Date/Time : 09 Sep 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Beomjun Choi, Korea Advanced Institute of Science & Technology (KAIST)

We will discuss how collective behavior in interacting particle systems can lead to qualitative changes in equilibria, and how these equilibria behave dynamically. The first part concerns long-time convergence for Keller–Segel equation, and more generally McKean–Vlasov equations, in relation to phase transitions and bifurcation. The second part concerns the local stability of mixed Nash equilibria for mean-field Langevin descent–ascent, where exponential convergence can be established despite the non-gradient and non-self-adjoint structure. We will also discuss a corresponding finite-particle stability result.

Add to calendar :

Date/Time : 09 Sep 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Sam McKeown, Nanyang Technological University

Last passage percolation (LPP) is a particularly simple and well-studied model of random geometry on a lattice. While questions on the typical shape of the geodesic between two points have attracted much attention in recent decades, we instead consider the shape of the “most typical” geodesic. A counterintuitive folk conjecture states that these modal geodesics should be the most extreme admissible paths. We give some quantitative results in this direction. In the integrable case of exponential LPP, we show that extreme paths are close to modal in a precise sense. Based on joint work with Shuta Nakajima.

Add to calendar :

Date/Time : 09 Sep 2026 13:30
Venue : S16 #05-18
Speaker : Toshihisa Kubo, Ryukoku University

Let X be a smooth manifold and Y a smooth submanifold of X. Let G’ ⊂ G be Lie groups, with G acting on X and G’ acting on Y. A differential operator D from the space of smooth sections of a G-equivariant vector bundle over X and to that of a G’-equivariant vector bundle over Y is called a differential symmetry breaking operator (DSBO for short) if D is G’-intertwining.

In general, the classification and construction of DSBOs are challenging problems. Around 2010, Toshiyuki Kobayashi introduced a fascinating idea for addressing these problems when both X and Y are flag manifolds. We refer to the resulting machinery as the F-method. The F-method reduces the classification and construction of DSBOs to solving a certain system of partial differential equations via the algebraic Fourier transform of generalized Verma modules. In this talk, we shall first discuss recent progress on the F-method. We shall then give explicit formulas for the DSBOs for (G,G’)=(GL(3,R), GL(2,R)) with minimal parabolic subgroups. This talk is based on joint work with Jonathan Ditlevsen and Víctor Pérez-Valdés.

Add to calendar :

Date/Time : 09 Sep 2026 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Miri Son , National University of Singapore

Recently, Fisher and Melnick classified SL(n,R)-actions on n-dimensional manifolds for n≥3. In this talk, we generalize their result by classifying smooth and real-analytic SLnR-actions on m-dimensional manifolds for 3≤n≤m≤2n-3. This problem is related to the Zimmer program, since any action of a Lie group restricts to an action of its lattices.

This classification relies on linearization of SL(n,R)-actions near a fixed point. The analytic case was proved by Guillemin-Sternberg and Kushnirenko. In the smooth case, the key is the linear representation of SL(n,R). We discuss the smooth case, which is ongoing joint work with Insung Park.

Add to calendar :

Date/Time : 08 Sep 2026 15:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Thomas Karam, Shanghai Jiao Tong University

It is a familiar fact that the size of a subset $A$ of $\mathbb{R}^n$ is bounded above by the product of the $n$ sizes of its one-dimensional axis-parallel projections: after all, it suffices to contain $A$ in the cartesian box that these projections enclose. Shearer’s lemma in its geometric form generalises this fact by providing sharp upper bounds on the size of $A$ in terms of the product of the sizes of its $k$-dimensional projections, for any given $1 \le k \le n$.

Yet not all mathematical notions of complexity are formulated in terms of sizes or measures. In particular many definitions involve decomposition length: given a class of objects viewed as basic building blocks, the complexity of an object is defined as the smallest number of these blocks in terms of which the object may be contained or decomposed. Compared to sizes or measures, understanding these complexity notions tends to be less straightforward, the fundamental difficulty being the general lack of uniqueness of the containments of decompositions.

Notions formulated in this other way include in particular (i) the smallest number of $d$-dimensional subspaces that suffice to contain a finite subset $A$ of $\mathbb{R}^n$ for a fixed $1 \le d \le n$, and (ii) the various rank notions on tensors defined in terms of partitions of the coordinates. In both settings we will establish new inequalities bounding the complexity of the multidimensional object in terms of the complexity of its lower-order projections, discuss the contrast with Shearer’s lemma, before concluding with an overview of the remaining difficulties standing before a comprehensive description of which such inequalities are true.

Add to calendar :

Date/Time : 07 Sep 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : David Hansen, National University of Singapore

I will formulate a collection of vanishing conjectures in the Fargues-Scholze setting, which describe the maps on suitable Grothendieck groups induced by Eisenstein functors, constant term functors, and the gluing functors between strata of Bun_G. I will also discuss the relationships among these conjectures, and explain how they imply a very general form of the Bertoloni Meli-Harris-Viehmann conjecture (which I will also recall in detail). I will then sketch a proof of the vanishing conjectures (and hence a proof of the generalized BMHV conjecture). Joint work in progress with Linus Hamann and Peter Scholze.

Add to calendar :

Date/Time : 03 Sep 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Guillaume Bal, University of Chicago

A surprising edge transport, displaying strong robustness to perturbations as an obstruction to Anderson localization, is guaranteed along interfaces separating two-dimensional insulators in different topological phases. We review the classification of several bulk and interface models of topological insulators and analyze their relation via a so-called bulk-edge correspondence. For suitable models, we present a spectral and scattering theory allowing for a quantitative description of the asymmetric edge transport along the waveguide in the presence of perturbations. Time permitting, we will also present recent results on the corresponding inverse scattering theory.

Add to calendar :

Date/Time : 02 Sep 2026 16:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Yubin Shin, National University of Singapore

Let G be a semisimple Lie group, Gamma be a lattice in G, and let A = {a_t} be a one-parameter diagonal subgroup. Given a point x in G/Gamma and a curve phi: I -> U^+ in the expanding horospherical subgroup of A, we consider the family of expanding translates a_t phi(I)x as t -> infinity. The equidistribution problem asks for conditions under which these translates eventually spread uniformly throughout G/Gamma with respect to the Haar probability measure.

Motivated by applications to Diophantine approximation and hyperbolic geometry, Shah initiated the study of this problem and obtained results in several important special cases involving SL_n(R) and a single copy of SO(n,1). Lei Yang later established equidistribution for analytic curves satisfying an algebraic condition when G = SO(n,1)^k. In this talk, I will discuss an extension of Lei Yang’s result from analytic curves to smooth curves when G = SO(n_1,1) x … x SO(n_k,1).

Add to calendar :

Date/Time : 02 Sep 2026 11:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Leong Wing Lup, Ben, National University of Singapore

We are past the point of debating whether students should be permitted to use generative AI. They already are. With AI, we are aiming at a moving target: the technology is evolving rapidly, while businesses are still working out how best to use it.

As universities, we have never been especially good at keeping our curriculum current with industry, and AI will widen that gap faster than we can close it. If we cannot chase the frontier, the only feasible response is to teach what we know will not become obsolete.

Nor does AI automatically make learning better. Cognitive offloading is a real and now measurable harm. Students must learn to use AI as a co-pilot, not an autopilot.

What remains, then, are critical thinking and human skills. These skills belong at the core of a university education rather than at its periphery, and the talk will consider what this demands of how we design our courses and how we assess them.

Add to calendar :