Video Lectures

We show that various classical theorems of linear incidence geometry, such as the theorems of Pappus, Desargues, Möbius, and so on, can be interpreted as special cases of a general result that involves a tiling of a closed oriented surface by...

The Boone-Higman conjecture (1973) predicts that a finitely generated group has solvable word problem if and only if it embeds in a finitely presented simple group. The "if" direction is true and easy, but the "only if" direction has been open for...

Parallels between elliptic and parabolic theory of partial differential equations have long been explored. In particular, since elliptic theory can be seen as a steady-state version of parabolic theory, if a parabolic estimate holds, then by...

In this talk we discuss a relation between the contact version

of the Hofer norm and positive loops of contactomorphisms.

This leads to a new criterion for the existence of contractible positive

loops in terms of open book decompositions and previously...

For every finite set of points in the plane, if every line going through any two of them contains a third, then they all lie on a single line. This ``local-to-global" theorem (which you can play with proving)  has many generalizations, to higher...

I will explain how several different moduli spaces of bundles on a smooth projective curve have abelian motives. Our starting point is a formula for the motive of the stack of vector bundles on the curve in Voevodsky's category of motives with...

Hel Braun (IAS member 1947-1948) was a mathematician who introduced approaches that continue to impact research today.  Braun's research contributions lie in three areas: classical number theory problems about integers, modular and automorphic forms...

In both computer science and economics, efficiency is a cherished property. The field of algorithms is almost solely focused on their efficiency. The goal of AI research is to increase efficiency by reducing human labor.  In economics, the main...

The parametrised Whitehead torsion is an invariant of families of manifolds, and can be viewed as a map to an algebraic K-theory space. A strong version of the nearby Lagrangian conjecture says that when applied to families of closed exact...

In this talk I will construct a “quasisymmetric flag variety”, a subvariety of the complete type A  flag variety built by adapting the BGG geometric construction of divided differences to the newly introduced “quasisymmetric divided differences”...