Organisers : Fred Diamond
The talks of the Number Theory workshop will be held in the Safra Lecture Theatre, in the King's Building.
Tea & Coffee will be offered in the Bush House Arcade.
The talks of the Number Theory workshop will be held in the Safra Lecture Theatre, in the King's Building.
Tea & Coffee will be offered in the Bush House Arcade.
Invited speakers
Pierre Colmez
Sorbonne U. France |
Javier Fresán
École polytechnique France |
Mahesh Kakde
IISc Bangalore India |
James Newton
Oxford U. UK |
Wiesława Nizioł
Sorbonne U. France |
Alice Pozzi
Imperial College UK |
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Tuesday 7th 14.15 - 15.10: Pierre Colmez
15.10 - 16.00: Wiesława Nizioł 16.00 - 16.40: Tea & Coffee [BH(N) Arcade] 16.40 - 17.30: James Newton |
Wednesday 8th 14.15 - 15.10: Javier Fresán
15.10 - 16.00: Alice Pozzi 16.00 - 16.40: Tea & Coffee [BH(N) Arcade] 16.40 - 17.30: Mahesh Kakde |
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Pierre Colmez
On the group GL2(Q) Abstract. I will give an introduction to some of the aspects of the p-adic Langlands program. |
Javier Fresán
A non-hyperpergeometric E-function Abstract. (Joint work with Peter Jossen) In a landmark 1929 paper, Siegel introduced the class of E-functions with the goal of generalising the transcendence theorems for the values of the exponential. E-functions are power series with algebraic coefficients subject to certain growth conditions of arithmetic nature that satisfy a linear differential equation. Besides the exponential, examples include Bessel functions and a rich family of hypergeometric series. Siegel asked whether all E-functions are polynomial expressions in these hypergeometric series. I will explain why the answer is negative and a possible amendment to Siegel's question in the form "all E-functions come from exponential motives". |
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Wiesława Nizioł
Factorization of the p-adic étale cohomology of coverings of Drinfeld’s upper half plane Abstract. I will report on joint work with Pierre Colmez and Gabriel Dospinescu giving a factorization à la Emerton of the p-adic étale cohomology of coverings of Drinfeld’s upper half-plane. |
Alice Pozzi
Rigid meromorphic cocycles and p-adic variations of modular forms Abstract. A rigid meromorphic cocycle is a class in the first cohomology of the group
SL2(Z[1/p]) acting on the non-zero rigid meromorphic functions on the Drinfeld
p-adic upper half plane by Möbius transformation. Rigid meromorphic cocycles
can be evaluated at points of “real multiplication”, and their values conjecturally
lie in composita of abelian extensions of real quadratic fields, suggesting striking
analogies with the classical theory of complex multiplication.
In this talk, we discuss the proof of this conjecture for a special class of rigid
meromorphic cocycles. Our proof connects the values of rigid meromorphic
cocycles to the study of certain p-adic variations of Hilbert modular forms. |
|
James Newton
Modularity of elliptic curves over CM fields Abstract. Since the seminal works of Wiles and Taylor-Wiles, robust methods were developed to prove the modularity of 'polarised' Galois representations. These include, for example, those coming from elliptic curves defined over totally real number fields. Over the last 10 years, new developments in the Taylor-Wiles method (Calegari, Geraghty) and the geometry of Shimura varieties (Caraiani, Scholze) have broadened the scope of these methods. One application is the recent work of Allen, Khare and Thorne, who prove modularity of a positive proportion of elliptic curves defined over a fixed imaginary quadratic field. I'll review some of these developments and work in progress with Caraiani which has further applications to modularity of elliptic curves over imaginary quadratic fields. |
Mahesh Kakde
On the Brumer-Stark conjecture Abstract. A theorem of Stickelberger gives an annihilator of ideal class group of finite abelian extensions of rational numbers. The Brumer-Stark conjecture generalises this statement to all totally real number fields. After stating the Brumer-Stark conjecture I will review its refinements. I will then sketch a proof of these conjectures away from p=2. This is all a joint work with Samit Dasgupta. |