talk, I will consider the special case when E=C and F=R. For real and complex groups, the local Langlands conjecture is a theorem (at least on the level of K groups), so there is a well-defined base change map from G(R)-representations to G(C)-representations (at least on the level of K groups). An interesting problem is to describe this correspondence directly, i.e. without appealing to the Langlands classification. I will describe a *partial* solution to this problem, following work of Clozel. Time permitting, I will formulate some conjectures regarding preservation of unitarity. This is joint work in progress with Andrei Ionov and David Nadler.

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Date/Time : 18 Mar 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Lucas Mason-Brown, University of Texas at Austin

A basic unsolved problem in representation theory is to classify the set of irreducible unitary representations of a reductive Lie group G. In this talk, I will describe a geometric approach to this problem, which has emerged over the past several years, based on the theory of quantizations of symplectic singularities. I will formulate a precise conjectural classification of the irreducible unitary representations of an arbitrary group G and present some recent progress towards its proof.

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Date/Time : 18 Mar 2026 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Sam G. Krupa, École Normale Supérieure, Paris

For hyperbolic systems of conservation laws in 1-D, fundamental questions about uniqueness and blow up of weak solutions still remain even for the apparently “simple” systems of two conserved quantities such as isentropic Euler and the p-system. Similarly, in the multi-dimensional case, a longstanding open question has been the uniqueness of weak solutions with initial data corresponding to the compressible vortex sheet. We address all of these questions by using the lens of convex integration, a general method of constructing highly irregular and non-unique solutions to PDEs. Our proofs involve computer-assistance. This talk is based on joint work with László Székelyhidi, Jr.

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Date/Time : 18 Mar 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Zihui Zhao, Johns Hopkins University

Free boundary problems are problems of solving an elliptic or parabolic PDE, but on a domain that is determined by the solution, and they arise naturally in the study of water waves and ice melting, etc. In this talk, we will focus on the regularity of the free boundaries for the Bernoulli problem, firstly studied by Alt and Caffarelli. More precisely, we study the behavior of such solutions near some well-known singularity models. In particular, our result implies that such singularity is not the typical behavior. This is joint work with Engelstein and Restrepo.

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Date/Time : 18 Mar 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Fan Chang, Nankai University

In this talk, I will present a short and elementary proof of the Poincaré inequality for increasing subsets of the hypercube, recently proved by Fei and Ferreira Pinto Jr. This result implies an $O(n^2)$ upper bound on the mixing time of censored random walks, improving on the earlier $O(n^3)$ bound of Ding and Mossel. This is joint work with Guowei Sun and Lei Yu.

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Date/Time : 17 Mar 2026 15:00
Venue : IMS Executive Seminar Room (S17 Level 3)
Speaker : Mihai Anitescu, Argonne National Laboratory and University of Chicago

Since 2018, with several co-authors, we have pursued a research program to explain a phenomenon first observed in long-horizon optimal control problems. That is when the data of the problem is perturbed at a certain temporal index, the effect of the perturbation on the solution at a different temporal index decays exponentially fast with respect to the distance between the two. We have shown, that, under uniform second order and linear independence constraint qualifications this phenomenon holds and we extended this proof for spatially-indexed, and more generally, graph-indexed problems. In turn, this allows proving that Schwarz-type decompositions with overlap used as either preconditioners or as solution schemes improve convergence exponentially fast with the size of the overlap. We discuss the consequences of this observation for design of efficient parallel algorithms and decentralized optimization schemes and present a few of their applications.

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Date/Time : 16 Mar 2026 16:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Svetlana Makarova, Australian National University

When introducing the notion of moduli problems, perhaps the most trivial example one may consider is the “functor of points” of a variety X, whose “classifying space” (moduli space) is X itself. Its very close relative is the stack of ideal sheaves of length 1 subschemes: when X is normal and of dimension at least 2, this stack is the product of X with BG_m. Despite the apparent triviality, modifying this stack gives rise to interesting birational phenomena, about which I will speak. I will describe a certain enlargement U of the stack of ideal sheaves that yields, via taking the good moduli space, a birational contraction of X, and an open substack of U that yields a surgery diagram via non-GIT wall-crossing. If time permits, I will explain how the interpretation of the surgery as a fine moduli of sheaves helps prove instances Kawamata’s DK-hypothesis in this setting. This is joint work with Andres Fernandez Herrero (https://arxiv.org/abs/2508.13395).

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