# Video Lectures

We consider systems of NN particles interacting through a repulsive potential in the Gross-Pitaevskii regime. We prove complete Bose-Einstein condensation and we determine the form of the low-energy spectrum, in the limit of large NN. Our results...

The celebrated Brunn-Minkowski inequality states that for compact subsets XX and YY of ?dRd, m(X+Y)1/d?m(X)1/d+m(Y)1/dm(X+Y)1/d?m(X)1/d+m(Y)1/d where m(?)m(?) is the Lebesgue measure. We will introduce a conjecture generalizing this inequality to...

"Games against Nature" [Papadimitriou '85] are two-player games of perfect information, in which one player's moves are made randomly. Estimating the value of such games (i.e., winning probability under optimal play by the strategic player) is an...

The talk will focus on the question of whether existing symplectic methods can distinguish pseudo-rotations from rotations (i.e., elements of Hamiltonian circle actions). For the projective plane, in many instances, but not always, the answer is...

This talk covers Chapters 4 and 5 in Jantzen's book.

The linkage principle says that the category of representations of a reductive group GG in positive characteristic decomposes into "blocks" controlled by the affine Weyl group. We will discuss the beautiful geometric proof of this result that Simon...

Determining whether or not a given finitely generated group is permutation stable is in general a difficult problem. In this talk we discuss work of Becker, Lubotzky and Thom which gives, in the case of amenable groups, a necessary and sufficient...

Symplectic implosion was developed to solve the problem that the symplectic cross-section of a Hamiltonian K-space is usually not symplectic, when K is a compact Lie group. The symplectic implosion is a stratified symplectic space, introduced in a...

Smith theory is a type of equivariant localization with respect to a cyclic group of prime order pp, with coefficients in a field of the same characteristic pp. It has been the source of various recent advances in modular representation theory and...

In this lecture I will describe the three concepts appearing in the title and how they connect with each other.