ENYGMMa I

Schedule

11:30 am - 12:50 pm Lunch at Simons Center Cafe

12:50 pm - 1:00 pm Opening Remarks

1:00 pm - 2:00 pm Talk by Dusa McDuff

2:00 pm - 2:30 pm Break

2:30 pm - 3:30 pm Talk by Daniela De Silva

3:30 pm - 3:45 pm Tea

3:45 pm - 4:45 pm Talk by Delaram Kahrobaei

5:00 pm - 6:30 pm Dinner

Arrival: if arriving before 11:30 a.m., please meet the organizers in the lobby of the Simons Center. Otherwise, you can come directly to the cafe for lunch.

Titles and Abstracts

Dusa McDuff: Embedded questions in symplectic geometry - Introduction and some recent results

A symplectic structure is a rather elusive geometric structure that can be put on an even dimensional space. After a brief introduction to its basic properties, I will introduce the symplectic embedding problem, explain its importance, and then discuss some recent developments in the calculation of the ellipsoidal capacity function for the ball (and perhaps other target spaces).

Daniela De Silva: On free boundary problems

In this talk, we will present an overview of techniques and results concerning the regularity theory for Free Boundary Problems (FBP); that is, problems in which one must solve a PDE and along the way find out the region in which the PDE holds. FBPs naturally arise in a variety of applications and research in this area has been very fruitful and active for several decades. Using the Bernoulli one-phase problem as a basic elliptic model, we will highlight main contributions and open questions often originating from a striking resemblance with the regularity theory for minimal surfaces. We will further consider parabolic problems, including the classical Stefan problem. If time permits it, we will describe so-called thin free boundary problems, in which the free boundary occurs on a lower dimensional subspace, and that arise in connection with non-local phenomena.

Delaram Kahrobaei: Applied Group Theory in the Quantum and Artificial Intelligence Era

In this talk I present an overview of the current state-of-the-art in post-quantum group-based cryptography. I describe several families of groups that have been proposed as platforms, with special emphasis in polycyclic groups and graph groups, dealing in particular with their algorithmic properties and cryptographic applications. I then describe some applications of combinatorial algebra in fully homomorphic encryption, and in particular homomorphic machine learning. I will discuss several open problems in this direction (https://arxiv.org/abs/2202.05917 to appear in the Notices of AMS).