学术报告报告主题1: Topologically Protected Wave Motion-Analysis and Numerics
报告人1: 朱毅副教授 (清华大学)
报告时间：2023年11月17日（星期五）上午 9：00-10：00
报告主题2: Finding algebraic solutions of isomonodromy equations via the
Riemann-Hilbert method
报告人2: 徐晓濛助理教授 (北京大学)
报告时间：2023年11月17日（星期五）上午10：00-11：00
报告主题3: On the full Kostant-Toda lattice and the flag varieties
报告人3: 谢远成 博士后(北京大学)
报告时间：2023年11月17日（星期五）上午11：00-12：00
报告主题4: On the Maxwell-Bloch System in the Sharp-Line Limit Without Solitons
报告人4: 李思泰 副教授(厦门大学)
报告时间：2023年11月17日（星期五）下午14：30-15：30
报告地点：腾讯会议, 会议号：182-104-924
邀请人: 凌黎明教授
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数学学院
2023年11月14日
报告1摘要：In the past decade, a revolution in materials sciences has been brought about by the recognition of topology in characterizing the physical properties. These materials which support nontrivial topological phases are termed as topological materials. The related research is now beyond the quantum systems and the phenomena have been realized in many fields such as photonics, acoustics and mechanics and so on. In this talk, I will introduce recent advances on the mathematical aspects--analysis and numerics of these materials. Especially, I will focus on photonic topological materials, including existence of conical spectrum points, topological edge states and topologically protected wave motions and corresponding numerical methods.
报告人1介绍：朱毅，清华大学丘成桐数学科学中心副教授，在清华大学取得学士、博士学位，随后在University of Colorado-Boulder进行博士后研究，回国后进入清华大学工作至今。研究领域为应用与计算数学，主要运用应用分析及数值计算等数学工具研究材料、生物、化学、光学、流体以及工程等应用学科中的复杂现象，近几年主要关注拓扑材料中波动现象的数学理论和数值方法。曾入选国家青年拔尖人才计划，目前主持承担国家重点研发计划、自然科学基金等项目，担任著名应用数学期刊Studies in Applied Mathematics编委。
报告2摘要：The isomonodromy equations have aroused much interest among mathematicians and physicists. Yet their solutions, as special functions, still remain almost unexplored. This talk explains how to find their algebraic solutions via the Riemann--Hilbert approach.
报告人2介绍：徐晓濛，北京大学数学科学学院助理教授，2010年本科毕业于河南大学数学与统计学院，2013年于北京大学数学学院获得硕士学位，2016年在瑞士日内瓦大学数学系获博士学位，2016年至2019年在美国麻省理工学院做博士后。现从事数学物理与可积系统、表示论等相关方面的研究。
报告3摘要：In 1967, Japanese physicist Morikazu Toda proposed an integrable lattice model to describe motions of a chain of particles with exponential interactions between nearest neighbors. Since then, Toda lattice and its generalizations have become the test models for various techniques and philosophies in integrable systems and wide connections are built with many other branches of mathematics. In this talk, I will characterize singular structure of solutions of the so-called full Kostant-Toda (f-KT) lattices defined on simple Lie algebras in two different ways: through the $\tau$-functions and through the Kowalevski-Painlev\'e analysis. Fixing the spectral parameters which are invariant under the f-KT flows, we build a one to one correspondence between solutions of the f-KT lattices and points in the corresponding flag varieties. This talk is based on preprint arXiv:2212.03679.
报告人3介绍：谢远成，现为北京国际数学研究中心博士后，师从Yuji Kodama，于2021年在俄亥俄州立大学取得博士学位。他的主要兴趣为与可积系统相关的代数和几何。
报告4摘要：We study the Cauchy problem for the Maxwell-Bloch equations (MBEs) of light-matter interaction via asymptotics, under assumptions that prevent the generation of solitons. Our analysis clarifies some features in which physically-motivated initial/boundary conditions are satisfied, including: (i) A boundary layer phenomenon is fully explained in which, even for smooth initial data, the solution makes a sudden transition over an infinitesimal propagation distance. At a formal level, this phenomenon has been described by other authors in terms of a self-similar solution related to the Painleve-III (PIII) transcendents. We make this observation precise and also identify this self-similar solution appearing exactly as the leading-order terms in the asymptotics. We show that such PIII functions are identical to the ones discovered recently to play an important role in several limiting processes involving the focusing nonlinear Schrodinger equation. (ii) Our analysis of the asymptotic behavior of solutions reveals slow decay of the electric field in one direction that is actually inconsistent with the simplest version of scattering theory. (iii) The asymptotic results validate a previous proposed causality requirement for MBEs, and demonstrate that it is a build-in mechanism of the Riemann-Hilbert problem studied in this work. (iv) Finally, the spontaneous decay process of an initially unstable medium is proved via a large family of incident optical pulses. This is join work with Peter D. Miller.
报告人4介绍：李思泰，厦门大学数学科学学院副教授。2010年获南开大学数学学士学位，2018年于美国State University of New York at Buffalo取得数学博士学位，2019-2021年在University of Michigan做博士后工作。长期从事非线性可积系统的研究，在Commun. Pure Appl. Math.，Commun. Math. Phys.，SIAM Rev. 等杂志发表多篇学术论文，主持国家自然科学基金项目1项。