Video Lectures

In their 2001 paper, Hofer, Wysocki and Zehnder conjectured that every autonomous Hamiltonian flow has either two or infinitely many simple periodic orbits on any compact star-shaped energy level; in the same paper, the authors prove this assuming...

Over the last two decades we have developed good understanding how to quantify the impact of strategic user behavior on outcomes in many games (including traffic routing and online auctions) and showed that the resulting bounds extend to repeated...

In spite of tremendous progress in the mean-field theory of spin glasses in the last forty years, culminating in Giorgio Parisi’s Nobel Prize in 2021, the more “realistic” short-range spin glass models have remained almost completely intractable. In...

Given a Lagrangian torus fibration on the complement of an anticanonical divisor in a Kahler manifold, one usually constructs a mirror space by gluing local charts (moduli spaces of objects of the Fukaya category supported on generic torus fibers)...

In the early 2000’s Ruijsenaars and Felder-Varchenko have introduced the elliptic gamma function, a remarkable multivariable meromorphic q-series that comes from mathematical physics. It satisfies modular functional equations under the group SL3(Z)...

I will discuss recent progress on approximating the metric traveling salesperson problem, focusing on a line of work beginning in 2011 that studies the behavior of the max entropy algorithm. This algorithm is a randomized variant of the beautiful...

In the search for possible blow-up of the incompressible Navier-Stokes equations, there has been much recent attention on the class of axisymmetric solutions with swirl. Several interesting structures of this system have led to regularity criteria...

An old open question in symplectic topology is whether all normalized capacities coincide on convex bounded domains in the standard symplectic vector space. I will discuss this question for domains which are close to the Euclidean ball and its...

I will present a new theory of motivic cohomology for general (qcqs) schemes. It is related to non-connective algebraic K-theory via an Atiyah-Hirzebruch spectral sequence. In particular, it is non-A1

-invariant in general, but it recovers classical...

Consider the process where a signal propagates downward an infinite rooted tree. On every edge some independent noise is applied to the signal. The reconstruction problem asks whether it is possible to reconstruct the original signal given...