IMS Anniversary Symposium on Algebra

IMS Anniversary Symposium on Algebra

Date: Friday, October 20, 2023.

Location: 301 Teaching Center

Schedule

Program

Guchuan Li (Peking University)

Title: The inverse topology of $K(n)$-local homotopy theory 

Abstract: Homotopy theory can be studied through its $p$-localization for all primes $p$. Chromatic homotopy theory allows one to further decompose $p$-local homotopy theory into $K(n)$-local homotopy theory for all heights $n$. In this talk, we introduce an inverse topology on $K(n)$-local homotopy theory. This allow us to identify the entire E1 and E2-pages of the descent spectral sequence for Picard groups of profinite Galois extensions of the $K(n)$-local sphere. This is joint work with Ningchuan Zhang. 

Dingxin Zhang (Tsinghua University)

Title: 消失圈的一些应用

Abstract: 我将解释如何用消失圈和偏屈层的Deligne消灭定理来得到一些有趣同调不变量在退化情形下的精确定量估计。在 Milnor-Thom, Katz, Bombieri, Adolphson-Sperber 等人考虑过的具体问题中，我们得到的改进上界是渐进意义下最优的。这项工作是与万大庆合作完成的。

Shuai Zhai (Shandong University)

Title: BSD Conjecture and Goldfeld’s Conjecture 

Abstract: In this talk, I will discuss some recent results of Goldfeld's conjecture and its connection with the Birch and Swinnerton-Dyer conjecture.

Miaofen Chen (East China Normal University)

Title: Two stratifications in $p$-adic Hodge theory

Abstract: There exists two stratifications on the $B_{dR}^+$-Grassmannian. One is called Newton strafication and the other is called Harder-Narasimhan stratification. Newton stratification is the image of the $p$-adic period mapping and Harder-Narasimhan stratification is its algebraic approximation. In this talk, we will explain the basic properties of these two stratifications and their relations. 

Wenchuan Hu (Sichuan University)

Title: Homotopy theoretic methods in the algebraic cycle theory 

Abstract: We plan to talk about homotopy theoretic methods in the study of the algebraic cycle theory, including the origin, developments, related problems and some recent progress.