PKU/BICMR Number Theory Seminar  2023
Venue
 Until further notice, the offline or hybrid talks will be held in room 77201, BICMR.
 For online or hybrid talks, the Zoom number is 743 736 2326, and the password is 013049.
Schedule
The series is also announced on researchseminars.org
Time and Date  Speaker  Topic  Slides / Recording 
March 15 15:0016:00 
Yupeng Wang (Chinese Academy of Sciences) 
Integral \(p\)adic nonabelian Hodge theory for small representations 
Video 
April 5 15:3016:30 
Li Lai (Tshinghua University) 
On the irrationality of certain \(2\)adic zeta values Let \( \zeta_2(\cdot) \) be the KubotaLeopoldt \(2\)adic zeta function. We prove that, for every nonnegative integer \(s\), there exists an odd integer \(j\) in the interval \( [s+3,3s+5] \) such that \( \zeta_2(j) \) is irrational. In particular, at least one of \( \zeta_2(7),\zeta_2(9),\zeta_2(11),\zeta_2(13)\) is irrational.

Slides Video 
April 12 15:3016:30 
Fan Gao (Zhejiang University) 
Some satisfactory and unsatisfactory aspects of the dual groups for central covers We consider finite degree central covers of a linear reductive group in the local setting. Using some examples as the highlights, we will explain the dual group of such a central cover, and illustrate how much it captures the representationtheoretic information of the central cover, and also how much it fails for the same purpose. We concentrate on two aspects of a representation: formal degree and wavefront set. 
Video 
April 26 15:3016:30 
King Fai Lai 
同调代数的一个注记 谈一谈关于非交换环的同调代数的几方面。 
Slides 
May 17 15:0016:00 
Juan Esteban Rodríguez Camargo (MPIM) 
Solid locally analytic representations (Joint with Joaquín Rodrigues Jacinto) In this talk I will introduce different categories of \(p\)adic representations in the framework of condensed mathematics. We give different geometric interpretations to them, construct explicit adjunctions that serve to compare cohomology theories, and see an application to \(p\)adic categorical local Langlands for \(\mathrm{GL}_1\). 

May 31 15:3016:30 
Koji Shimizu (YMSC) 
Robba site and Robba cohomology We will discuss a \(p\)adic cohomology theory for rigid analytic varieties with overconvergent structure (dagger spaces) over a local field of characteristic \(p\). After explaining the motivation, we will define a site (Robba site) and discuss its basic properties. 

June 7 09:0010:00 
Alexander Bett (Harvard University) 
padic obstructions and Selmer sections In 1983, shortly after Faltings' resolution of the Mordell Conjecture, Grothendieck formulated his famous Section Conjecture, positing that the set of rational points on a projective curve Y of genus at least two should be equal to a certain section set defined in terms of the etale fundamental group of Y. To this day, this conjecture remains wide open, with only a small handful of very special examples known. In this talk, I will discuss recent work with Jakob Stix, in which we proved a Mordelllike finiteness theorem for the "Selmer" part of the section set for any smooth projective curve Y of genus at least 2 over the rationals. This generalises the FaltingsMordell Theorem, and implies strong constraints on the finite descent locus from obstruction theory. The key new idea in our proof is an adaptation of the recent proof of Mordell by Lawrence and Venkatesh to the study of the Selmer section set. Time permitting, I will also briefly describe recent work with Theresa Kumpitsch and Martin Lüdtke in which we compute the Selmer section set in one example using the ChabautyKim method. 

June 21 
Rui Chen (Zhejiang University) 
TBA 

July 12 
Lie Qian (Stanford University) 
TBA 