Events and Activities

We briefly review combinatorics and algebraic representation of reductive groups: root systems, Weyl groups and (extended) affine Weyl groups, weight spaces, and classification of irreducible representations in terms of highest weights. We define...

The Linear Ordering Principle (LOP) is a total search problem that generalizes the task of finding the minimum element of a given order to settings in which the order need not be total. Building on this, Korten and Pitassi (FOCS 2024) introduced the...

The P vs. NP problem was formulated about 50 years ago, and was chosen to be one of the seven Clay millenium problems 25 years ago. In this period our understanding of the depth, breadth and impact of the problem has changed dramatically. I plan to...

In a seminal paper from 2011, Wilfried Schmid and Kari Vilonen made a bold proposal that apparently intractable questions in the representation theory of real reductive groups could be resolved with the help of natural Hodge structures coming from...

Two vector spaces of the same finite dimension are related by a linear isomorphism; that’s how the dimension is defined. Similarly, two simple subalgebras over complex numbers that are closed under conjugate transpose are related by a unitary...

Ricci solitons, introduced by R. Hamilton in the mid-80s, are self-similar solutions to the Ricci flow and natural generalizations of Einstein manifolds. Shrinking Ricci solitons, in particular,  model Type I singularities of the Ricci flow and...

In recent years it has become possible to import some ideas and methods from homogeneous dynamics to the general smooth dynamics setting. I will discuss some results and open problems in this area.  

A Lipschitz velocity field gives a reassuring picture of particle motion: each starting point traces a single, well-defined trajectory. But many velocity fields arising in geometry, kinetic theory, and fluid dynamics are far rougher, and then the...