IASM Sub-forum of the 9th International Youth Scholars Shenzhou Forum of Harbin Institute of Technology

Release time:2023-12-22Views:11


一、论坛日期:2023年1225(星期一)

二、论坛时间:14:00-17:00

三、论坛地点:明德楼B区201-1学术报告厅

    ZOOM会议号:979 8735 6629 密码:1225

四、论坛安排:

Ø14:00-14:10 开幕式致辞

Ø14:10-14:50 学术报告

题  目: Metastability for expanding bubbles on a sticky substrate

报告人:杨尚杰

摘要:We study the dynamical behavior of a one dimensional interface interacting with a sticky impenetrable substrate or wall. The interface is subject to two effects going in opposite directionsone is the pinning attraction force from the sticky wall and another is the external force extracting the interface away from the sticky wall. We investigate the static phase transition and dynamical phase transition of the model. Joint work with Hubert Lacoin.

Ø14:50-15:00 交流讨论

Ø15:00-15:20 休息

Ø15:20-16:00 学术报告

题  目:NONCOMMUTATIVE RATIONAL FUNCTIONS IN FREE PROBABILITY AND RANDOM MATRICES

报告人:尹

要:A seminal work of Voiculescu revealed a deep connection between random matrix theory and free probability theory. That is, independent random matrices are asymptotic freely independent (an noncommutative analogue of the independence in probability theory). In this talk, we will first present our work that extends above convergence result from noncommutative polynomials to noncommutative rational functions. Then we will discuss the atoms/ranks of rational functions in freely independent random variables. Our study of such problems non only promotes our understanding on freely independent random variables and corresponding random matrices but also give insights to a question called Atiyah conjecture in topology.  

Ø16:00-16:10 交流讨论

Ø16:10-16:50 学术报告(线上)

        目:约化群主丛的Grothendieck—Serre猜想

报告人:郭

要:1958年,Serre和Grothendieck先后提出的猜想预言:连通光滑代数流形上的约化群主丛若在某个开集上平凡,则此主丛在任意开集上都平凡,这里均采用Zariski拓扑. Grothendieck把猜想推广至一般正则环. 七十余年来此猜想仍未彻底解决. 其中,正则环包含域的情况被Panin和Fedorov解决,因而猜想只剩下混合特征情况,其中Cesnavicius和其与Fedorov的工作解决了一部分“非分歧”正则环的情况。

本次报告介绍该猜想的历史和已知情形,其中包含我的三个贡献:

1. 完整解决了半局部Dedekind情况,这是所有已知高维情况的基础

2. 完整解决了赋值环情况,这是猜想的第一个非诺特变种,并且被奇点消解猜想所预言

3. 混合特征下,我和刘飞的工作建立了离散赋值环上光滑代数上常值约化群的情形  

报告的最后将展望Grothendieck—Serre猜想的后续发展。

Ø16:50-17:00 交流讨论

 


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