Du 27 au 29 mai 2019
IRMA
Organizers : Carlo Gasbarri, Nalini Ananthamaran (IRMA Strasbourg)
Speakers (list in progress) :
- Andrei Okounkov (Columbia University, New York)
- Barbara Fantechi (SISSA, Trieste)
- Vladimir Fock (IRMA, Strasbourg)
- Guo-Niu Han (IRMA, Strasbourg)
- Gianluca Pacienza (IECL, Nancy)
Venue : Grand Amphithéâtre, UFR de Mathématique et Informatique, University of Strasbourg.
-
Lundi 27 mai 2019
-
09:30
Andrei Okounkov, Columbia University, NY
Multivariate special functions and duality from the point of view of enumerative geometry, I
Special functions in this lecture series will be generalizations of
characters of irreducible representations of Lie groups, spherical
functions of symmetric spaces, and more general Macdonald-type
hypergeometric functions. They are not all that special from the point
of view of analysis, because they satisfy certain linear differential or
q-difference equations. However, these difference equations have a very
delicate structure involving roots, coroots, and the like. In
particular, they enjoy a certain powerful Langland-like duality, which
in the Lie groups context would interchange the argument of the
functions, that is, an element in the maximal torus of the groups $G$
with the label of the function, which has to do with the highest weight
and the dual torus. In this lecture series, my goal is to explain this
phenomenon from the point of view of enumerative geometry and related
modern high-energy physics. This seems to be a natural generality in
which to consider these questions, in particular, it is much broader
than the domain of the traditional Lie theory. -
14:00
Barbara Fantechi, SISSA, Trieste
Algebraic and symplectic methods in enumerative geometry, I
We start with a brief historical overview of classical enumerative geometry, focused on definitions and examples. We then introduce the notion of stable map to a projective complex manifold, motivate the need for a virtual fundamental class, and outline is definition in the algebraic and symplectic language. We emphasize the differences (and indeed the complementarity) among the two approaches. Prerequisites: differentiable manifolds, holomorphic functions of one complex variable, differential forms. A nodding acquaintance with any homology theory, basic category theory and vector bundles would be helpful but is not necessary. -
15:30
Guo-Niu Han, IRMA, Strasbourg
Hook length expansion technique for integer partitions I
-
Mardi 28 mai 2019
-
09:30
Andrei Okounkov, Columbia University, NY
Multivariate special functions and duality from the point of view of enumerative geometry, II
-
14:00
Gianluca Pacienza, IECL, Nancy
A survey on Newton-Okounkov bodies from the viewpoint of algebraic geometry
-
Mercredi 29 mai 2019
-
09:30
Barbara Fantechi, SISSA, Trieste
Algebraic and symplectic methods in enumerative geometry II
-
11:00
Guo-Niu Han, IRMA, Strasbourg
Hook length expansion technique for integer partitions II
-
14:00
Andrei Okounkov, Columbia University, NY
Multivariate special functions and duality from the point of view of enumerative geometry, III