Apr 15 2019

### Etale and crystalline companions

Speaker: Kiran Kedlaya

2:00pm | Simonyi Hall 101
Deligne's "Weil II" paper includes a far-reaching conjecture to the effect that for a smooth variety on a finite field of characteristic p, for any prime l distinct from p, l-adic representations of the etale fundamental group do not occur in isolation: they always exist in...

Apr 01 2019

### A recent perspective on invariant theory

Speaker: Viswambhara Makam

2:00pm | Simonyi Hall 101
Invariant theory is a fundamental subject in mathematics, and is potentially applicable whenever there is symmetry at hand (group actions). In recent years, new problems and conjectures inspired by complexity have come to light. In this talk, I will describe some of these...

Mar 25 2019

### The general case?

Speaker: Amie Wilkinson

2:00pm | Simonyi Hall 101
In the early 1930's, the Ergodic theorems of von Neumann and Birkhoff put Boltzmann's Ergodic Hypothesis in mathematical terms, and the natural question was born: is ergodicity the "general case" among conservative dynamical systems? Oxtoby and Ulam tackled this question...

Mar 18 2019

### Tracking trajectories in Hamiltonian systems using holomorphic curve tools.

Speaker: Barney Bramham

2:00pm | Simonyi Hall 101
The goal is to describe how techniques from symplectic dynamics can be used to study orbit travel in three dimensions, for systems like the restricted 3-body problem from celestial mechanics. The pseudo-holomorphic curve theory initiated by Hofer, Wysocki and Zehnder gives a...

Mar 11 2019

### Geometry of 2-dimensional Riemannian disks and spheres.

Speaker: Regina Rotman

2:00pm | Simonyi Hall 101
I will discuss some geometric inequalities that hold on Riemannian 2-disks and 2-spheres. For example, I will prove that on any Riemannian 2-sphere there M exist at least three simple periodic geodesics of length at most 20d, where d is the diameter of M, (joint...

Feb 25 2019

### Positive geometries

Speaker: Thomas Lam

2:00pm | Simonyi Hall 101
Positive geometries are real semialgebraic sets inside complex varieties characterized by the existence of a meromorphic top-form called the canonical form. The defining property of positive geometries and their canonical forms is that the residue structure of the canonical...

Feb 11 2019

### Quantum Jacobi forms and applications

Speaker: Amanda Folsom

2:00pm | Simonyi Hall 101
Quantum modular forms were defined in 2010 by Zagier; they are somewhat analogous to ordinary modular forms, but they are defined on the rational numbers Q as opposed to the upper half complex plane H, and they transform in Q under the action of the modular group, but only...

Feb 04 2019

### The Sample Complexity of Multi-Reference Alignment

Speaker: Philippe Rigollet

2:00pm | Simonyi Hall 101
How should one estimate a signal, given only access to noisy versions of the signal corrupted by unknown cyclic shifts? This simple problem has surprisingly broad applications, in fields from aircraft radar imaging to structural biology with the ultimate goal of...