Tue, 02 Mar 2021
12:00
Virtual

Some mathematical problems posed by the conformal bootstrap program

Slava Rychkov
(IHES)
Abstract

The conformal bootstrap program for CFTs in d>2 dimensions is
based on well-defined rules and in principle it could be easily included
into rigorous mathematical physics. I will explain some interesting
conjectures which emerged from the program, but which so far lack rigorous
proof. No prior knowledge of CFTs or conformal bootstrap will be assumed.

Thu, 18 May 2017
17:30
L6

Theories of presheaf type as a basic setting for topos-theoretic model theory

Olivia Caramello
(IHES)
Abstract

I will review the notion of classifying topos of a first-order (geometric) theory and explain the central role enjoyed by theories of presheaf type (i.e. classified by a presheaf topos) in the context of the topos-theoretic investigation of the model theory of geometric theories. After presenting a few main results and characterizations for theories of presheaf type, I will illustrate the generality of the point of view provided by this class of theories by discussing a topos-theoretic framework unifying and generalizing Fraissé’s construction in model theory and topological Galois theory and leading to an approach to the problem of the independence from l of l-adic cohomology.

Fri, 07 Jun 2013
16:30
L2

Langlands functoriality and non linear Poisson formulas

Professor Laurent Lafforgue
(IHES)
Abstract

"We introduce some type of generalized Poisson formula which is equivalent 
to Langlands' automorphic transfer from an arbitrary reductive group over a 
global field to a general linear group."

Wed, 14 Mar 2012

15:45 - 16:45
L2

(HoRSe seminar) Defining the refined vertex using equivariant K-theory II

Nikita Nekrasov
(IHES)
Abstract

String theory derives the features of the quantum field theory describing the gauge interactions between the elementary particles in four spacetime dimensions from the physics of strings propagating on the internal manifold, e.g. a Calabi-Yau threefold. A simplified version of this correspondence relates the SU(2)-equivariant generalization of the Donaldson theory (and its further generalizations involving the non-abelian monopole equations) to the Gromov-Witten (GW) theory of the so-called local Calabi-Yau threefolds, for the SU(2) subgroup of the rotation symmetry group SO(4). In recent years the GW theory was related to the Donaldson-Thomas (DT) theory enumerating the ideal sheaves of curves and points. On the toric local Calabi-Yau manifolds the latter theory is studied using localization, producing the so-called topological vertex formalism (which was originally based on more sophisticated open-closed topological string dualities).

In order to accomodate the full SO(4)-equivariant version of the four dimensional Donaldson theory, the so-called "refined topological vertex" was proposed. Unlike that of the ordinary topological vertex, its relation to the DT theory remained unclear.

In these talks, based on joint work with Andrei Okounkov, this gap will be partially filled by showing that the equivariant K-theoretic version of the DT theory reproduces both the SO(4)-equivariant Donaldson theory in four dimensions, and the refined topologica vertex formalism, for all toric Calabi-Yau's admitting the latter.

Thu, 04 Mar 2010
14:00
L3

On the field with one element

Pierre Cartier
(IHES)
Abstract
We shall explain how to give substance to an old dream of Tits, to invent exotic new zeta functions, and discover the skeleton of algebraic varieties (toric manifolds and tropial geometry).
Wed, 03 Mar 2010
11:00
L1

On the field with one element

Pierre Cartier
(IHES)
Abstract
We shall explain how to give substance to an old dream of Tits, to invent exotic new zeta functions, and discover the skeleton of algebraic varieties (toric manifolds and tropical geometry).
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