Date/Time : 21 Sep 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Shuang Miao, Wuhan University

Constructing dynamical global-in-time solutions to 3D incompressible Euler equation is in general challenging. Recently Guo-Pausader-Widmayer made a breakthrough in this direction by proving asymptotic stability of a uniform-rotating static solution. Their approach heavily depends on the “uniform-rotating” of the background solution. In this talk I will present some recent progress on asymptotic linear stability of a more general columnar flow with non-uniform rotation. This is a joint work with Siqi Ren and Zhifei Zhang.

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Date/Time : 16 Sep 2026 13:30
Venue : S16 #05-18
Speaker : Teruhisa Koshikawa, Keio University

By the categorical local Langlands conjecture, the semiorthogonal decomposition indexed by the Kottwitz set and Bernstein decompositions in the geometric side are expected to have counterparts in the spectral side. I will discuss my joint work with Bertoloni Meli realizing them directly. It is closely related to the theory of cuspidal coherent sheaves, but also has connections to some recent developments in algebraic geometry.

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Date/Time : 16 Sep 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Nikolay Bazhenov, Nanyang Technological University

In recent years, there has been renewed interest in the algorithmic aspects of various Stone-type dualities. For instance, Harrison-Trainor, Melnikov, and Ng (2020) proved that a Boolean algebra B has a computable isomorphic copy if and only if its dual Stone space St(B) is homeomorphic to a computable Polish space. In this talk, following the approach of Ershov and Schwidefsky, we work with effective presentations of topological T_0-spaces with base. We establish a computable version of a Stone-type duality due to Schwidefsky (2023), and we discuss its applications in computable topology.

This is joint work with Iskander Kalimullin and Marina Schwidefsky.

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Date/Time : 16 Sep 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Jackie Lok, National University of Singapore

Recently, a class of algorithms based on combining classical fixed-point iterations with repeated random sparsification has been successfully applied to very large-scale linear algebra problems, where storing the full solution vector itself may be prohibitive. However, a general mathematical understanding of when this approach can achieve dimension-independent computational and storage requirements remains limited.

In this talk, we study a randomly sparsified power method for computing the leading eigenvector of a column-stochastic matrix. We prove a dimension-independent error bound that depends on the approximate sparsity of the solution vector and the mixing time of the Markov chain associated with the matrix, establishing the possibility for high-quality approximation in very high dimensions. On the other hand, we show that a deterministically sparsified counterpart can fail, demonstrating a provable separation between deterministic and random sparsification.

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Date/Time : 14 Sep 2026 15:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Jack Sempliner, University of California (Los Angeles)

We will discuss a new result on the p-adic geometry of Igusa stacks, which allows one to relate the p-adic geometry of Shimura varieties for a pair of groups $G, G’$ which are global extended pure inner forms. Using this geometric input and the spectral action of Fargues-Scholze, we will discuss how this input may be used to prove the existence of Hecke-equivariant cohomological “Jacquet-Langlands” maps between the cohomology (even with integral or torsion coefficients) of the two Shimura varieties of abelian type associated to $G, G’$.

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Date/Time : 10 Sep 2026 14:00
Venue : S16 #03-06
Speaker : Thomas Karam, Shanghai Jiao Tong University

Can we determine in a reasonably “simple” way all inequalities between notions of complexity on an object that are always true regardless of the specific choice of the object?

In some contexts, practically sufficient versions of that dream have already been meaningfully realised. In information theory, for instance, one can characterise the linear combinations of joint Shannon entropies in finite sets of variables that hold for all choices of the variables. Although not all entropy inequalities fall into that class, it is in practice sufficient for most applications.

We will focus on current progress for two notions of complexity: covering numbers of finite sets of points, and ranks of tensors, where we will essentially restrict our attention to rank notions arising from partitioning the coordinates. In the latter setting, we will particularly emphasise how the majority of rank inequalities studied so far can be classified into six types of inequalities.

Afterwards, we will delve more closely in each of these categories of inequalities, first summarising known results, then describing progress from the speaker, and finally outlining the remaining bottlenecks.

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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.

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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.

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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.

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