晨兴学术报告

发布时间：2023-02-20 【字体：大中小】

Speaker: Prof. Koji Shimizu (Tsinghua)

Time: 14:00-15:30 February 20th, 2023 (Monday)

Inviter: Prof. Shizhang Li (MCM)

Language: English

Place: MCM 110 & Online (Zoom ID: 4663562952 Password: mcm1234)

Title: Filtrations and endomorphisms

Abstract: Cover Bhatt's notes 1.3-1.4 and 2.1-2.2.

This is a periodic series learning seminar organized by Koji Shimizu and Shizhang Li on Banach--Colmez spaces held on each Monday at MCM110. More info can be found on the website.

Speaker: Dr. Ning Guo (Euler International Mathematical Institute)

Time: 10:00-11:00 February 22, 2023 (Wednesday)

Inviter: Prof. Weizhe Zheng (MCM)

Language: English

Place: MCM110 & Online (Zoom ID: 4663562952 Password: mcm1234)

Title: Purity and torsors over Prüfer bases

Abstract: In algebraic geometry, purity refers to a diverse range of phenomena in which certain invariants or categories associated to geometric objects are insensitive to the removal of closed subsets of large codimension. In this talk, we present Zariski-Nagata purity concerning finite étale covers on smooth schemes over Prüfer rings by proving Auslander's flatness criterion in this non-Noetherian context. By Gabber—Ramero's upper bound of projective dimensions, we present an Auslander—Buchsbaum formula. Finally, we take advantage of these cohomological results to establish the parafactoriality of schemes and the purity of torsors over Prüfer bases. This is a joint work with Fei Liu.

Speaker: Dr. Arnaud Plessis (MCM)

Title: On Lehmer's problem

Language: English

Time: 10:30-11:30am, March 2, 2023 (Thursday)

Place: MCM110 & Online (Zoom ID: 466 356 2952 Password: mcm1234)

Abstract: Let x be an algebraic number. Lehmer's problem predicts that the product of the degree of x and the Weil height of x is bounded by an absolute constant. The basic idea to tackle this problem is to study the points of small Weil height (or short, small points) in an algebraic closure of Q. The case where small points of an algebraic field L are either 0 or a root of unity is intensively studied and we will provide a few explicit examples. Then we will explain why it is complicated to precisely locate small points of L if the latter contains more small points than 0 and the roots of unity. Time permitting, we will discuss about Lehmer's problem on elliptic curves.

This is a periodic series seminar organized by members and postdoctors of Morningside Center of Mathematics held on each Thursday at MCM110. More info can be found on the website.

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