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

 Enquiries

.The closing date for applications has now passed and no late submissions will be accepted.

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 will be to bring together people working on the different theories of p-adic automorphic forms and various applications (or potential applications). We hope that this will inspire new collaborations and insights.

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Programme

MONDAY 8 JULY 2024
09.10 - 09.45 Registration and Refreshments
09.50 - 10.00 Welcome and Housekeeping
10.00 - 11.00 David Loeffler, UniDistance Suisse Big parabolic eigenvarieties and Iwasawa theory
11.00 - 11.30 Refreshments
11.30 - 12.30 Rebecca Bellovin, IAS/Glasgow Local $\varepsilon$-isomorphisms for $(\varphi,\Gamma)$-modules in mixed characteristic
12.30 - 14.15 Lunch
14.15 - 15.15 Bin Zhao, Capital Normal University On The Ghost Conjecture of Bergdall & Pollock, I
15.30 – 16.00 George Boxer, Imperial College London Modularity theorems for abelian surfaces
16.00 - 16.30 Refreshments
16.30 - 17.30 Eugen Hellmann, Muenster University Moduli space of rigid analytic (phi,Gamma)-modules and spaces of overconvergent p-adic automorphic forms
17.30 - 18.30 Welcome Reception, hosted at ICMS
TUESDAY 9 JULY 2024
09.30 - 10.30 Ashay Burungale, UT Austin Zeta elements for elliptic curves and applications
10.45 – 11.15 Alice Pozzi, University of Bristol P-adic and Tame triple product periods
11.15 - 11.45 Refreshments
11.45 - 12.45 Ruochuan Liu, Beijing International Center for Mathematical Research, Peking University On the ghost conjecture of Bergdall and Pollack, II
12.45 - 14.30 Lunch
14.30 – 15.00 Vlad Serban, New College of Florida p-adic interpolation and Lubin's dynamical systems
15.00 - 15.30 Refreshments
15.30 - 16.30 Xenia Dimitrakopoulou, University of Warwick Anticyclotomic $p$-adic $L$-functions for Coleman families of $U_n \times U_{n+1}$
19.00 - 21.00 Workshop Dinner
WEDNESDAY 10 JULY 2024
09.30 - 10.30 Giada Grossi, CNRS/Paris 13 (Higher) p-adic families of Hilbert cuspforms and applications
10.45 - 11.15 Juan Esteban Rodriguez Camargo, Columbia University Analytic D-modules and p-adic automorphic forms
11.15 - 11.45 Refreshments
11.45 – 12.45 Liang Xiao, Peking University Reduction of 2-dimensional triangulline representations over the halo region, and Emerton--Gee stack
12.45 Lunch & Free Afternoon
THURSDAY 11 JULY 2024
09.30 - 10.30 Christian Johansson, Chalmers/Gothenburg On categorical p-adic local Langlands for GL(2,Qp)
10.45 - 11.15 Håvard Damm-Johnsen, University of Oxford Diagonal restrictions of Hilbert modular forms
11.15 - 11.45 Refreshments
11.45 – 12.45 Lennart Gehrmann, Bielefeld University The Gross-Kohnen-Zagier theorem via p-adic uniformization
12.45 - 14.30 Lunch
14.30 - 15.00 Jaclyn Lang, Temple University Eisenstein Hecke algebras in prime-square level
15.00 – 15.30 Refreshments
15.30 – 16.30 Si Ying Lee, Stanford University Integral Hecke correspondences
FRIDAY 12 JULY 2024
09.15 - 10.15 Ellen Eischen, University of Oregon Algebraic and p-adic aspects of L-functions, with a view toward Spin L-functions for GSp_6
10.30 – 11.00 Aleksander Horawa, University of Oxford Balanced triple product p-adic L-functions and the JL transfer in families
11.00 - 11.30 Refreshments
11.30 - 12.30 Lue Pan, Princeton University Some vanishing results for rational completed cohomology of Shimura varieties
12.30 Packed Lunch and End of Workshop

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