Monday
2025/12/1
Heat kernel asymptotics and analytic torsion on non-degenerate CR manifolds
Speaker: Guokuan SHAO（Sun Yat-sen University）
Time : Dec 1, 2025, 09:30-10:30
Tencent meeting ID: 647-395-085
Host: Bochen Liu
Language: Chinese/English
Abstract
Ray-Singer introduced the concept of holomorphic analytic torsion. One key step to define the analytic torsion is small time asymptotics of the heat kernel.
In this talk, we establish the small time asymptotics of the kernel of the difference of the heat operator and Szegő projector, then give the definition of the analytic torsion on a non-degenerate CR manifold, which answers Bismut’s question.
We also establish Bismut-Vasserot type asymptotics of the analytic torsion associated with high powers of a CR line bundle.
This is a joint work with C.-Y. Hsiao and R.-T. Huang.
Lattice polytopes and their Lefschetz properties
Speaker: Karim Alexander Adiprasito（Sorbonne Université）
Time: Dec 1, 2025, 15:00-16:00
Venue: M1001, College of Science Building
Host: Jana Hertz
Language: English
Abstract
Ehrhart theory is the theory studying how many lattice points are contained in the dilate of a given (lattice) polytope; it has rich applications to combinatorial problems, and deep connections to algebraic geometry, representation theory and more. Some of the most fundamental problems remain open. We developed a new approach to understanding the fundamental class of associated semigroup algebras via Parseval-Rayleigh identities. This leads to the resolution of several combinatorial conjectures, such as unimodality of the $h^\ast$-polynomial for large classes of lattice polytopes, among them integrally closed Gorenstein polytopes. Based on joint work with Papadakis and Petrotou. If time permits, I will also give glimpses of upcoming work that involves in addition Katz and Oba.
Biography
Karim Alexander Adiprasito is a Directeur de Recherche Exceptionelle at the Jussieu Institute of Mathematics - Paris Rive Gauche , Sorbonne Université. His research interests are in Combinatorics and metric geometry.
After being an EPDI fellow at IHES, a Minerva fellow at Hebrew University and a member at the Institute for Advanced Study, he joined the faculty of the Hebrew University in 2015 (tenured 2016) and since 2019 in Copenhagen.In 2016, he won a grant by the European Research Council (ERC) and the Israel Science foundation (ISF), which support his research projects. In addition, he was awarded the European Prize in Combinatorics in 2015, the Klachky prize of the Hebrew University in 2017, was named a Knut & Alice Wallenberg fellow (at KTH) in 2018, and was awarded the 2019 New Horizons Prize in Mathematics. Since 2022/23, he is at CNRS.
An exponential improvement for Ramsey lower bounds
Speaker: Jie Ma（University of Science and Technology of China）
Time: Dec 1, 2025, 16:30-17:30
Venue: M1001, College of Science Building
Host: Qing Xiang
Language: English/Chinese
Abstract
We prove a new lower bound on the Ramsey number r(\ell, C\ell) for any constant C> 1 and sufficiently large \ell, showing that there exists \varepsilon(C) > 0 such that r(\ell, C\ell) ≥ \left(p_C^{-1/2} + \varepsilon(C)\right)^\ell, where p_C denotes the unique solution in (0, 1/2) satisfying C = \log p_C / \log (1 - p_C). This provides the first exponential improvement over the classical lower bound by Erdos since 1947. Joint work with Wujie Shen and Shengjie Xie.
个人简介
马杰，中国科学技术大学/清华大学教授，从事组合图论领域的研究工作及其在理论计算机和信息科学中的应用，在极值组合、结构图论和概率组合等领域分支取得了系列理论创新成果。曾获海外高层次人才引进计划青年项目、基金委优秀青年科学基金项目、基金委国家杰出青年科学基金项目，担任科技部国家重点研发计划项目负责人、基金委数学天元基金学术领导小组成员、JCTB和SIDMA等杂志编委。
Tuesday
2025/12/02
How small can the aperiodic autocorrelations of a binary sequence be?
Speaker: Jonathan Jedwab (Simon Fraser University, Canada)
Time: Dec 2, 2025, 16:30-17:30
Venue: M1001, College of Science Building
Host: Qing Xiang
Language: English
Abstract
Binary sequences whose aperiodic autocorrelations are collectively small have been sought since the 1950s as modulating signals in digital communications. Two popular measures of smallness are the merit factor and the peak sidelobe level. Studies of these two measures, often motivated by numerical experiments, involve diverse mathematical tools including Fourier analysis, estimation of character sums, estimation of the number of lattice points in polyhedra, finite fields, and probabilistic methods. Despite a large and growing body of theory, numerical experiments suggest that there are unexplained infinite families of binary sequences having record asymptotic merit factor or peak sidelobe level.
I shall describe the merit factor problem and peak sidelobe level problem from scratch, outline their history, and explain the intriguing numerical experiments whose results await explanation.
Biography
Jonathan Jedwab received the B.A. degree in mathematics and the Diploma degree in mathematical statistics from Cambridge University, UK in 1986 and 1987, respectively, and the Ph.D. degree in mathematics from the University of London, UK in 1991. He spent 14 years at the Mathematics Consultancy Group, Hewlett-Packard Laboratories, UK. Since 2003, he has been with the Department of Mathematics, Simon Fraser University, Burnaby, BC, Canada. His research interests include combinatorial design theory, often motivated by practical problems of digital communications engineering.
Thursday
2025/12/04
Some extremal problems on (non-) color critical graphs
Speaker: Shuchao Li（Central China Normal University）
Time: Dec 4, 2025, 10:00-11:00
Venue: M1001, College of Science Building
Tencent Meeting ID: 654 651 904
Host: Ziqing Xiang
Language: Chinese
Abstract
Turán-type problem is a fundamental problem in extremal graph theory. The spectral Turán-type problem is a newly developed one in this field. Both of these two types of extremal problems attract more and more researchers’ attention. In this talk, we first introduce the background in this field. Then we present our new results on (non-) color critical graphs along this line. Finally, we propose some further research issues in this field.
BRW in IID environment
Speaker: Xinxin Chen（Beijing Normal University）
Time: Dec 4, 2025, 14:00-15:00
Venue: M3009, College of Science Building
Host: Jieliang Hong
Language: English/Chinese
Abstract
We consider a branching random walk in i.i.d. random environment where the branching law depends on the spatial environment and the motion is simple random walk. We discuss the survival behavior in some supercritical case. And in some critical branching case, we prove the Yaglom theorem via Stein method. This is a joint work with Chenlin Gu and Zhiqi Zhao.
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END
南方科技大学数学系
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