A few years ago Ichino-Ikeda formulated a quantitative version
of the Gross-Prasad conjecture, modeled after the classical work of
Waldspurger. This is a powerful local-to-global principle which is
very suitable for analytic and arithmetic...
The trace formula has been the most powerful and mainstream tool
in automorphic forms for proving instances of Langlands
functoriality, including character relations. Its generalization,
the relative trace formula, has also been used to prove...
Application of Plancherel's theorem to integral kernels
approximating compact period functionals yields estimates on
(global) automorphic Levi-Sobolev norms of the functionals. The
utility of this viewpoint can be illustrated in reconsideration
of...
Abstract:
Associated to an abelian variety A/K is a Galois representation
which describes the action of the absolute Galois group of K on the
torsion points of A. In this talk, we shall describe how large the
image of this representation can be (in...
We study open-closed orbifold Gromov-Witten invariants of toric
Calabi-Yau 3-orbifolds with respect to Lagrangian branes of
Aganagic-Vafa type. We prove an open mirror theorem which expresses
generating functions of orbifold disk invariants in terms...
We consider Galois cohomology groups over function fields F of
curves that are defined over a complete discretely valued
field.
Motivated by work of Kato and others for n=3, we show that
local-global principles hold for
$H^n(F, Z/mZ(n-1))$ for all...
For an abelian surface A over a number field k, we study the
limiting distribution of the normalized Euler factors of the
L-function of A. Under the generalized Sato-Tate conjecture, this
is equal to the distribution of characteristic...
We establish a derived equivalence of the Fukaya category of the
2-torus, relative to a basepoint, with the category of perfect
complexes on the Tate curve over Z[q]. It specializes to an
equivalence, over Z, of the Fukaya category of the...
Welschinger invariants, real analogs of genus 0 Gromov-Witten
invariants, provide non-trivial lower bounds in real algebraic
geometry. In this talk I will explain how to get some wall-crossing
formulas relating Welschinger invariants of the same...
This talk is part of a circle of ideas that one could call
``categorical dynamics''. We look at how objects of the Fukaya
category move under deformations prescribed by fixing an odd degree
quantum cohomology class. This is an analogue of moving...
