Recently Added

A variational approach to the regularity theory for the Monge-Ampère equation

Felix Otto
Max Planck Institute Leipzig
April 20, 2020
We present a purely variational approach to the regularity theory for the Monge-Ampère equation, or rather optimal transportation, introduced with M. Goldman. Following De Giorgi’s philosophy for the regularity theory of minimal surfaces, it is based on the approximation of the displacement by a harmonic gradient, which leads to a One-Step Improvement Lemma, and feeds into a Campanato iteration on the C1,α-level for the displacement, capitalizing on affine invariance.

A Tutorial on Entanglement Island Computations

Raghu Mahajan
Member, School of Natural Sciences, Institute for Advanced Study
April 17, 2020
In this talk we will present details of quantum extremal surface computations in a simple setup, demonstrating the role of entanglement islands in resolving entropy paradoxes in gravity. The setup involves eternal AdS2 black holes in thermal equilibrium with auxiliary bath systems. We will also describe the extension of this setup to higher dimensions using Randall-Sundrum branes.

Equivariant quantum operations and relations between them

Nicholas Wilkins
University of Bristol
April 17, 2020
There is growing interest in looking at operations on quantum cohomology that take into account symmetries in the holomorphic spheres (such as the quantum Steenrod powers, using a Z/p-symmetry). In order to prove relations between them, one needs to generalise this to include equivariant operations with more marked points, varying domains and different symmetry groups. We will look at the general method of construction of these operations, as well as two distinct examples of relations between them.

Local-global compatibility in the crystalline case

Ana Caraiani
Imperial College
April 16, 2020
Let F be a CM field. Scholze constructed Galois representations associated to classes in the cohomology of locally symmetric spaces for GL_n/F with p-torsion coefficients. These Galois representations are expected to satisfy local-global compatibility at primes above p. Even the precise formulation of this property is subtle in general, and uses Kisin’s potentially semistable deformation rings. However, this property is crucial for proving modularity lifting theorems. I will discuss joint work with J.

A New Topological Symmetry of Asymptotically Flat Spacetimes

Uri Kol
New York University
April 13, 2020
Abstract: I will show that the isometry group of asymptotically flat spacetimes contains, in addition to the BMS group, a new dual supertranslation symmetry. The corresponding new conserved charges are akin to the large magnetic U(1) charges in QED. They factorize the Hilbert space of asymptotic states into distinct super-selection sectors and reveal a rich topological structure exhibited by the asymptotic metric.

Legal Theorems of Privacy

Kobbi Nissim
Georgetown University
April 13, 2020
There are significant gaps between legal and technical thinking around data privacy. Technical standards such as k-anonymity and differential privacy are described using mathematical language whereas legal standards are not rigorous from a mathematical point of view and often resort to concepts such as de-identification and anonymization which they only partially define. As a result, arguments about the adequacy of technical privacy measures for satisfying legal privacy often lack rigor, and their conclusions are uncertain.

On the Kudla-Rapoport conjecture

Chao Li
Columbia University
April 9, 2020
The Kudla-Rapoport conjecture predicts a precise identity between the arithmetic intersection number of special cycles on unitary Rapoport-Zink spaces and the derivative of local representation densities of hermitian forms. It is a key local ingredient to establish the arithmetic Siegel-Weil formula and the arithmetic Rallis inner product formula, relating the height of special cycles on Shimura varieties to the derivative of Siegel Eisenstein series and L-functions. We will motivate this conjecture, explain a proof and discuss global applications.