Scientific organisers
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Judith Ludwig , Universitat Heidelberg
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James Newton , University of Oxford
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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 | ||
| 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 |
