Date/Time : 01 Dec 2026 15:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Ichiro Shimada , Hiroshima University

The affine Conway group is the group of affine isometries of the Leech lattice. This group is isomorphic to the automorphism group of a standard fundamental domain for the action of the Weyl group on the even hyperbolic lattice of rank 26. The affine Conway group has exactly nine conjugacy classes of involutions. I explain their properties and show that, among these nine classes, one class can be regarded as an analogue of Enriques involutions of K3 surfaces.

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Date/Time : 19 Nov 2026 13:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Sheng Meng, East China Normal University

The study of endomorphisms f: P^n → P^n with degree >1 is a central topic in complex dynamics. For any point in projective space, the Zariski closure of its forward orbit is an f-invariant closed subvariety, and the restriction of f to this subvariety naturally yields a polarized endomorphism. Conversely, Fakhruddin pointed out the reverse direction: every polarized endomorphism on a projective variety (X, f) can be realized as the restriction of a polarized endomorphism on some ambient projective space P^N to an invariant subvariety.

In this talk, I will introduce birational geometric methods, centered on the equivariant minimal model program, and develop a systematic birational classification of polarized dynamical pairs (X, f).

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Date/Time : 18 Nov 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Kenji Nakanishi, Kyoto University

Since the pioneering work of Kenig and Merle, there have been numerous results on global behavior of large general solutions to nonlinear dispersive equations that vary depending on the initial data, from asymptotically linear or scattering solutions to solitons and blow-up. The main question is to distinguish the types of solutions or to predict them from the initial data, without any asymptotic solution formula such as those provided by the inverse scattering theory in the special case of completely integrable systems. Despite of some spectacular progress such as the soliton resolution without size restriction, the range of applicable equations has been rather limited, such as the nonlinear wave equation or Schrodinger with simple nonlinearity, because certain monotonicity or invariance properties play crucial roles in the analysis without small factor. The Zakharov system is a model of the Langmuir turbulence in plasma, coupling the Schrodinger and the wave equations, and may be regarded also as a mathematical model to extend the methods from the simple scalar equations. It has been quite successful in the last decade for space dimensions 3 and 4, in spite of a few difficulties such as the derivative loss, the lower degree of nonlinear interactions, and the loss of invariance for scaling and for momentum or coordinate velocity. This talk will review the state of art, together with some detail on most recent results and open problems.

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Date/Time : 18 Nov 2026 14:00
Venue : S17 #06-11 (Seminar Room 6)
Speaker : Trinh T. Nguyen, Shanghai Jiao Tong University

We justify the vortex–wave system introduced by Marchioro and Pulvirenti as the vanishing-viscosity limit of the two-dimensional Navier–Stokes equations on arbitrary finite time intervals. The initial vorticity consists of a point vortex and a smooth, compactly supported background that vanishes near the vortex. The proof relies on two key ingredients. First, we track the transported support of the approximate background to maintain separation from the point vortex, removing the restriction involving the region swept out by past wave supports. Second, we use Gallay’s weighted energy method to cancel the leading ambient-strain contribution. The regular component converges strongly to the background vorticity in L^p, while the concentrated component converges to a Lamb–Oseen vortex centered on the limiting point-vortex trajectory. We obtain quantitative estimates for both components, with a viscosity threshold depending on the chosen time interval, thus establishing the global-in-time validity of the vortex–wave system.

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Date/Time : 12 Nov 2026 15:00
Venue : S16 #05-17
Speaker : Chen Yanyu, National University of Singapore

Random sampling is a basic tool for sparsifying graphs while preserving useful structure. Instead of sampling edges independently, we study a vertex-constrained sampling model called the $k$-out model, where every vertex independently selects $k$ incident edges uniformly at random. On $K_n$, two distinct choices per vertex already give connectivity with high probability (Fenner and Frieze, 1982). For arbitrary simple graphs, connectivity can no longer be guaranteed, so a natural question is how many original edges join distinct components of the sample.

We prove the tight bound $O(n/k)$ in expectation for every simple $n$-vertex graph and every integer $k \geq 2$, even with replacement. This resolves the conjecture of Holm, King, Thorup, Zamir, and Zwick (2019), who established the bound for logarithmically many choices per vertex.

A main motivation comes from algorithms for connectivity, spanning forests, and minimum cut, where sampling helps reduce instance size. Our bound certifies that contracting just two sampled choices per vertex leaves only $O(n)$ edges in expectation, providing small instances for these algorithmic tasks.

The proof uses switching arguments to connect intercomponent edges with bridges and a degree-weighted component potential.

Based on joint work with Yu Chen.

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Date/Time : 12 Nov 2026 16:00
Venue : S16 #05-17
Speaker : Fang Yijia, National University of Singapore

A pair $(\mathcal{A}, \mathcal{B})$ of families of subsets of $[n]$ is called cancellative if whenever $A, A’ \in \mathcal{A}, B \in \mathcal{B}$ satisfy $A \cup B=A’ \cup B$, then $A=A’$, and whenever $A \in \mathcal{A}, B, B’ \in \mathcal{B}$ satisfy $A \cup B=A \cup B’$, then $B=B’$. For a cancellative pair, how large can the product of their sizes be? Tolhuizen’s elegant construction gives the lower bound $(2.25-o(1))^n$. In this talk, I will present the upper bound $|\mathcal{A}||\mathcal{B}| \le 2.25^n$, determining the optimal growth rate for cancellative pairs. The proof uses the entropy method with a novel coupling technique. This is a joint work with Hao Huang.

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Date/Time : 11 Nov 2026 16:30
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Hu Yukuan, National University of Singapore

This talk presents a geometric and optimization-based perspective on computing electronic excited states. Starting from the many-body Schrödinger equation, we discuss variational wavefunction approximations and the nonlinearity introduced by restricting the electronic energy to parameter manifolds. We review linear-response, state-averaged, and state-specific approaches, emphasizing their distinct formulations of approximate excited states.

Focusing on state-specific calculations, we introduce a constrained saddle dynamic for locating saddle points of prescribed Morse index on Riemannian manifolds. The Grassmann bundle geometry provides a framework for analyzing the dynamic and constructing discretizations using retractions and vector transport, with linear stability and local linear convergence guarantees at nondegenerate saddle points. Numerical experiments with Hartree–Fock and complete active space self-consistent field models illustrate the approach. We conclude with challenges in developing faster saddle-search methods and navigating excited-state potential energy surfaces.

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Date/Time : 11 Nov 2026 13:30
Venue : S16 #05-18
Speaker : Sudarshan Narasimhan, National University of Singapore

In a seminal paper published in 1955, J. A. Green gave a construction of the irreducible characters of the finite general linear groups GL_n(F_q), drawing upon ideas from the representation theory of symmetric groups and the theory of symmetric functions.

The irreducible characters of the symmetric group S_n are parametrised by partitions of n, and their character values can be described using the theory of symmetric functions, in particular Schur functions. A remarkable feature of Green’s construction is that analogous ideas can be used to describe the irreducible characters of GL_n(F_q).

In this talk, we will outline the main ingredients of Green’s construction, beginning with the relationship between the representation theory of S_n and the classical theory of symmetric functions. We will then introduce Hall–Littlewood functions and Hall polynomials, and explain how they connect the theory of symmetric functions to the representation theory of finite general linear groups. Finally, we will discuss how generalised Schur functions arise in this setting and explain their role in the construction of the irreducible characters of GL_n(F_q) and illustrate how this construction can be used to compute character values of GL_n(F_q) for small n.

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Date/Time : 11 Nov 2026 17:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Kyle Gannon, Peking University

In model theory, and in logic more broadly, we are often interested in the first-order theory of a given mathematical structure. Probabilistic constructions, however, typically produce not a single structure but a random one. For example, the first-order theory obtained by percolating edges on a graph may depend on the particular outcome of the percolation. This project addresses this issue by introducing a syntactic object, a random theory, associated with random constructions. We argue that random theories accurately encode the first-order consequences of such constructions. In this talk, we will focus on the basic definitions and examples surrounding these ideas. This is currently ongoing research with Nikolay Bazhenov and Sam Braunfeld.

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