# Automorphic Forms and Arithmetic

## Fall 2019

 September 13th Tony Feng (MIT) Shtukas and the base change fundamental lemma September 20th Wei Zhang (MIT) The arithmetic fundamental lemma for diagonal cycles October 4th Fabrizio Andreatta (Milan) Eichler Shimura morphisms October 11th Ziyang Gao (CNRS/IMJ-PRG) Bound on the number of rational points on curves October 25th Nikos Diamantis (Nottingham U.) Eichler cocycles associated to modular iterated integrals of length one November 1st Jessica Fintzen (University of Michigan) From representations of p-adic groups to congruences of automorphic forms November 8th Kestutis Cesnavicius (CNRS/University Paris-Sud) Purity for flat cohomology November 22 David Soudry (Columbia) An explicit realization of stable L-packets on (split) classical groups December 6th Adrian Iovita (Concordia) Special values of p-adic L-functions and rational points on CM elliptic curves. December 13th Aaron Landesman (Stanford) The geometric distribution of ranks and Selmer groups over function fields

## Spring 2019

 February 1 Dimitri Wyss (Sorbonne University Paris 6) p-adic integration and geometric stabilization February 8 Hang Xue (Arizona) Epsilon dichotomy for linear models February 15 Xinyi Yuan (Berkeley) Weak Lefschetz theorems for Brauer groups February 22 Baiying Liu (Purdue) On automorphic descent from GL(7) to G2 March 1 Rong Zhou (IAS) Motivic cohomology of quaternionic Shimura varieties and level raising March 8 Rahul Krishna (Northwestern) The semi-Schrödinger model of an exceptional representation of $\widetilde{GL}_{2q}$ March 29 Luis Garcia (Toronto) Transgression of the Euler class and Eisenstein cohomology April 5 Guangyu Zhu (Yale) The Galois group of the category of mixed Hodge-Tate structures April 19 Wanlin Li (Wisconsin-Madison) Vanishing of Hyperelliptic L-functions at the Central Point April 26 Weizhe Zheng (MCM/Princeton) Compatible systems along the boundary May 3 Charlotte Chan (Princeton) Flag varieties and representations of p-adic groups May 10 Raphaël Beuzart-Plessis (Aix-Marseille University) Spectral decomposition of certain symmetric spaces and the Ichino-Ikeda conjecture

## Fall 2018

 September 14th Giacomo Micheli (Oxford) Permutations and codes using a density method September 21st Ted Chinburg (U. Penn) Higher codimension Iwasawa theory September 28th Matthew Welsh (Rutgers) Spacing and a Large Sieve Type Inequality for Roots of a Cubic Congruence October 12th Alexandra Florea (Columbia) Moments of cubic L-functions over function fields October 19th Yihang Zhu (Columbia) Irreducible components of affine Deligne-Lusztig varieties, and orbital integrals. November 2nd Asbjorn Nordentorft (U. Copenhagen) Central values of additive twists of modular L-functions November 9th Xuhua He (University of Maryland) Good and semi-stable reduction of Shimura varieties November 16th Samit Dasgupta (Duke University) The Stark conjecture and the 12th Hilbert problem November 30th Will Sawin (Columbia) Ramanujan and the Other Geometry December 7th Tom Haines (University of Maryland) Smoothness of Schubert varieties in twisted affine Grassmannians

## Spring 2018

 January 26th Adrian Iovita (Concordia) An overconvergent crystalline Eichler-Shimura isomorphism February 16th Kazim Buyukboduk (Dublin) Non-ordinary symmetric squares and Euler systems of rank 2 February 23rd Daniel Gulotta (Columbia) Vanishing of cohomology for some Shimura varieties at level \Gamma_1(p^{\infty}) March 9th Lucia Mocz (Princeton) A New Northcott Property for Faltings Height March 30th Ari Shnidman (Boston College) A higher order Gross-Kohnen-Zagier formula April 6th Tony Feng (Stanford/IAS) On a conjecture of Tate concerning the Brauer group of a surface April 13th Aaron Pollack (IAS) The generalized Whittaker function on quaternionic exceptional groups May 1st (*) Jared Weinstein (BU) The cohomology of local Shimura varieties

## Fall 2017

 September 8th Rachel Ollivier (UBC) A derived Hecke algebra in the context of the mod p Langlands program September 22nd A. Raghuram (Purdue U.) Eisenstein cohomology and the special values of automorphic L-functions. October 6th Pierre Colmez (IMJ & CNRS) On the cohomology of p-adic analytic curves October 13th Kai-Wen Lan (U. Minnesota) Local systems over Shimura varieties: a comparison between two constructions October 20th Bao Le Hung (IAS) Towards algebraic models for certain potentially crystalline deformation rings November 3rd Umberto Zannier (SNS Pisa) Representing isogeny classes of elliptic curves over $\overline\Q$. November 14th (*) Jacques Tilouine (Univ. Paris 13 & UCLA) Integral period relations and the Bloch-Kato Conjecture for the quadratic twists of the adjoint motive of a classical modular form December 1st Laurent Clozel (Univ. Paris Sud & IAS) Solvable descent for cuspidal automorphic representations of GL(n).

## Spring 2017

 February 17th Michael Harris (Columbia)) Derived Hecke algebras for weight one forms (work in progress with A. Venkatesh) February 24th Rong Zhou (Harvard)) Mod p isogeny classes on Shimura varieties with parahoric level structure. March 31st Jingwei Xiao (Columbia) Endoscopic fundamental lemma for unitary groups and the Jaquet-Rallis transfer April 14th Jack Thorne (Cambridge) Automorphy and potential automorphy beyond the polarizable case April 19th at 1pm Shrenick Shah (Columbia) A class number formula for Picard modular surfaces April 28th Soren Galatius (Stanford) Simplicial deformation rings and the homology of arithmetic groups May 5th Ananth Shankar (Harvard) The $p$-curvature conjecture and monodromy about simple closed loops

## Fall 2016

 September 9th Chao Li (Columbia) Congruence between Heegner points and applications to elliptic curves September 16th David Hansen (Columbia) How to filter a modified vector bundle for fun and profit I September 23rd David Hansen (Columbia) How to filter a modified vector bundle for fun and profit II September 30th Patrick Allen ( U. Illinois Urbana-Champaign) Automorphic points in polarized deformation space October 28th Brandon Levin (U. Chicago) Weight elimination in Serre-type conjectures November 4th Chen Wan (U. Minnesota) Multiplicity one theorem for the Ginzburg-Rallis model November 11th Yihang Zhu (Harvard) The Hasse-Weil zeta functions of the intersection cohomology of minimally compactified orthogonal Shimura varieties November 18th Sean Howe (U. Chicago) Overconvergent modular forms and the p-adic Jacquet-Langlands correspondence. December 2nd Francesc Castella (Princeton) On Howard's and Greenberg's nonvanishing conjectures.

## Spring 2016

 February 5th Jacques Tilouine (Paris 13) Galois levels and congruence ideals for p-adic families of automorphic forms February 26th Michael Rapoport (Bonn) On the Drinfeld moduli problem of p-divisible groups March 4th Sarah Zerbes Euler systems for Rankin-Selberg convolutions and generalisations March 11th Wei Zhang (Columbia) Cycles on the moduli of Shtukas and Taylor coefficients of L-functions March 25th Francesco Lemma (IMJ) Higher regulators and non-critical values of degree eight L-functions for GSp(4)xGL(2) April 1st Nicolas Templier (Cornell) Kloosterman families, Quantum coholomogy and geometric Langlands April 8th Jie Lin (Paris) An automorphic version of the Deligne conjecture April 15th Daniel Kriz (Princeton) Generalized Heegner cycles and congruences of p-adic L-functions April 22nd (10 am) Haruzo Hida (UCLA) A new type of Taylor--Wiles system. April 22nd (11 am) Ashay Burungale (U. of Arizona) Horizontal variation of Mordell-Weil groups April 29th Cheng-Chiang Tsai (IAS) Old and new methods on orbital integrals May 16th (2:30 pm) Shai Haron (Technion) New Foundations for Geometry

## Fall 2015

 September 11th David Hansen (Columbia) Motivic cohomology actions and the geometry of eigenvarieties October 16th Carl Erickson (Brandeis University) Modularity of ordinary Galois representations via coarse moduli November 13th Arthur-Cesar Lebras (IMJ) Drinfeld's coverings and the $p$-adic Langlands correspondence November 20th Laurent Fargues (IMJ/CNRS & Chicago) p-adic twistors December 11th Ila Varma (Harvard) Crystallinity of Galois representations associated to regular algebraic cuspidal representations of GL(n)

## Spring 2015

 February 9th Atsushi Ichino (Kyoto University) On the formal degrees of square-integrable representations of odd special orthogonal and metaplectic groups April 10th Christopher Skinner (Princeton) The p-part of the BSD formula in ranks zero and one. April 24th Przemyslaw Chojecki (Oxford) Companion points on definite unitary eigenvarieties May 8th Eknath Ghate (TIFR and IAS) Reductions of Galois representations of small slopes

## Fall 2014

 September 19th Francesc Castella (UCLA) Heegner cycles and p-adic L-functions October 3rd Benoit Stroh (Paris-Nord) Hecke algebras and Shimura varieties October 10th Giovanni Rosso (Columbia & U. Leuven) Derivative of the symmetric square p-adic L-function via pull-back formula October 24th Dipendra Prasad (TIFR) Branching laws and period integrals for non-tempered representations November 7th Shrenik Shah (Columbia) Some strong twisted base changes for unitary similitude groups November 21st Xin Wan (Columbia) Iwasawa Main Conjecture for Supersingular Elliptic Curves December 12th Riccardo Brasca Hida theory over some Shimura varieties without ordinary locus.

## Spring 2014

 February 7th Eric Urban Introduction/presentation of the seminar February 14th David Hansen (Jussieu) p-adic L-functions for GL(2) February 28th Feiqi Jiang Hida Theory for GL(2) March 7th Pak-Hin Lee Compact operators on p-adic Banach spaces and applications March 14th Xin Wan The canonical subgroup (after Fargue) March 28th Daniel Disegni (MacGill) p-adic Gross-Zagier formulas for Shimura curves April 4th Daniel Gulotta Overconvergent modular forms (after Pilloni) April 18th Zheng Liu Overconvergent Siegel modular forms (after Andreatta-Iovita-Pilloni) April 25th Jeanine Van Order (Eisntein Institute of Math.) Average values of automorphic L-functions via spectral decomposition of shifted convolution sums. May 30th at 1pm Vincent Pilloni (ENS Lyon)) Coherent cohomology and Galois representations

## Fall 2013

 September 27th Shunsuke Yamana (Kyushu University) L-function and Theta correspondence October 4th Wei Zhang (Columbia) Heegner points and a B-SD type conjecture I October 18th John Bergdall (Boston University) Overconvergent companion forms November 1st Wei Zhang (Columbia) Heegner points and a B-SD type conjecture II November 15th Lei Zhang (Boston College) Tensor Product L-functions of Quasi-split Classical Groups of Hermitian Type. November 19th (special lecture at 6pm in 507) Lin Jie (Jussieu) On the Ramanujan conjecture for cuspidal representations of GL_n, after Clozel November 22nd Shrenik Shah (Princeton) Spin L-functions for GSp(6) December 6th Raphael Beuzart-Plessis (IAS) The local Gan-Gross-Prasad conjecture for tempered representations of unitary groups

## Spring 2013

 Wednesday Feb.13th Florian Sprung (Brown U.) The arithmetic of elliptic curves in towers of number fields Wednesday March 13th Michael Rapoport (U. Bonn) Towards a theory of local Shimura varieties Wednesday April 3rd Manish Patnaik (U. of Alberta and Brown) Hecke Algebras for p-adic Loop Groups Wednesday April 17th Philippe Blanc (Inst. de Mathmatiques de Luminy) Rational building of H-invariant distributions on induced G-modules for G/H  a symmetric, reductive, p-adic space Monday May 13th Giovanni Rosso (U. Paris 13) Trivial zero for the symmetric square of an elliptic curve over a totally real field Monday June 10th Romyar Sharifi (U. Arizona) Refining the Iwasawa main conjecture

## Fall 2012

 Friday Oct. 26th Michael Harris (Paris 7) Central values of Rankin-Selberg L-functions and period relations Friday Nov. 2nd Xin Wan (IAS) Iwasawa Theory for Unitary Groups Friday Nov. 9th Rachel Ollivier (Columbia) Duality for representations of pro-p Iwahori-Hecke algebras Friday Nov. 30th Marc Masdeu (Columbia) Computing Darmon points Friday Dec. 7th Stefano Morra (U. Toronto) Cohomology of p-adic analytic groups and Iwasawa theory in the p-modular Langlands Program

Organizer: Eric Urban