Video Lectures

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...

Powerful techniques have been developed in quantum field theory that employ algebras of local operators, yet local operators cannot create physical charged states in gauge theory or physical nonzero-energy states in perturbative quantum gravity. ...

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...

The so-called galaxy--halo connection is a vast topic concerning how galaxies populate their host dark matter halos.  I will present some works we have made under this grand theme, including (1) the detection of assembly bias signal with the help of...

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”...

Postnikov's divided symmetrization, introduced in the context of volume polynomials of permutahedra, possesses a host of remarkable ``positivity'' properties. These turn out to be best understood using a family of operators we call quasisymmetric...

The Oppenheim conjecture, proved by Margulis in 1986, states that for a non-degenerate indefinite irrational quadratic form Q in n≥

3 variables, the image set Q(Zn) of integral vectors is a dense subset of the real line. Determining the distribution...