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 #06-11 (Seminar Room 6)
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 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Rafael Saavedra, Harvard University

I will discuss new infinite sum identities for the length and twists of simple geodesics on a hyperbolic once-punctured torus. These formulas arise unexpectedly from the geometry of the unit length ball associated with a hyperbolic torus. This analysis also leads to new results on the Thurston geometry of Teichmuller space and (two) new proofs of an identity of Hengnan Hu and Ser Peow Tan.

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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 : 13 Nov 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Marcel Nutz, Columbia Univ

Perpetual futures are the main instruments in cryptocurrency trading. Instead of expiring at a finite date, the contract includes periodic funding payments designed to align the prices of future and spot. This talk will review how perpetual futures are implemented on platforms like Binance and develop theoretical results about their risk-neutral pricing.

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Date/Time : 13 Nov 2026 14:00
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Huu-Hoan Nguyen, National University of Singapore

We study the rigidity phenomenon of the time changed unipotent flows on general Lie groups. Under some spectral gap assumptions, we prove that every ergodic nonsplitting sl_2-induced unipotent flow on a finite volume quotient space G/\Gamma is time changed rigid. We also prove that for sl_2-induced unipotent flow, the splitting condition is equivalent to loosely Kroneckerness. Our result in particular applies to the case that G is the semi-direct product of S and N, where S is the identity component of a real semisimple linear algebraic group without compact factors and N is simply connected and connected nilpotent Lie group. These are extensions of Kanigowski-Vinhage-Wei 21 and Lindenstrauss-Wei 25. This is a joint work with Daren Wei.

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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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