The London-Paris Number Theory Seminar meets twice per year, once in London and once in Paris. It is supported by grants from ANR Projet ArShiFo ANR-BLAN-0114, EPSRC Platform Grant EP/I019111/1, PerCoLaTor (Grant ANR-14-CE25), the Heilbronn Institute for Mathematical Research, and ERC Advanced Grant AAMOT.

London organizers: David Burns, Kevin Buzzard Fred Diamond, Yiannis Petridis, Alexei Skorobogatov, Andrei Yafaev, Sarah Zerbes.

Paris organizers: Matthew Morrow, Olivier Fouquet, Michael Harris, Marc Hindry, Benjamin Schraen, Jacques Tilouine.

The 23rd meeting of the LPNTS took place in Paris (in Jussieu), on 27th and 28th November 2017. The topic was Periods. This was the schedule:

12.15--2.15 lunch

2.15--3.15 Jean-Benoît Bost -- Transcendence proofs and infinite-dimensional geometry of numbers

3.15--4.15 Javier Fresán -- Gamma values as exponential periods

4.15--5.00 Tea break (room 1516-417)

5.00--6.00 Francis Brown -- Invariants attached to periods

10.15--11.00 Tea break (room 1516-417)

11.00--12.00 Jie Lin -- On factorization of automorphic periods

12.15 Lunch

Abstract : This talk will discuss some possibilities for gaining insight into arithmetic geometric structures by actively employing the language and ideas of geometric gauge theory.

Jean-Benoît Bost : Transcendence proofs and infinite-dimensional geometry of numbers.

Abstract : I will explain how some classical transcendence results concerning periods, notably the theorem of Schneider-Lang, may be given "natural proofs" based on the consideration of some infinite dimensional avatars of Euclidean lattices.

Javier Fresán : Gamma values as exponential periods

Abstract : As one can already guess from the Gaussian integral, the values of the gamma function at rational arguments are not expected to be periods, although suitable products of them do become periods of abelian varieties with complex multiplication. To deal with single gamma values, one needs to consider

Francis Brown : Invariants attached to periods

Abstract : Kontsevich and Zagier asked whether there exists an algorithm to determine if two periods are equal. I shall explain how, in some cases, a conjectural algorithm exists and is highly effective in practice. It enables one to discover identities between periods without any prior knowledge of relations.

Tony Scholl : Real plectic cohomology

Abstract : We will discuss joint work with Jan Nekovar on aspects of plectic cohomology and its connection with L-values.

Jie Lin : On factorization of automorphic periods

Abstract: The question on the factorization of automorphic periods was initiated by Shimura where periods refer to the Petersson inner products of algebraic forms. Essentially, he predicted that periods related to Hilbert modular forms, or more generally to algebraic forms on a division algebra, factorize as products of periods indexed by the split archimedean places of the division algebra. The initial conjecture was first proved by M. Harris and completed by H. Yoshida. However, their methods seem very difficult to generalize to higher ranks.
In this talk, we will explain a new and simple proof for general rank. We will also explain how to read this factorization from the point of view of motives, and why it is important in the study of special values of L-functions.

Previous meetings:

17th meeting (Jussieu, 10/11/14)

18th meeting (Imperial, 4--5/6/15)

19th meeting (Paris 13, 9/11/15)

20th meeting (UCL, 6--7/6/16)

21st meeting (Jussieu, 14--15/11/16)

22nd meeting (UCL, 5--6/6/17)

This page is maintained by Kevin Buzzard.