Number Theory Seminar

Jun 04 2020

Dynamical generalizations of the Prime Number Theorem and disjointness of additive and multiplicative actions

Speaker: Florian Richter
3:00pm |
  One of the fundamental challenges in number theory is to understand the intricate way in which the additive and multiplicative structures in the integers intertwine. We will explore a dynamical approach to this topic. After introducing a new dynamical framework for...
May 28 2020

Joint equidistribution of adelic torus orbits and families of twisted L-functions

Speaker: Farrell Brumley
10:00am |
The classical Linnik problems are concerned with the equidistribution of adelic torus orbits on the homogeneous spaces attached to inner forms of GL2, as the discriminant of the torus gets large. When specialized, these problems admit beautiful classical interpretations,...
May 21 2020

Iwasawa theory and Bloch-Kato conjecture for unitary groups

Speaker: Xin Wan
9:00am |
We describe a new method to study Eisenstein family and Iwasawa theory on unitary groups over totally real fields of general signatures. As a consequence we prove that if the central L-value of a cuspidal eigenform on the unitary group twisted by a CM character is 0, then...
May 14 2020

A geometric view on Iwasawa theory

Speaker: Mladen Dimitrov
2:30pm |
We will investigate the geometry of the p-adic eigencurve at classical points where the Galois representation is locally trivial at p, and will give applications to Iwasawa and Hida theories.
May 07 2020

On triple product L functions

Speaker: Jayce Robert Getz
4:30pm |
Establishing the conjectured analytic properties of triple product L-functions is a crucial case of Langlands functoriality. However, little is known. I will present work in progress on the case of triples of automorphic representations on GL_3; in some sense this is the smallest case that...
Apr 30 2020

Eulerianity of Fourier coefficients of automorphic forms

Speaker: Henrik Gustafsson
4:30pm |
The factorization of Fourier coefficients of automorphic forms plays an important role in a wide range of topics, from the study of L-functions to the interpretation of scattering amplitudes in string theory. In this talk I will present a transfer theorem which derives the Eulerianity of...
Apr 23 2020

Symmetric power functoriality for holomorphic modular forms

Speaker: Jack Thorne
9:00am |
Langlands’s functoriality conjectures predict the existence of “liftings” of automorphic representations along morphisms of L-groups. A basic case of interest comes from the irreducible algebraic representations of GL(2), thought of as the L-group of the reductive group GL(2...
Apr 16 2020

Local-global compatibility in the crystalline case

Speaker: Ana Caraiani
3:00pm |
Let F be a CM field. Scholze constructed Galois representations associated to classes in the cohomology of locally symmetric spaces for GL_n/F with p-torsion coefficients. These Galois representations are expected to satisfy local-global compatibility at primes above p. Even...
Apr 09 2020

On the Kudla-Rapoport conjecture

Speaker: Chao Li
4:30pm |
The Kudla-Rapoport conjecture predicts a precise identity between the arithmetic intersection number of special cycles on unitary Rapoport-Zink spaces and the derivative of local representation densities of hermitian forms. It is a key local ingredient to establish the...
Apr 02 2020

Density conjecture for horizontal families of lattices in SL(2)

Speaker: Mikolaj Fraczyk
4:30pm |
Let G be a real semi-simple Lie group with an irreducible unitary representation \pi. The non-temperedness of \pi is measured by the parameter p(\pi) which is defined as the infimum of p\geq 2 such that \pi has matrix coefficients in L^p(G). Sarnak and Xue conjectured that...