Video Lectures

Given a set E of Hausdorff dimension s>d/2 in ℝd , Falconer conjectured that its distance set Δ(E)={|x−y|:x,y∈E} should have positive Lebesgue measure. When d is even, we show that dimHE>d/2+1/4 implies |Δ(E)|>0. This improves upon the work of Wolff...

(joint work with Assaf Naor) A key problem in metric geometry asks: given metric spaces X and Y, how well does X embed in Y? In this talk, we will consider this problem for the case of the Heisenberg group and explain its connections to geometric...

We prove new lower bounds on the well known Gap-Hamming problem in communication complexity. Our main technical result is an anti-concentration bound for the inner product of two independent random vectors. We show that if A, B are arbitrary subsets...

A public Presentation by Professor Francesca Trivellato, followed by a discussion with IAS Academic Trustee Lorraine Daston

  Spacetime wormholes have played an important role in recent progress in black hole physics. However, in the context of AdS/CFT, these wormholes lead to a basic puzzle: the "factorization problem", introduced by Maldacena and Maoz. In this talk we...

We will give an explicit construction and description of a supercuspidal local Langlands correspondence for any p-adic group G that splits over a tame extension, provided p does not divide the order of the Weyl group. This construction matches any...

High-precision astrometric data from space observatories, such as the Hubble Space Telescope (HST) and Gaia, are revolutionizing our ability to study the Local Group. 6D phase space measurements (3-dimensional position and velocity) now make it...

Black holes create the most extreme gravitational fields imaginable, and therefore offer a unique and unprecedented opportunity to test our current understanding of gravity. We've known about the existence of black holes in space for many years but...

This is the third talk in a series of three talks on the derived Satake equivalence. I will give an overview of the article of Bezrukavnikov and Finkelberg which explains how the equivariant derived category of the affine Grassmannian can be...

We show that if G=⟨S|E⟩ is a discrete group with Property (T) then E, as a system of equations over S, is not stable (under a mild condition). That is, E has approximate solutions in symmetric groups Sym(n), n≥1, that are far from every solution in...