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...
I will report on some recent work on multiple zeta values. I
will sketch the definition of motivic multiple zeta values, which
can be viewed as a prototype of a Galois theory for certain
transcendental numbers, and then explain how they were used...
The families of motives of the title arise from classical
one-variable hypergeometric functions. This talk will focus on the
calculation of their corresponding L-functions both in theory and
in practice. These L-functions provide a fairly wide...
