杰出学者讲座

发布时间:2023-04-01浏览次数:799

The colloquium offers survey talks in mathematics and related fields, the time for all the faculty and graduate students to get together to learn of somebody else's perspective on mathematics, and to broaden their own. A colloquium talk should be addressed to a general mathematical audience rather than technical details for specialists. The first 15 minutes should be completely understandable to graduate students.      

                                                                                     

The colloquium talks begin on Tuesdays at 2:00 p.m. Colloquium coffee succeeding talks around 3:00 pm. 


Contact: Jiange LI (jiange.li AT hit.edu.cn)

 

Upcoming talks


December28, 2023. 16:00 (Beijing time)

Speaker: Meiyue Jiang(Peking University)

Title: Uniqueness of Positive Solutions of Nonlinear Elliptic Equations

Abstract 

Let  be a bounded and regular domain. In this talk we will discuss some uniqueness results of positive solutions of the following nonlinear elliptic equation

 

 

via a kind of convexity of the associated functional

 

where . Some related results for the -Laplacian equation and other equations will also be discussed. 



Past talks


November24, 2023. 16:00 (Beijing time)

Speaker: Zeqian Chen(Chinese Academy of Sciences)

Title: 量子人工智能的拓扑斯理论形式

Abstract 

本报告介绍近期我们用拓扑斯理论(Topos theory)研究人工智能的工作。依据图灵测试对智能给出的科学定义, 我们将人工智能系统定义为由拓扑斯理论所描述的物理系统(Isham等人在2008年建立的物理理论), 它们具有自身的高阶形式语言及逻辑推理系统。特别是,我们用Hilbert空间上算子理论构造相应的拓扑斯以给出量子人工智能系统的数学描述。我们还将介绍量子计算的拓扑斯理论模型。


October27, 2023. 15:00 (Beijing time)

Speaker: Fabcrice Béthuel(Sorbonne Université)

Title: On Sobolev maps between manifolds and branched transportation

Abstract 

In the talk, I wish to stress the link between branched transportation theory, and some issues in the study of Sobolev maps between manifold. In particular, I will present a counterexample to the sequential weak density of smooth maps between two manifolds 𝑀 and 𝑁 in the Sobolev space 𝑊1,𝑝 (𝑀, 𝑁), in the case 𝑝 is an integer. It has been shown quite a while ago that, if 𝑝 < 𝑚 = 𝑑𝑖𝑚(𝑀) is not an integer and the [𝑝]-th homotopy group 𝜋[𝑝] (𝑁) of 𝑁 is not trivial, [𝑝] denoting the largest integer less than 𝑝, then smooth maps are not sequentially weakly dense in 𝑊1,𝑝 (𝑀, 𝑁). On the other hand, in the case 𝑝 < 𝑚 is an integer, examples of specific manifolds 𝑀 and 𝑁 have been provided where smooth maps are sequentially weakly dense in 𝑊1,𝑝 (𝑀, 𝑁)with 𝜋[𝑝] (𝑁) ≠ 0, although they are not dense for the strong convergence. This is the case for instance for 𝑀 = 𝐵 𝑚. Such a property does not hold for arbitrary manifolds 𝑁 and integers 𝑝.

The counterexample deals with the case 𝑝=3, 𝑚 ≥ 4 and 𝑁 = 𝑆 , for which 𝜋(𝑆 ) = 𝑍 is related to the Hopf fibration. We provide an explicit map which is not weakly approximable in 𝑊1,3 (𝑀, 𝑆 ), by smooth. One of the central ingredients in our argument is related to issues in branched transportation and irrigation theory in the critical exponent case.


October27, 2023. 16:15 (Beijing time)

Speaker: Sami Mustapha (Sorbonne Université)

Title: Potential theory and combinatorics

Abstract 

“... But the most general and direct method for resolving questions of probability consists of making them depend on difference equations ...” 

The aim of this talk is to illustrate this quote from Laplace (Philosophical essay on probabilities) by developing certain aspects of the theory of discrete potential theory attached to a random walk in 𝑍 𝑑 ; the difference equations playing in this framework the same role played by the PDEs in the theory of the classical potential theory. Although the presentation will be mainly limited to simple walks in quadrants, some extensions to walks in discrete Lipschitzian domains and to inhomogeneous walks will be discussed. The emphasis will be placed on the role that tools from discrete potential theory can play (harmonic functions and discrete caloric functions, maximum principle, Harnack inequalities, boundary Harnack inequalities at the boundary) in establishing optimal estimates for the number of paths confined to a region as well as the number of excursions.


September26, 2023. 14:00 (Beijing time)

Speaker: Adam Skalski (IMPAN)

Title: `What is a good definition? In search of quantum groups'

Abstract 

Definitions form a fundamental part of the mathematical study. I will discuss the requirements that mathematicians put on `good' definitions and explain how such definitions develop, based on the notion of a locally compact quantum group, originating in 1970s and 1980s, and reaching a (possibly?) final form in the work of Kustermans and Vaes in 2000. Later developments will also be mentioned, but in general the talk will be accessible to general mathematical audience.

About the speaker: Adam Skalski is a full professor and the scientific director of the Institute of Mathematics of of the Polish Academy of Sciences, and the chairman of ERCOM (European Research Centers on Mathematics). His areas of interest include topological quantum groups, operator algebras and quantum stochastic processes. He has been awarded the Kuratowski Prize of the Polish Mathematical Society in 2008 and the Sierpinski Prize of the Polish Academy of Sciences in 2014. He is one of the executive editors of Studia Mathematica and Banach Center Publications.



June12, 2023. 14:00 (Beijing time)

Speaker: Xiangdong LiAcademy of Methematics and System Science,Chinese Academy of Sciences

Title: 最优传输问题与经济资源的最优分配

Abstract 

1781年,法国数学家G. Monge从军事工程问题中提出了最优传输映射问题。1942年,苏联数学家L. Kantorovich提出了最优传输计划问题,并将其应用于国民经济资源最优分配问题的研究。1975年,Kantorovich与美国数理经济学家T. Koopmans共同分享了Nobel经济学奖。2010年和2018年,法国数学家C. Villani与意大利数学家A. Figalli先后获得菲尔兹奖,其研究工作均与最优传输问题密切有关。在本报告中,我们将回顾最优传输问题的历史发展和重要的标志性成果,并介绍Kantorovich等人关于经济资源最优分配问题的研究成果。


May30, 2023. 16:00 (Beijing time)

Speaker: Jean-Paul AlloucheCNRS, IMJ-PRG

Title: Playing with Kempner-like harmonic series

Abstract

Though the series of the inverses of integers diverges, a nice,now classical, result of Kempner (in 1914) states that the sum of the inverses of the integers whose expansion in base 10 contains no occurrence of a given digit converges. Several generalizations or extensions of this result have been given. In particular a paper of Farhi (in 2008) proves the somehow unexpected result that

where s10(n) is the sum of the digits of n in base 10.

We show how to extend this result, first by replacing s10(n) with s2(n), the sum of the binary digits of the integer n; then by replacing s2(n) by any binary pattern counting sequence (i.e., any sequence aw(n) that counts the number of occurrences of a fixed block w of 0’s and 1’s in the binary expansion of the integer n).


April 11, 2023. 16:00 (Beijing time)

Speaker: Liming WuHarbin Institute of Technologyl'Université Clermont-Auvergne

Title: 马氏过程的集中不等式

Abstract

这个报告的主题是马氏过程观察量的经验均值趋于真实均值的集中不等式,或者说随机算法的错误概率的绝对估计。我将介绍与集中不等式等价的“运费vs Fisher信息量”不等式,以及怎样使用PoincarelogSobolev不等式,与最优传输,熵这些工具去证明“运费vs Fisher信息量”不等式。作为应用例子,我将介绍高维分布Gibbs算法的错误概率绝对估计。


March 7, 2023. 16:00 (Beijing time)

Speaker: Changgui Zhang (University of Lille)

Title: Some problems about a family of linear functional differential equations

Abstract 

Given q between 0 and 1, one considers the following problems about the q-difference-differential equation y′(x) = ay(qx) + by(x) + f (x),where a and b are two complex numbers and where f is a rational function:

(1) The pantograph equations following Kato and McLeod;

(2) The indexes of the associated operator d/dx − aσ_q − b;

(3) The connection formulas between zero and infinity;

(4) The asymptotic behavior of the solutions at infinity.

This talk is partially based on a joint work with H. Dai and G. Chen (HITSZ). 


November 26, 2022. 10:00 (Beijing time)

Speaker: Yitang Zhang (University of California)

Title: 关于朗道-西格尔零点猜想

Abstract 

张益唐,世界著名领军数学家,现任加州大学-圣巴巴拉分校教授,在解析数论领域做出了一系列重要性工作,特别是在孪生素数问题上取得了里程碑式成果,应邀在第27届世界数学家大会作1小时大会报告。 获得第6届世界华人数学家大会颁发的晨兴数学卓越成就奖Morningside Special Achievement Award in Mathematics,美国数学会颁发的柯尔数论奖Cole Prize in Number Theory, 麦克阿瑟基金会颁发的麦克阿瑟奖MacArthur Award,瑞典皇家学院颁发的罗夫-肖克奖Rolf Schock Prize in Mathematics, 瑞士奥斯特洛夫斯基基金会颁发的奥斯特洛夫斯基奖Ostrowski Prize

  



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