MCM-YMSC p-adic Geometry Learning Seminar

Instructor:Xu Shen (MCM)
Organizer:Shizhang Li (MCM), Koji Shimizu (YMSC), Yihang Zhu (YMSC), Xiangqian Yang (PKU)
Time:Monday 2:30-4 pm
Venue:MCM 110

Title: The stacks of tame and unipotent parameters



Talks this semester

We study the tame categorical local Langlands correspondence in the Fall of 2025.

X. Zhu, Tame categorical local Langlands correspondence, arXiv:2504.07482.


Date: September 22

Time: 2:30-4 pm

Venue: MCM 110

Title: Overview of the seminar

Speaker: Yihang Zhu (YMSC)


Date: September 29  

Time: 2:30-4 pm

Venue: MCM 110

Title: Review of L-parameters and the moduli stack

Speaker: Koji Shimizu (YMSC)


Date: October 13  

Time: 2:30-4 pm

Venue: MCM 110

Title: Irreducible components of the stack of L-parameters, structure of discrete parameters

Speaker: Fanyi Li (THU)


Date: October 20               

Time: 2:30-4 pm

Venue: MCM 110

Title: The stacks of tame and unipotent parameters

Speaker: Xu Shen (MCM)


Date: October 27               

Time: 2:30-4 pm

Venue: MCM 110

Title: The category of coherent sheaves

Speaker: Liang Xiao (PKU)


Date: November 3               

Time: 2:30-4 pm

Venue: MCM 110

Title: Spectral affine Hecke categories, and spectral DL induction (I)

Speaker: Lin Chen (YMSC)


Date: November 10               

Time: 2:30-4 pm

Venue: MCM 110

Title: Spectral DL induction (II)

Speaker:


Date: November 17  

Time: 2:30-4 pm

Venue: MCM 110

Title: Categorical trace (I)

Speaker: Daxin Xu (MCM)


Date: November 24  

Time: 2:30-4 pm

Venue: MCM 110

Title: Categorical trace (II)

Speaker: Penghui Li (YMSC)


Date: December 1  

Time: 2:30-4 pm

Venue: MCM 110

Title: The stack of local G-shtukas

Speaker: Heng Du (YMSC)


Date: December 8  

Time: 2:30-4 pm

Venue: MCM 110

Title: The stack of G-isocrystals

Speaker: Yichao Tian (MCM)


Date: December 15  

Time: 2:30-4 pm

Venue: MCM 110

Title: Representations of locally profinite groups

Speaker:


Date: December 22  

Time: 2:30-4 pm

Venue: MCM 110

Title: Theory of l-adic sheaves

Speaker:


Date: January 5  

Time: 2:30-4 pm

Venue: MCM 110

Title: The local Langlands category

Speaker:


 


Past talks:


We studied the Lawrence-Venkatesh method in the Spring of 2025.

B. Lawrence and A. Venkatesh, Diophantine problems and p-adic period mappings, Invent. Math. 221 no.3 (2020), 893-999.

Date: February 24

Time: 2:30-4 pm

Venue: MCM 110

Title: Overview of the seminar

Speaker: Koji Shimizu (YMSC)


Date: March 3

Time: 2:30-4 pm

Venue: MCM 110

Title: Fibers with good reduction in a family

Speaker: Han Hu (PKU)


Date: March 17

Time: 2:30-4 pm

Venue: MCM 110

Title: The S-unit equation

Speaker: Koji Shimizu (YMSC)


Date: March 24

Time: 2:30-4 pm

Venue: MCM 110

Title: Outline of the argument for Mordell’s conjecture

Speaker: Khai-Hoan Nguyen-Dang (MCM)


Date: March 31

Time: 2:30-4 pm

Venue: MCM 110

Title: Rational points on the base of an abelian-by-finite family

Speaker: Koji Shimizu (YMSC)


Date: April 7

Time: 2:30-4 pm

Venue: MCM 110

Title: The Kodaira–Parshin family

Speaker: Yong Suk Moon (BIMSA)


Date: April 14

Time: 2:30-4 pm

Venue: MCM 110

Title: The monodromy of Kodaira–Parshin families

Speaker: Koji Shimizu (YMSC)




We studied alterations and semistable reduction in the Fall of 2024.

Date: September 9

Time: 2:30-4 pm

Venue: MCM 110

Title: Overview of the seminar

Speaker: Koji Shimizu (YMSC)


Date: September 23

Time: 2:30-4 pm

Venue: MCM 110

Title: Semistable curves and normal crossing divisors

Speaker: Shizhang Li (MCM)


Date: October 14

Time: 2:30-4 pm

Venue: MCM 110

Title: Alterations of varieties

Speaker: Weimufei Wu (PKU)


Date: October 21

Time: 2:30-4 pm

Venue: MCM 110

Title: Semistable alterations

Speaker: Ruiping Gong (AMSS)


Date: October 28

Time: 2:30-4 pm

Venue: MCM 110

Title: Semistable models for rigid-analytic spaces

Speaker: Yong Suk Moon (BIMSA)


 

Date: November 4

Time: 2:30-4 pm

Venue: MCM 110

Title: Toric varieties 1

Speaker: Qinru Zhong (AMSS)


 

Date: November 11

Time: 2:30-4 pm

Venue: MCM 110

Title: Toric varieties 2

Speaker: Shengyu Hou (AMSS)


 

Date: November 18

Time: 2:30-4 pm

Venue: MCM 110

Title: Toric varieties 3

Speaker: Ningjun Jiang (THU)


 

Date: November 25

Time: 2:30-4 pm

Venue: MCM 110

Title: Toroidal embeddings

Speaker: Shengkai Mao (AMSS)


 

Date: December 2

Time: 2:30-4 pm

Venue: MCM 110

Title: Semistable reduction theorem in characteristic 0

Speaker: Han Hu (PKU)


 

 

We studied rigid connections in the Spring of 2024.

The main goal of this seminar is to study various results around rigid connections: existence of a Frobenius structure on a rigid connection due to EsnaultGroechenig [EG23], application to Simpson's integral conjecture, and the Fourier transform algorithm for rigid connections on the projective line due to Katz and Arinkin [Ari10].

[Ari10] D. Arinkin, Rigid irregular connections on P1, Compos. Math. 146 (2010)

[EG23] H. Esnault and M. Groechenig, Cristallinity of rigid flat connections revisited, arXiv:2309.15949v2 (2023)


Date: May 27

Time: 2:30-4 pm

Venue: MCM 110

Title: Proof of main results

Speaker: Yong Suk Moon (BIMSA)


Date: May 20

Time: 2:30-4 pm

Venue: MCM 110

Title: Rigidity index and rank of the Fourier transform

Speaker: Yezheng Gao (MCM)


Date: May 13

Time: 2:30-4 pm

Venue: MCM 110

Title: Fourier transform preserves cohomological rigidity II

Speaker: Daxin Xu (MCM)


Date: May 6Time: 2:30-4 pm

Venue: MCM 110

Title: Fourier transform preserves cohomological rigidity

Speaker: Hongjie Yu (MCM)


Date: April 29

Time: 2:30-4 pm

Venue: MCM 110

Title: Review of Fourier transform and local Fourier transform

Speaker: Xiecheng Nie (MCM)


Date: April 22Time: 2:30-4 pm

Venue: MCM 410

Title: Review of formal connections on a punctured disc

Speaker: Yupeng Wang (PKU)


Date: April 15Time: 2:30-4 pm

Venue: MCM 110

Title: Applications to integrality and p-curvature conjectures

Speaker: Jiahong Yu (PKU)


Date: April 8

Time: 2:30-4 pm

Venue: MCM 110

Title: Integral Frobenius structure

Speaker: Zhaofeng Yu (Tsinghua)


Date: April 1

Time: 2:30-4 pm

Venue: MCM 110

Title: Rational F-isocrystal property

Speaker: Chenglong Ma (PKU)


Date: March 25Time: 2:30-4 pm

Venue: MCM 110

Title: Frobenius pullback functor for flat connections

Speaker: Koji Shimizu (YMSC)


Date: March 18

Time: 2:30-4 pm

Venue: MCM 110

Title: p-adic topology on W-points of schemes and stacks

Speaker: Junwei Wu (MCM)


Date: March 11

Time: 2:30-4 pm

Venue: MCM 110

Title: Higgs–de Rham flow

Speaker: Mao Sheng (YMSC)


Date: March 4

Time: 2:30-4 pm

Venue: MCM 110

Title: Overview of the p-adic geometry learning seminar

Speaker: Daxin Xu (MCM)




We studied the Drinfeld half-spaces in the Fall of 2023.

The main goal of this semester is to learn topics related to Drinfeld half-spaces: basic properties, the Drinfeld theorem, and the Čerednik–Drinfeld uniformization theorem for Drinfeld half-plane [BC91]; the cohomology of the Drinfeld half-spaces [SS91, Dat06].

[BC91] Boutot and Carayol, Uniformisation p-adique des courbes de Shimura: les théorèmes de Čerednik et de Drinfeld

[SS91] Schneider and Stuhler, The cohomology of p-adic symmetric spaces

[Dat06] Dat, Espaces symétriques de Drinfeld et correspondance de Langlands locale


Date: December 18

Time: 2:30-4 pm

Venue: MCM 110

Title: Cohomology complex and Galois representations

Speaker: Heng Du (YMSC)


Date: December 11

Time: 2:30-4 pm

Venue: MCM 110

Title: Cohomology with compact support of Drinfeld half-space

Speaker: Zhefan Duan (Tsinghua)

   

Date: December 4

Time: 2:30-4 pm

Venue: MCM 110

Title: Extensions of principal series representations

Speaker: Zicheng Qian (MCM)

   

Date: November 27

Time: 2:30-4 pm

Venue: MCM 110

Title: Cohomology of quotient varieties

Speaker: Yong Suk Moon (BIMSA)


Date: November 20

Time: 2:30-4 pm

Venue: MCM 110

Title: Explicit expressions for the cohomology of Drinfeld half-space

Speaker: Yongquan Hu (MCM)

   

Date: November 13

Time: 2:30-4 pm

Venue: MCM 110

Title: Cohomology of Drinfeld half-space and the Tits building

Speaker: Shuaishuai Duan (MCM)


Date: November 6

Time: 2:30-4 pm

Venue: MCM 110

Title: Drinfeld half-spaces

Speaker: Yi Zhu (Tsinghua)


Date: October 30  

Time: 2:30-4 pm

Venue: MCM 110

Title: The Čerednik–Drinfeld uniformization theorem

Speaker: Yihang Zhu (YMSC)


Date: October 23

Time: 2:30-4 pm

Venue: MCM 110

Title: Drinfeld’s theorem: proof

Speaker: Yupeng Wang (PKU)

   

Date: October 16

Time: 2:30-4 pm

Venue: MCM 110

Title: Drinfeld’s theorem: statement and construction

Speaker: Tian Qiu (PKU)


Date: October 9

Time: 2:30-4 pm

Venue: MCM 110

Title: Special formal OD-modules over an algebraically closed field

Speaker: Jiahong Yu (PKU)


Date: September 25

Time: 2:30-4 pm

Venue: MCM 110

Title: Moduli interpretation and the Cartier theory

Speaker: Shanwen Wang (RUC)


                                                                     

Date: September 18

Time: 2:30-4 pm

Venue: MCM 110

Title: Overview of the p-adic geometry learning seminar

Speaker: Koji Shimizu (YMSC)




We studied the prismatic F-gauges in the Spring of 2023.


Date: May 29

Time: 2-3:30 pm

Venue: MCM 110

Title: Syntomic cohomology and Galois cohomology II

Speaker: Shanwen Wang (RUC)


Date: May 22

Time: 2-3:30 pm

Venue: MCM 110

Title: Syntomic cohomology and Galois cohomology I

Speaker: Koji Shimizu (YMSC)


Date: May 8

Time: 2-3:30 pm

Venue: MCM 110

Title: Syntomification

Speaker: Heng Du (YMSC)


Date: April 24

Time: 2-3:30 pm

Venue: MCM 110

Title: Filtered prismatization

Speaker: Jiahao Niu (AMSS)


Date: April 17

Time: 2-3:30 pm

Venue: MCM 110

Title: Prismatization

Speaker: Jiedong Jiang (BICMR)


Date: April 10

Time: 2-3:30 pm

Venue: MCM 110

Title: Syntomic cohomology in characteristic p

Speaker: Yong Suk Moon (BIMSA)


Date: April 3

Time: 2-3:30 pm

Venue: MCM 110

Title: Syntomification in characteristic p

Speaker: Yichao Tian (MCM)

   

Date: March 27

Time: 2-3:30 pm

Venue: MCM 110

Title: Gauges over k

Speaker: Daxin Xu (MCM)


Date: March 20

Time: 2-3:30 pm

Venue: MCM 110

Title: Prismatization over k

Speaker: Shanwen Wang (RUC)


Date: March 13

Time: 2-3:30 pm

Venue: MCM 110

Title: The conjugate filtration

Speaker: Shizhang Li (MCM)


Date: March 6

Time: 2-3:30 pm

Venue: MCM 110

Title: The de Rham cohomology of p-adic formal schemes

Speaker: Shizhang Li (MCM)


Date: February 27

Time: 2-3:30 pm

Venue: MCM 110

Title: The de Rham cohomology in characteristic 0

Speaker: Yupeng Wang (MCM)


Date: February 20

Time: 2-3:30 pm

Venue: MCM 110

Title: Filtrations and endomorphisms

Speaker: Koji Shimizu (YMSC)




We studied the BanachColmez spaces in the Fall of 2022.


Date: December 26

Time: 2-3:30 pm

Venue: Online (Zoom ID: 466 356 2952, Passcode: mcm1234)

Title: Semistable comparison theorem

Speaker: Yong Suk Moon (BIMSA)


Date: December 19

Time: 2-3:30 pm

Venue: Online (Zoom ID: 466 356 2952, Passcode: mcm1234)

Title: Syntomic cohomology and (phi, Gamma)-modules

Speaker: Shanwen Wang (Renmin University of China)


Date: December 12

Time: 2-3:30 pm

Venue: Online (Zoom ID: 466 356 2952, Passcode: mcm1234)

Title: Overview and local syntomic computations

Speaker: Koji Shimizu (YMSC)


Date: December 5

Time: 2-3:30 pm

Venue: Online (Zoom ID: 466 356 2952, Passcode: mcm1234)

Title: The category \mathscr{BC} in terms of the Fargues–Fontaine curve

Speaker: Heng Du (YMSC)


Date: November 28

Time: 2-3:30 pm

Venue: Online (Zoom ID: 466 356 2952, Passcode: mcm1234)

Title: Pro-etale cohomology of affine spaces

Speaker: Ruochuan Liu (Peking University)


Date: November 21

Time: 2-3:30 pm
Venue: Online

Title: Banach—Colmez spaces
Speaker: Jiedong Jiang (BICMR)


Date: November 14

Time: 2-3:30 pm
Venue: MCM 110

Title: Weakly admissibility implies admissibility
Speaker: Zekun Chen (BICMR)


Date: November 7

Time: 2-3:30 pm

Venue: MCM 110

Title: Fundamental exact sequence

Speaker: Yong Suk Moon (BIMSA)


Date: October 31

Time: 2-3:30 pm

Venue: MCM 110

Title: p-adic period rings

Speaker: Daxin Xu (MCM)


Special Lecture

Date: October 31
Time: 4:15-5:30 pm
Venue: Lecture Hall, Jin Chun Yuan West Bldg.
Title: Overview of the Emerton-Gee stack and beyond

Speaker: Yong Suk Moon (BIMSA)


Date: October 24

Time: 2-3:30 pm

Venue: MCM 110

Title: Finite-dimensional Banach Spaces

Speaker: Zhefan Duan (Tsinghua)


Date: October 17  

Time: 2-3:30 pm

Venue: MCM 110

Title: Vector Spaces  

Speaker: Yupeng Wang (MCM)  


Date: October 10

Time: 2-3:30 pm

Venue: MCM 110

Title: A funny field \mathfrak{C}

Speaker: Qijun Yan (BICMR)


Date: September 26

Time: 2-3:30 pm

Venue: MCM 110

Title: Sympathetic closure

Speaker: Yongquan Hu (MCM)


Date: September 19

Time: 2-3:30 pm

Venue: MCM 110

Title: Sympathetic algebras

Speaker: Shizhang Li (MCM)


Date: September 5

Time: 3:30-5 pm

Venue: MCM 110
Title: Introduction and organization  
Speaker: Koji Shimizu (YMSC)