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 16:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Schwab Christoph, ETH Zurich, Switzerland

We report mathematical results on numerical methods for the fractional Laplacian. Emphasis will be on polygonal and polyhedral domains, weighted analytic regularity of solutions and exponential convergence results for hp-Galerkin Finite Element Approximation of solutions. Integral and spectral fractional Laplacians will be considered.

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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 : 27 Mar 2026 14:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Wu Xingyu, National University of Singapore

Let F be a local field and let G be a split exceptional group over F. The theta correspondence for the dual pair (SL2, G) relates irreducible representations of SL2(F) and G(F), and a basic problem is to determine which representations of G(F) occur in the lift and with what multiplicity. In this talk, based on Hanzer and Savin’s work, I will explain a multiplicity-one statement for an oscillator-type model attached to a fixed additive character, and how it leads to a classification of those irreducible representations of G(F) that appear as its quotients. As a consequence, one obtains a clean criterion: a representation of G(F) occurs precisely when it is the theta lift of a generic irreducible representation of SL2(F). I will sketch the main ideas behind this reduction and indicate how it guides the computation of the correspondence.

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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 17:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Stefan Ludwig, University of Freiburg

What is the common theory of all finite fields equipped with an additive and/or multiplicative character? Hrushovski answered this question in the additive case working in (a mild version of) continuous logic. Motivated by natural number-theoretic examples we generalise his results to the case allowing for both (non-trivial) additive character and (sufficiently generic) multiplicative character. Apart from answering the above question we obtain a quantifier elimination result and a generalisation of the definability of the Chatzidakis-van den
Dries-Macintyre counting measure to this context. The proof relies on classical results on bounds of character sums following from the work of Weil.

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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 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 #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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