2022-10-17

On TQFT representations of mapping class groups with boundary

BIMSA Topology Seminar

报告人 明爽 BIMSA

时 间 15:30-17:00 Mon

地 点 1129B

Zoom 537 192 5549（PW: BIMSA）

摘要

In the talk, I would like to outline a skein theoretical construction of Reshetikhin-Turaev-Witten invariants and TQFTs(Topological quantum field theory) by Christian Blanchet, Nathan Habegger, Gregor Masbaum, and Pierre Vogel. In particular, these TQFTs provides (projective)representations of mapping class groups. If time permit, I will also discuss some generalizations and some connections to hyperbolic geometry.

组织者：吴杰, 杨南君, 李京艳

2022-10-18

Counting polynomials with a prescribed Galois group

BIMSA-YMSC Tsinghua Number Theory Seminar

报告人 Vlad Matei Simion Stoilow Institute of Mathematics of the Romanian Academy

时 间 16:00-17:00 Tue

地 点 1131

Zoom 293 812 9202（PW: BIMSA）

摘要

An old problem, dating back to Van der Waerden, asks about counting irreducible polynomials degree $n$ polynomials with coefficients in the box $[-H,H]$ and prescribed Galois group. Van der Waerden was the first to show that $H^n+O(H^{n-\delta})$ have Galois group $S_n$ and he conjectured that the error term can be improved to $o(H^{n-1})$. Recently, Bhargava almost proved van der Waerden conjecture showing that there are $O(H^{n-1+\varepsilon})$ non $S_n$ extensions, while Chow and Dietmann showed that there are $O(H^{n-1.017})$ non $S_n$, non $A_n$ extensions for $n\geq 3$ and $n\neq 7,8,10$. In joint work with Lior Bary-Soroker, and Or Ben-Porath we use a result of Hilbert to prove a lower bound for the case of $G=A_n$, and upper and lower bounds for $C_2$ wreath $S_{n/2}$ . The proof for $A_n$ can be viewed, on the geometric side, as constructing a morphism $\varphi$ from $A^{n/2}$ into the variety $z^2=\Delta(f)$ where each $varphi_i$ is a quadratic form. For the upper bound for $C_2$ wreath $S_{n/2}$ we improve on the monic version of Widmer's result on counting polynomials with an imprimitive Galois group. We also pose some open problems/conjectures.

组织者：Hansheng Diao, Yueke Hu, Emmanuel Lecouturier, Cezar Lupu

2022-10-19

Two weight inequality for Hankel form on weighted Bergman spaces induced by doubling weights

BIMSA-Tsinghua Quantum Symmetry Seminar

报告人 Yongjiang Duan Northeast Normal University

时 间 10:30-11:30 Wed

地 点 1131

Zoom 537 192 5549（PW: BIMSA）

摘要

The boundedness of the small Hankel operator induced by an analytic symbol $f$ and the Bergman projection $P_\nu$ associated to $\nu$, acting from the weighted Bergman space $A^p_\omega$ to $A^q_\nu$ is characterized on the full range $0<p,q<\infty$ when="" $\omega,\nu$="" belong="" to="" the="" class="" $\mathcal{d}$="" of="" radial="" weights="" admitting="" certain="" two-sided="" doubling="" conditions.="" results="" obtained="" are="" equivalent="" boundedness="" bilinear="" hankel="" forms,="" which="" in="" turn="" used="" establish="" weak="" factorization="" bergman="" spaces.="" talk="" is="" based="" on="" recent="" joint="" work="" with="" j.~rattya,="" s.="" wang="" and="" f.="" wu.

组织者：刘正伟, Sebastien Palcoux, 王亦龙, 吴劲松

2022-10-19

G2 vs. Kahler

BIMSA-BIT Differential Geometry Seminar

报告人 Tommaso Pacini University of Torino

时 间 16:00-17:00 Wed

地 点 Online

Zoom 559 700 6085（PW: BIMSA）

摘要

We shall compare two categories of manifolds, known as G2 and Kahler, focusing on (i) their submanifold geometry, (ii) their function theory. We shall also discuss interactions between these topics. The talk is intended for a general audience. In particular, we shall survey results in the preprints arXiv:2107.14117, arXiv:2207.13956, arXiv:2208.1253

组织者：Kotaro Kawai, Sebastian Heller, Lynn Heller, Chao Qian

2022-10-20

Data-Driven Modeling and Learning Using the Weak Form

BIMSA-Tsinghua Seminar on Machine Learning and Differential Equations

报告人 David Bortz University of Colorado Boulder

时 间 08:50-12:15 Thu

地 点 1129B

Zoom 537 192 5549（PW: BIMSA）

摘要

Data-driven modeling approaches have proven highly successful in a wide range of fields in science and engineering. In this talk, I will discuss several ubiquitous challenges with the conventional model development / discretization / parameter inference / model revision loop (illustrating the issues with examples from Microbial Electrolysis Cells, chemotaxis, and HIV viral dynamics). I will present our Weak form Sparse Identification of Nonlinear Dynamics (WSINDy) framework which addresses several of these challenges and offers substantial advantages in terms of computational efficiency, noise robustness, and modest data needs (in an online learning context). Lastly, I will illustrate applications of WSINDy to several benchmark problems as well as to the inference of interacting particle systems, specifically learning anisotropic interaction rules from individual trajectories in a heterogeneous cellular population.

人物介绍

Prof. Bortz earned his PhD in 2002 with H.T. Banks at North Carolina State University. He was then a postdoc at the University of Michigan in Mathematics and joined the faculty in Applied Math at the University of Colorado in 2006. The core of his research interests are in scientific computation methodologies for data-driven modeling and inverse problems at the intersection of applied math and statistics. His research has received support from NSF, NIH, DOE, DOD, and NVIDIA.

组织者：熊繁升, 杨武岳, 雍稳安, 朱毅