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...
To any essentially self-dual, regular algebraic (ie
cohomological) automorphic representation of GL(n) over a CM field
one knows how to associate a compatible system of l-adic
representations. These l-adic representations occur (perhaps
slightly...
We discuss a quantum counterpart, in the sense of the
Berezin-Toeplitz quantization, of certain constraints on Poisson
brackets coming from "hard" symplectic geometry. It turns out that
they can be interpreted in terms of the quantum noise of...
For GL(2) over Q_p, the p-adic Langlands correspondence is
available in its full glory, and has had astounding applications to
Fontaine-Mazur, for instance. In higher rank, not much is known.
Breuil and Schneider put forward a conjecture, which...
