Video Lectures

Abstract: I will discuss recent results regarding the problem of counting intersections of eigenfunction nodal sets with real analytic curves H and the connection to eigenfunction restriction bounds over H.

We present joint work with Jan Maas showing that Quantum Markov semigroups satisfying a detailed balance condition are gradient flow for quantum relative entropy, and use this prove some conjectured inequalities arising in quantum information theory...

I will explain the construction and the geometry of the non-archimedean SYZ fibration.

Abstract: The classical Liouville theorem says that if a harmonic function on the plane is bounded then it is a constant. At the same time for any angle on the plane, there exist non-constant harmonic functions that are bounded outside the angle...

Abstract: We present a sequence of positive quadratic forms associated with harmonic functions on Abelian groups. We show how the positivity property recovers the polynomial Liouville property and we prove a three spheres theorem in terms of random...

Berkovich geometry is an enhancement of classical rigid analytic geometry. Mirror symmetry is a conjectural duality between Calabi-Yau manifolds. I will explain (1) what is mirror symmetry, (2) what are Berkovich spaces, (3) how Berkovich spaces...

I will show a new efficient approximate nearest neighbor search (ANN) algorithm over an arbitrary high-dimensional *symmetric* norm. Traditionally, the ANN problem in high dimensions has been studied over the $\ell_1$ and $\ell_2$ distances with a...

Edward T. Cone Concert Series: February 10, 2017 A concert of new and traditional Balinese music will be performed by Boston’s large percussion orchestra, Gamelan Galak Tika. An ensemble comprised of gongs, metallophones and hand drums, cymbals...