Video Lectures

The problem of classification of perverse sheaves on the quotient h/W for a semisimple Lie algebra g has an explicit answer which turns out to be related to the algebraic properties of induction and restriction operations for parabolic subalgebras...

The Hecke algebra admits an involution which preserves the standard basis and exchanges the canonical basis with its dual. This involution is categorified by "monoidal Koszul duality" for Hecke categories, studied in positive characteristic in my...

I'll present joint work with Tsao-Hsien Chen on the geometry of real and symmetric matrices. For classical groups, we use hyperkahler geometry to lift the Kostant-Sekiguchi correspondence to an equivariant homeomorphism. As an application, we show...

Polymers are macromolecules that cannot cross each other without breaking their bonds. This leads to polymer chain entanglement which determines bulk viscoelastic responses of the material. Understanding the relation between entanglement and...

Triangulated categories play an important role in symplectic topology. The aim of this talk is to explain how to combine triangulated structures with persistence module theory in a geometrically meaningful way. The guiding principle comes from the...

Earth-based radar observations in 2006–2019 enable the first measurement of the spin precession rate and moment of inertia of Venus. The observations also show that the spin period of the solid planet changes by tens of minutes. The length-of-day...

The Generalized Ramanujan Conjecture (GRC) for GL(n) is a central open problem in modern number theory. Its resolution is known to yield several important applications. For instance, the Ramanujan-Petersson conjecture for GL(2), proven by Deligne...

Given a representation of a reductive group, Braverman-Finkelberg-Nakajima defined a Poisson variety called the Coulomb branch, using a convolution algebra construction. This variety comes with a natural deformation quantization, called a Coulomb...

For a finite group G one has a process of modular reduction which takes a KG-module, over a field K of characteristic zero, and produces a kG-module, over a field k of positive characteristic. Starting with a simple KG-module its modular reduction...

Reverse plane partitions - or RPPs for short - are order reversing maps of minuscule posets in types ADE. We report on joint work in progress with Elek, Kamnitzer, Libman, and Morton-Ferguson in which we give a type independent proof that RPPs form...