Scrambling Time and Causal Structure in a Schwarzchild Black Hole

Peter Shor
December 4, 2018

Please Note: This workshop is not open to the general public, but only to active researchers.

This workshop will focus on quantum aspects of black holes, focusing on applying ideas from quantum information theory.

This meeting is sponsored by the “It from Qubit collaboration” and is followed by the collaboration meeting in New York City.

Symmetry in QFT and Gravity

Hirosi Ooguri
December 4, 2018

Please Note: This workshop is not open to the general public, but only to active researchers.

This workshop will focus on quantum aspects of black holes, focusing on applying ideas from quantum information theory.

This meeting is sponsored by the “It from Qubit collaboration” and is followed by the collaboration meeting in New York City.

Recent Progress on Zimmer's Conjecture

David Fisher
Indiana University, Bloomington; Member, School of Mathematics
December 3, 2018
Lattices in higher rank simple Lie groups are known to be extremely rigid. Examples of this are Margulis' superrigidity theorem, which shows they have very few linear represenations, and Margulis' arithmeticity theorem, which shows they are all constructed via number theory. Motivated by these and other results, in 1983 Zimmer made a number of conjectures about actions of these groups on compact manifolds and in a recent breakthrough with Brown and Hurtado we have proven many of them.

Mean action of periodic orbits of area-preserving annulus diffeomorphisms

Morgan Weiler
University of California, Berkeley
December 3, 2018
An area-preserving diffeomorphism of an annulus has an "action function" which measures how the diffeomorphism distorts curves. The average value of the action function over the annulus is known as the Calabi invariant of the diffeomorphism, while the average value of the action function over a periodic orbit of the diffeomorphism is the mean action of the orbit.

Branched conformal structures and the Dyson superprocess

Govind Menon
Brown University; Member, School of Mathematics
November 30, 2018

In the early 1920s, Loewner introduced a constructive approach to the Riemann mapping theorem that realized a conformal mapping as the solution to a differential equation. Roughly, the “input” to Loewner’s differential equation is a driving measure and the “output” is a family of nested, conformally equivalent domains. This theory was revitalized in the late 1990s by Schramm. The Schramm-Loewner evolution (SLE) is a stochastic family of slit mappings driven by Loewner’s equation when the driving measure is an atom executing Brownian motion.

The Lucky Logarithmic Derivative

Will Sawin
Columbia University
November 29, 2018
We study the function field analogue of a classical problem in analytic number theory on the sums of the generalized divisor function in short intervals, in the limit as the degrees of the polynomials go to infinity. As a corollary, we calculate arbitrarily many moments of a certain family of L-functions, in the limit as the conductor goes to infinity. This is done by showing a cohomology vanishing result using a general bound due to Katz and some elementary calculations with polynomials.

Homotopical effects of k-dilation

Larry Guth
Massachusetts Institute of Technology
November 27, 2018
Back in the 70s, Gromov started to study the relationship between the Lipschitz constant of a map (also called the dilation) and its topology. The Lipschitz constant describes the local geometric features of the map, and the problem is to understand how it relates to the global geometric features of the map -- a bit like trying to understand the relationship between the curvature of a Riemannian manifold and its topology.