Sep 18  Michele Fornea (Columbia)

Points on elliptic curves via padic integration
The work of Bertolini, Darmon and their schools has shown that padic multiplicative integrals can be successfully employed to study the global arithmetic of elliptic curves. Notably, Guitart, Masdeu and Sengun have recently constructed and numerically computed StarkHeegner points in great generality. Their results strongly support the expectation that StarkHeegner points completely control the MordellWeil group of elliptic curves of rank 1.
In our talk, we will report on work in progress about a conjectural construction of global points on modular elliptic curves, generalizing the padic construction of Heegner points via CerednikDrinfeld uniformization. Inspired by Nekovar and Scholl's plectic conjectures, we expect the nontriviality of these plectic Heegner points to control the MorderllWeil group of higher rank elliptic curves. We provide some evidence for our conjectures by showing that higher derivatives of anticyclotomic padic Lfunctions compute plectic Heegner points.

Sep 25  Dennis Gaitsgory (Harvard)

The stack of local systems with restricted variation and the passage from
geometric to classical Langlands theory
The goal of this talk is two explain to closely related phenomena: the
existence of the categorical geometric Langlands theory for ladic sheaves
and the link between geometric to classical Langlands via the operation of
categorical trace. A key ingredient is played by a new geometric object:
the stack of local systems with restricted variation.
Video  Notes

Oct 2  Hector Pasten (PUC Chile)

A ChabautyColeman estimate for surfaces in abelian threefolds
Coleman's explicit version of Chabauty's theorem gives a remarkable upper bound for the number of rational points in hyperbolic curves over number fields, under a certain rank condition. This result is obtained by padic methods. Despite considerable efforts in this topic, higher dimensional extensions of such a bound have remained elusive. In this talk I will sketch the proof for hyperbolic surfaces contained in abelian threefolds, which provides the first case beyond the scope of curves. This is joint work with Jerson Caro.
Video  Slides

Oct 9  Jonathan Wang (MIT)

Local Lvalues and geometric harmonic analysis on spherical varieties
Almost a decade ago, Sakellaridis conjectured a vast generalization of the RankinSelberg method to produce integral representations of Lfunctions using affine spherical varieties. The conjecture is still very much unknown, but generalized IchinoIkeda formulas of SakellaridisVenkatesh relate the global problem to certain problems in local harmonic analysis. I will explain how we can use techniques from geometric Langlands to compute integrals which give special values of unramified local Lfunctions over a local function field, for a large class of spherical varieties. This is joint work with Yiannis Sakellaridis. Our results give new integral representations of Lfunctions (in a right half plane) over global function fields when the integral "unfolds".
Video  Slides

Oct 16  George Boxer (ENS de Lyon)

Higher Coleman Theory
We introduce a higher coherent cohomological analog of overconvergent modular forms on Shimura varieties and explain how to compute the finite slope part of the coherent cohomology of Shimura varieties in terms of them. We also discuss how they vary padically. This is joint work with Vincent Pilloni.
Video  Notes

Oct 23  Sarah Zerbes (UCL)

The BlochKato conjecture for GSp(4)
In my talk, I will sketch a proof of new cases of the BlochKato conjecture for the spin Galois representation attached to genus 2 Siegel modular forms. More precisely, I will show that if the Lfunction is nonvanishing at some critical value, then the corresponding Selmer group is zero, assuming a number of technical hypotheses. I will also mention work in progress on extending this result to Siegel modular forms of parallel weight 2, with potential applications to the BirchSwinnertonDyer conjecture for abelian surfaces. This is joint work with David Loeffler.

Oct 30  David Loeffler (Warwick)


Nov 6  ChiYun Hsu (UCLA)


Nov 13  Yuanqing Cai (Kyoto)


Nov 20  Takuya Yamauchi (Tohoku)


Dec 4  Eugen Hellmann (Münster)


Dec 11  Zhilin Luo (Minnesota)


Dec 18 

