p-adic Families of Automorphic Forms: Theories and Applications

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p-adic Families of Automorphic Forms: Theories and Applications

 08 - 12 Jul 2024

ICMS, Bayes Centre, Edinburgh

Scientific organisers

  • Judith Ludwig , Universitat Heidelberg
  • James Newton , University of Oxford
  • Jack Thorne, University of Cambridge

About:

The idea of p-adic families of automorphic forms grew out of work of Serre and Swinnerton-Dyer in the 70s exploring congruences between the q-expansion coefficients of modular forms. Work of Hida, Coleman and Mazur made the investigation of p-adic families one of the central topics in the arithmetic of modular forms. In the following decades there were striking applications to the construction of p-adic L-functions, Iwasawa theory and modularity of Galois representations.

One powerful organising principle has been to parametrize p-adic modular forms (or, more generally, p-adic automorphic forms) by p-adic analytic spaces known as eigenvarieties (or eigencurves, in the one-dimensional case originally considered by Coleman and Mazur). Our understanding of the geometry of eigenvarieties and their relationship to moduli spaces of Galois representations has rapidly developed, but there are still many important open questions.

An overarching objective of this meeting was to bring together people working on the different theories of p-adic automorphic forms and various applications (or potential applications). We hope that this inspired new collaborations and insights.

The YouTube Playlist of Recorded Talks from this workshop can be found here 

p-adic Families of Automorphic Forms: Theories and Applications - YouTube

Programme

MONDAY 8 JULY 2024
Registration and Refreshments
Welcome and Housekeeping
David Loeffler, UniDistance Suisse Big parabolic eigenvarieties and Iwasawa theory
Refreshments
Rebecca Bellovin, IAS/Glasgow Local $\varepsilon$-isomorphisms for $(\varphi,\Gamma)$-modules in mixed characteristic
Lunch
Bin Zhao, Capital Normal University On The Ghost Conjecture of Bergdall & Pollock, I
George Boxer, Imperial College London Modularity theorems for abelian surfaces
Refreshments
Eugen Hellmann, Muenster University Moduli space of rigid analytic (phi,Gamma)-modules and spaces of overconvergent p-adic automorphic forms
Welcome Reception, hosted at ICMS
TUESDAY 9 JULY 2024
Ashay Burungale, UT Austin Zeta elements for elliptic curves and applications
Alice Pozzi, University of Bristol P-adic and Tame triple product periods
Refreshments
Ruochuan Liu, Beijing International Center for Mathematical Research, Peking University On the ghost conjecture of Bergdall and Pollack, II
Lunch
Vlad Serban, New College of Florida p-adic interpolation and Lubin's dynamical systems
Refreshments
Xenia Dimitrakopoulou, University of Warwick Anticyclotomic $p$-adic $L$-functions for Coleman families of $U_n \times U_{n+1}$
Workshop Dinner
WEDNESDAY 10 JULY 2024
Giada Grossi, CNRS/Paris 13 (Higher) p-adic families of Hilbert cuspforms and applications
Juan Esteban Rodriguez Camargo, Columbia University Analytic D-modules and p-adic automorphic forms
Refreshments
Liang Xiao, Peking University Reduction of 2-dimensional triangulline representations over the halo region, and Emerton--Gee stack
Lunch & Free Afternoon
THURSDAY 11 JULY 2024
Christian Johansson, Chalmers/Gothenburg On categorical p-adic local Langlands for GL(2,Qp)
Håvard Damm-Johnsen, University of Oxford Diagonal restrictions of Hilbert modular forms
Refreshments
Lennart Gehrmann, Bielefeld University The Gross-Kohnen-Zagier theorem via p-adic uniformization
Lunch
Jaclyn Lang, Temple University Eisenstein Hecke algebras in prime-square level
Refreshments
Si Ying Lee, Stanford University Integral Hecke correspondences
FRIDAY 12 JULY 2024
Ellen Eischen, University of Oregon Algebraic and p-adic aspects of L-functions, with a view toward Spin L-functions for GSp_6
Aleksander Horawa, University of Oxford Balanced triple product p-adic L-functions and the JL transfer in families
Refreshments
Lue Pan, Princeton University Some vanishing results for rational completed cohomology of Shimura varieties
Packed Lunch and End of Workshop

Sponsors and Funders:

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