Mon, 14 May 2018
15:45
L6

Lie groupoids and index theory

Georges Skandalis
(Paris VII)
Abstract

My talk is based on joint work with Claire Debord (Univ. Auvergne).
We will explain why Lie groupoids are very naturally linked to Atiyah-Singer index theory.
In our approach -originating from ideas of Connes, various examples of Lie groupoids
- allow to generalize index problems,
- can be used to construct the index of pseudodifferential operators without using the pseudodifferential calculus,
- give rise to proofs of index theorems, 
- can be used to construct the pseudodifferential calculus.

Thu, 18 Oct 2012

16:00 - 17:00
L3

Rational points of bounded height over number fields.

Daniel Loughran
(Paris VII)
Abstract

Given a variety X over a number field, one is interested in the collection X(F) of rational points on X. Weil defined a variety X' (the restriction of scalars of X) defined over the rational numbers whose set of rational points is naturally equal to X(F). In this talk, I will compare the number of rational points of bounded height on X with those on X'.

Mon, 27 Oct 2008
15:45
Oxford-Man Institute

Backward SDEs with constrained jumps and Quasi-Variational Inequalities

Prof. Huyen Pham
(Paris VII)
Abstract

We introduce a class of backward stochastic differential equations (BSDEs) driven by Brownian motion and Poisson random measure, and subject to constraints on the jump component. We prove the existence and uniqueness of the minimal solution for the BSDEs by using a penalization approach. Moreover, we show that under mild conditions the minimal solutions to these constrained BSDEs can be characterized as the unique viscosity solution of quasi-variational inequalities (QVIs), which leads to a probabilistic representation for solutions to QVIs. Such a representation in particular gives a new stochastic formula for value functions of a class of impulse control problems. As a direct consequence we obtain a numerical scheme for the solution of such QVIs via the simulation of the penalized BSDEs. This talk is based on joint work with I. Kharroubi, J. Ma and J. Zhang.

Thu, 24 Apr 2008
13:00
Gibson 1st Floor SR

Some results on the three dimensional Navier-Stokes equations

I. Gallagher
(Paris VII)
Abstract
It is well known that the three dimensional, incompressible Navier-Stokes equations have a unique, global solution provided the initial data is small enough in a scale invariant space (say L3 for instance). We are interested in finding examples for which no smallness condition is imposed, but nevertheless the associate solution is global and unique. The examples we will present are due to collaborations with Jean-Yves Chemin, and with Marius Paicu.
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