Année 2016- 2017

Greg Kuperberg - UC Davis

Geometric Topology Meets Computational Complexity

Jeudi 2 février 17:00-18:00

Jussieu, salle 15-25-502

Now that the geometrization conjecture has been proven, and the virtual Haken conjecture has been proven, what is left in 3-manifold topology ? One remaining topic is the computational complexity of geometric topology problems. How difficult is it to distinguish the unknot ? Or 3-manifolds from each other ? The right approach to these questions is not just to consider quantitative complexity, i.e., how much work they take for a computer ; but also qualitative complexity, whether there are efficient algorithms with one or another kind of help. I will discuss various results on this theme, such as that knottedness and unknottedness are both in NP ; and I will discuss high-dimensional questions for context.

Gonçalo Tabuada - MIT

Noncommutative Motives

Jeudi 12 janvier 17:00-18:00

Bât. Sophie Germain, amphi Turing

The theory of motives, introduced in the sixties, studies the common properties of the different cohomology theories (de Rham, Betti, etale, crystalline, etc) of algebraic varieties. In the same vein, the theory of noncommutative motives, introduced much more recently, studies the common properties of the different invariants (K-theory, cyclic homology, topological Hochschild homology, etc) of "noncommutative algebraic varieties". The bridge from the former theory to the latter consists of the passage from an algebraic variety to its derived category. The aim of this talk, prepared for a broad audience, is to give an overview of the theory of noncommutative motives and to describe some of its manyfold applications to adjacent areas of mathematics.

Hugo Duminil-Copin - IHES

Universalité et modèle d’Ising planaire

Jeudi 24 novembre 2016 17:00-18:00

Jussieu, salle 15-25-502

Le modèle d’Ising, introduit au début du vingtième siècle, décrit la transition de phase des matériaux ferro/paramagnétiques. Depuis son introduction, ce modèle a non seulement eu un impact retentissant sur la compréhension physique des phénomènes de changements d’états, mais il a également été à l’origine de profondes théories en mathématiques. Dans cet exposé, nous présenterons certaines de ces théories ainsi que le concept d’universalité en physique statistique en prenant l’exemple du modèle d’Ising sur les réseaux planaires.

János Kollár - Princeton University

Celestial surfaces and quadratic forms

Jeudi 27 octobre 2016 17:00-18:00

Bât. Sophie Germain, salle 1016

We discuss a project, started by Kummer and Darboux, to describe all surfaces that contain at least 2 circles through every point by relating it to the problem of finding polynomial solutions of quadratic forms.

Dusa McDuff - Columbia

Symplectic Topology today

Lundi 10 octobre 2016 16:45-18:00

amphi Astier, bâtiment Esclangon, Jussieu

This talk will describe the main features of symplectic topology, why it is interesting, some known results and some open questions. It will be aimed at a general audience who have some mathematical knowledge, but know nothing about symplectic geometry and topology.