Date/Time : 21 Jan 2026 17:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Andre Nies, University of Auckland

Let R be the structure of r.e. many-one degrees. Lachlan showed that each finite distributive lattice is embeddable in R as an initial segment, thereby showing its theory is hereditarily undecidable. In this retrospective of some of my results from the 1990s, I will discuss how this proof in fact leads to undecidability of the Sigma-3 theory. I showed that the whole theory is Turing equivalent to true arithmetic. The technique used there paved the way for the similar result for the theory of the lattice of r.e. sets (with Harrington).

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Date/Time : 21 Jan 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Ming Hong Tee, Boston College

Given any Jordan domain U in the Riemann sphere equipped with the hyperbolic metric, one can construct the Epstein surface in hyperbolic 3 space corresponding to it. One important property of the Epstein surface is that its principal curvatures are related to the Schwazian derivative of the uniformization map of U. In this talk, we will exploit this property to relate the bending lamination of a pleated surface with the Schwazian derivative. Furthermore, if U is a domain for a Weil-Peterson curve, we will show that the hyperbolic metric and the quasi-hyperbolic metric are arbitrary closed and the two corresponding Epstein surfaces are arbitrary closed.

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Date/Time : 21 Jan 2026 16:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Kim Jeongho, Kyung Hee University

In this talk, I will present two different topics on numerical methods for solving PDEs.

In the first part, I will focus on the numerical methods for two-dimensional quantum mechanical systems interacting with electromagnetic fields. Precisely, we will discuss finite difference time domain method and time splitting Fourier Pseudospectral methods for Chern-Simons-Schrodinger/Dirac equations. In the second part, I will move on to the adaptive finite difference method for solving the Poisson equation. I will introduce the quad/octree structure on which the Poisson equation is solved. This provides a stable Hodge decomposition step in the projection method for incompressible flow.

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Date/Time : 19 Jan 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Jasper Lee, University of California, Davis

Mean estimation is perhaps the most fundamental task in statistics, yet there is a divide between the standard theory and practice. The standard theory recommends taking the sample mean, but whose brittleness forces users to apply ad-hoc outlier removal techniques in practice, leading to documented cases of wrong experimental conclusions. On the other hand, theoretical algorithms designed specifically to mitigate such brittleness (e.g. median-of-means and high-dimensional generalizations) have poor empirical performance that they cannot/should not be adopted either.

In this talk, I’ll discuss our efforts to fully resolve the mean estimation problem, achieving (minimax) estimation error that is sharp even in the leading multiplicative constant. I will present a new multivariate mean estimator that has sharp estimation error in any (small) constant dimensions (in preparation), generalizing our previous 1-dimensional mean estimator (FOCS 2021, ICML 2025). I will also discuss a very simple multivariate mean estimator that achieves sharp error guarantees in the “very high-dimensional” regime (ITCS 2022).

The constant-dimensional mean estimator is joint work with Suraj Mathashery, Paul Valiant and Kun Wang, in preparation. The very high-dimensional mean estimator is joint work with Paul Valiant, which appeared in ITCS 2022.

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Date/Time : 16 Jan 2026 16:00
Venue : S17 #04-05 (Seminar Room 2)
Speaker : Dou Dou, Nanjing University

Ranging from irrational rotations to mixing transformations like horocycle flows, zero entropy systems exhibit very rich and diverse complex structures and dynamical behaviors. In this talk, we will introduce recent developments in the theory of complexity and entropy-type invariants for zero entropy systems, along with our related work on entropy dimensions.

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Date/Time : 16 Jan 2026 16:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Seog-Jin Kim, Konkuk University, Korea

The square of a graph G, denoted G^2, has the same vertex set as G and has an edge between two vertices if the distance between them in G is at most 2. Thomassen (2018) showed that \chi(G^2)<=7 if G is a subcubic planar graph. A natural question is whether \chi_l(G^2)<=7 or not if G is a subcubic planar graph. Recently Kim and Lian (2024) showed that \chi_l(G^2)<=7 if G is a subcubic planar graph of girth at least 6. And Jin, Kang, and Kim (2025) showed that \chi_l(G^2)<=7 if G is a subcubic planar graph without 4-cycles and 5-cycles. In this talk, we show that the square of a subcubic planar graph without 5-cycles is 7-choosable, which improves the previous results.

This is joint work with Xiaopan Lian, Atsuhiro Nakamoto, and Kenta Ozeki.

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Date/Time : 14 Jan 2026 15:00
Venue : S17 #04-06 (Seminar Room 1)
Speaker : Denny Wu , New York University

Modern machine learning systems operate in high-dimensional regimes, with large numbers of data points, features, and parameters. High-dimensional statistical tools, such as random matrix theory, enable sharp, quantitative analyses of tractable model abstractions that nevertheless capture empirical phenomena in modern deep learning. In this talk I will highlight several examples in which such analyses yield precise characterizations of: (i) optimal ridge regularization in the overparameterized regime and the surprising “negative ridge” observation; (ii) how neural networks acquire useful features during the early phase of gradient-based training; and (iii) how emergent risk curves connect to neural scaling laws in SGD learning. Beyond the mathematical insight, I will also discuss the predictive power of these results and the algorithmic implications in more realistic settings.

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Date/Time : 14 Jan 2026 16:30
Venue : S17 #05-11 (Seminar Room 5)
Speaker : Li Xiaoli, Shandong University

The magnetization structures in the form of topological solitons have become important research interest following the fabrication of various ferromagnetic materials. In this talk we first present new higher-order implicit-explicit (IMEX) schemes for the LLG equation. These schemes are linear, length preserving, modified energy stable and only require solving one elliptic equation at each time step. We show that numerical solutions of these schemes are uniformly bounded without any restriction on the time step size, and establish rigorous error estimates of orders 1 to 5 in a unified framework. Next we present some recent developments in constructing the linear, length preserving and original energy preserving schemes.

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Date/Time : 14 Jan 2026 14:00
Venue : S17 #04-04 (Seminar Room 3)
Speaker : Pierre-Louis Blayac, Strasbourg University

Given a closed surface S of genus at least 2 and an integer d>2, the space of marked hyperbolic structures, called Teichmüller space T(S), can be seen as the space of representations of the fundamental group of S into PSL(2,R) modulo conjugation.

By postcomposing with the irreducible representation of PSL(2,R) in PSL(d,R), T(S) embeds in representations valued in PSL(d,R). The connected component containing T(S) is the Hitchin component H(S), which is homeomorphic to a vector space and consists of discrete and faithful representations by work of Hitchin, Labourie, Fock and Goncharov.

A decade ago, Bridgeman, Canary, Labourie and Sambarino constructed on H(S) several metrics, called pressure metrics, that extend the famous Weil–Petersson metric on T(S). Their construction uses a characterisation of the WP metric in terms of hyperbolic lengths due to Thurston and Wolpert. We will describe the pressure metrics on certain subspaces of H(S) that are transverse to T(S), consisting of deformations through the famous bending procedure. This will allow us, in genus>2, to show that T(S) is distorted in H(S), in the sense that there is a sequence of points in T(S) whose distance to the origin diverge for the WP metric, but remains bounded for the pressure metrics.

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