### Centre de recherches mathématiques

Pavillon André-Aisenstadt

Université de Montréal

Salle / Room 6214

14:30 - 15:30

Walter Craig
Directeur du Fields Institute
Department of Mathematics and Statistics, McMaster University

**On the size of the Navier - Stokes singular set**

A beautiful and influential subject in the study of the question of smoothness of solutions for the Navier – Stokes equations in three dimensions is the theory of partial regularity. A major paper on this topic is Caffarelli, Kohn & Nirenberg (1982) which gives an upper bound on the size of the singular set S(u) of a suitable weak solution u. In this talk we describe a complementary lower bound. More precisely, we study the situation in which the energy of a weak solution fails to be continuous at some singular time t = T. We identify a closed set in space on which the L^2 norm concentrates at this time T, and we study microlocal properties of the Fourier transform of the solution in the cotangent bundle T^*(R^3) above this set. Our main result is that energy concentration can only occur on subsets of T^*(R^3) which are sufficiently large. An element of the proof is a novel global estimate on weak solutions of the Navier – Stokes equations which have sufficiently smooth initial data.

15:30 - 16:00

Pause-café / Coffee Break (Salon Maurice-l'Abbé)

16:00 - 17:00

Alejandro Adem
Directeur du PIMS
Department of Mathematics, UBC

**The topology of commuting matrices**

Consider the space of all n-tuples of unitary m x m matrices which pairwise commute. In this talk we will discuss the topology of these spaces of matrices and how they can be used to construct a classifying space for commutativity with many interesting properties.

*Un vin et fromage sera servi au Salon Maurice-l'Abbé suite à la dernière présentation.*

A wine and cheese reception will be held at Salon Maurice-l'Abbé following the last lecture.