哈尔滨工业大学第八届国际青年学者神舟论坛数学研究院分论坛

发布时间:2023-04-27浏览次数:459

一、论坛日期:2023年727日(星期四)

二、论坛时间:14:00-17:30

三、论坛地点:明德楼B区201-1学术报告厅

四、论坛安排:

Ø14:00-14:10 开幕式致辞

Ø14:10-15:00 学术报告

  题 目:关于Stefan型问题的广义解的连续性

  报告人:廖乃安

  摘 要:Stefan问题描述物态变化过程中的温度。该问题的广义解在1960年代初被Kamin和oleinik入,但广义解是否连续的问题却悬而未决。该问题在1980年代初由Caffarelli-Evans,DiBenedetto等人给出肯定回答。但是,连续模的最佳估计依然不得而知。本报告将介绍这方面最新的一些工作.

Ø15:00-15:10 交流讨论

Ø15:10-15:30 休息

Ø15:30-16:20 学术报告

  题 目:Counting l-adic local systems over a curve

  报告人:余红杰

  摘要: In 1981, Drinfeld enumerated the number of irreducible l-adic local systems of rank two on a projective smooth curve fixed by the Frobenius endomorphism. Interestingly, this number looks like the number of points on a variety over a finite field. Deligne proposed conjectures to extend and comprehend Drinfeld's result. In this talk, I will present Deligne's conjectures and discuss some mysterious phenomena that have emerged in various cases where this number is related to the number of stable Higgs bundles.

Ø16:20-16:30 交流讨论

Ø16:30-17:20 学术报告

  题 目:Asymptotic behavior of the heat semigroup on Riemannian manifolds

  报告人:张鸿伟

  摘 要:Consider the heat equation with L1 initial data. In the Euclidean setting, the solution to the heat equation approaches, as time tends to infinity, the product of the initial data's mass and the heat kernel. This can be seen as the PDE version of the Central Limit Theorem. When dealing with more general Riemannian manifolds, analogous heat asymptotics are affected by the underlying geometry. In this talk, we will give an overview of recent developments on this topic. We will see that such a long-time convergence result holds for some positively curved manifolds, but fails for some negatively curved manifolds, unless one adds additional assumptions on the initial data. Joint works with Jean-Philippe Anker (Orléans), Alexander Grigor’yan (Bielefeld), and Effie Papageorgiou (Crete).

Ø17:20-17:30 交流讨论



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