Date/Time : 14 Aug 2024 17:00
Venue : S17 #04-04 (SR3)
Speaker : Koh Heer Tern, Nanyang Technological University

We explore a recent program in comparing effective topological spaces up to (not necessarily computable) homeomorphism. We provide a survey of some earlier results separating some of the common notions of presentations for Polish spaces. By pushing existing definability techniques and effective versions of Stone duality, we also provide some new counterexamples. Most interestingly, that there exists a Polish space both left-c.e. and right-c.e. presentable but not computably presentable.

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Date/Time : 14 Aug 2024 16:00
Venue : S17 #06-11 (SR6)
Speaker : Felix Schremmer, The University of Hong Kong

This talk presents a novel, interdisciplinary study that leverages a Machine Learning (ML) assisted framework to explore the geometry of affine Deligne-Lusztig varieties (ADLV). The primary objective is to investigate the nonemptiness pattern, dimension and enumeration of irreducible components of ADLV. Our proposed framework demonstrates a recursive pipeline of data generation, model training, pattern analysis, and human examination, presenting an intricate interplay between ML and pure mathematical research. Notably, our data-generation process is nuanced, emphasizing the selection of meaningful subsets and appropriate feature sets. We demonstrate that this framework has a potential to accelerate pure mathematical research, leading to the discovery of new conjectures and promising research directions that could otherwise take significant time to uncover. We rediscover the virtual dimension formula and provide a mathematical proof of a newly identified problem concerning a certain lower bound of dimension. This is joint work with Bin Dong, Xuhua He, Pengfei Jin and Qingchao Yu, and the corresponding paper can be found on arXiv and the Peking Mathematical Journal.

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Date/Time : 14 Aug 2024 14:00
Venue : S17 #04-06 (SR1)
Speaker : Zhang Tengren, National University of Singapore

Anosov subgroups are a special class of discrete subgroups of a non-compact semisimple Lie group. This notion was first discovered by Labourie, who used it to prove the discreteness of Hitchin representations. In this talk, I will discuss my recent contributions to our understanding of Anosov subgroups and their various generalizations, as well as some applications to studying character varieties.

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Date/Time : 14 Aug 2024 14:00
Venue : S17 #04-04 (SR3)
Speaker : Jie Han, Beijing Institute of Technology

Random graphs are important objects in discrete probability theory. There has been a growing interest in extending graph theory theorems into the random graph setting. We will survey this line of problems and mention some recent developments.

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Date/Time : 14 Aug 2024 16:15
Venue : S17 #04-05 (SR2)
Speaker : Trung Tuyen Truong, University of Oslo

This talk presents a new equivalence and approach to the Riemann hypothesis, via a relatively new root finding method called Backtracking New Q-Newton’s method (BNQN), which is a variant of Newton’s method. Besides having strong global guarantee for finding roots of meromorphic functions, this new method also has connections to Voronoi’s diagrams, which is an important input for the new approach. This is joint work with Thuan Quang Tran (University of Oslo).  

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Date/Time : 14 Aug 2024 10:00
Venue : S17 #06-11 (SR6)
Speaker : Jinxin Xue, Tsinghua University

The mean curvature flow is to evolve a hypersurface in Euclidean space using the mean curvatures at each point as the velocity field. The flow has good smoothing property, but also develops singularities. The singularities are modeled on an object called shrinkers, which give homothetic solutions to the flows. As there are infinitely many shrinkers that seem impossible to classify, it is natural to explore the idea of generic mean curvature flows that is to introduce a generic perturbation of the initial conditions. In this talk, we shall explain our work on this topic, including perturbing away nonspherical and noncylindrical shrinkers, and generic isolatedness of cylindrical singularities. The talk is based on a series of works jointly with Ao Sun.

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Date/Time : 12 Aug 2024 15:00
Venue : S17 #04-06 (SR1)
Speaker : Daniel Bartl, University of Vienna

A major challenge in modern optimization problems is their instability, where small data perturbations can have disproportionately significant effects. We address this challenge in two settings. First, we focus on a distributionally robust approach, a popular method to counteract instability generically using optimal transport. Specifically, we demonstrate how this approach can systematically quantify the (in-)stability of a given optimization problem. In the second part, we focus on statistical robustness, dealing with data subject to outliers, such as those caused by adversarial corruption. We design robust estimators for optimization problems and risk measures.

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Date/Time : 08 Aug 2024 15:00
Venue : S17 #05-12 (SR4)
Speaker : Tirasan Khandhawit, Mahidol University

Seiberg-Witten invariants and monopole Floer homology have been important tools in the study of 3-manifolds and 4-manifolds. In this talk, I will give an overview of the stable homotopy refinement of these invariants. In particular, I will describe Bauer-Furuta invariants of 4-manifolds and Seiberg-Witten-Floer spectra of 3-manifolds. I will also discuss some applications of these refinements.

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Date/Time : 08 Aug 2024 13:45
Venue : S17 #06-11 (SR6)
Speaker : Binbin Xu, Nankai University

One generalization of flat structure on torus to oriented closed surface of genus greater than 1 is called translation surface structure. When a surface is equipped with such a structure, we call it a translation surface. Given a translation surface S, like on a flat torus, there is a globally well-defined notion of direction on S, and geodesics on S along a same direction are disjoint from each other, hence induces a flow on S. Such flows and their dynamical properties are important in the study of the symmetry group of S which is called Veech group. In particular, when the flow on S along one direction has only periodic regular orbits, we call this direction a periodic direction of S. In a joint-work with Anja Randecker, using the close relation between interval exchange transformations and flows on surfaces, we obtain a full classification of translation surfaces of genus 2 with one singularity according to the size of their periodic directions sets. In this talk, I will first give some necessary background, then I will explain our result and give the rough idea of the proof.

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