Prochains séminaires
Séminaires passés
Jeudi 10 Avril 2014, à 16h15, Villa Battelle
Grigory Mikhalkin (UniGe)
The so-called "Gromov-Witten invariants" are known to provide a field theory
set-up where the evolution is described by means of enumeration of
holomorphic
curves passing via certain constraints (points, etc.). In some simple
situations
these curves collapse to metric graphs known as "tropical curves".
On one hand the tropical curves can be interpreted as worldlines of
interacting
particles. On another hand their enumeration literally coincides with
that given
by the holomorphic curves through passing the so-called tropical limit. This
provides a down-to-earth interpretation for Gromov-Witten theories and alike
in simple cases, in particular for toric surfaces and 3-folds. In the
talk we review
the basic notions related to tropical enumeration and its interpretations.
Jeudi 3 Avril 2014, à 16h15, Villa Battelle
Rinat Kashaev (UniGe)
Twenty years ago, in 1994, Ludwig Faddeev discovered that the five term functional relation f(p)f(q)=f(q)f(p+q)f(p), where p and q are Heisenberg's momentum and position operators, is satisfied by a special function called "quantum dilogarithm". Faddeev's relation underlies many applications of the quantum dilogarithm in mathematical physics and quantum topology. This talk will be a review of some of the remarkable properties of this function.
Lundi 3 Fevrier 2014, à 14h30, Villa Battelle
Michael Polyak (Technion)
We will discuss the relation of Kontsevich's quantization of Poisson
structures to configuration spaces and their maps. We will also explain how algebraic properties of the Kontsevich's star-product are related to geometric properties of configuration spaces and the Jacobi relation on Feynman graphs.
Mercredi 5 Fevrier 2014, à 17h15, Villa Battelle
Tobias Ekholm (Uppsala)
We introduce knot contact homology and describe how to compute it from a
braid representation of a knot. We also discuss generalizations of the
theory and its relation to the HOMFLY polynomial.
Vendredi 10 janvier 2014, 11h00, Villa Battelle
Anton ALEXEEV (UniGe)
We recall the Kostant's approach to geometric quantization and illustrate it with an example of the Borel-Weil-Bott Theorem on quantization of coadjoint orbits of compact Lie groups.
Tropical curve enumeration and its interpretations in two and three
dimensions.
The quantum dilogarithm.
Deformation quantization of Poisson structures and geometry of configuration spaces.
Knot contact homology and its ramifications.
Introduction to geometric quantization .