Oct 10 2018

### Stirring efficiently

Speaker: Camillo De Lellis

6:00pm | Dilworth Room
I will consider a very simple open problem in the theory of ODEs and give a brief overview on what is known about it. The problem is also an excuse to talk about a widely open subject in modern PDEs.

Apr 11 2018

### Ordinary points mod $p$ of hyperbolic 3-manifolds

Speaker: Mark Goresky

6:00pm | White Levy Room
Hyperbolic 3-manifolds with arithmetic fundamental group exhibit many remarkable number theoretic properties. Is it possible that such manifolds live over finite fields (whatever that means)? In this talk I will give some evidence for this possibility.

Mar 28 2018

### Hyperbolic geometry and quantum invariants in dimension 3

Speaker: Helen Wong

6:00pm | Dilworth Room
The end of the previous century saw radical changes to three-dimensional topology, which arose from two completely different approaches. One breakthrough came from Thurston's introduction of hyperbolic geometry into the field. The second one came from the discovery of new...

Mar 14 2018

### Synthetic homotopy theory: going beyond set-level mathematics

Speaker: Guillaume Brunerie

6:00pm | Dilworth Room
In addition to offering a formal system for doing ordinary (or "set-level") mathematics, Vladimir Voevodsky’s Univalent Foundations also suggest a new way of studying homotopy theory, called "synthetic homotopy theory". I will show how synthetic homotopy theory...

Feb 28 2018

### Bad behavior

Speaker: Lillian Pierce

6:00pm | Dilworth Room
What do you do with a person who behaves in the worst possible way at every point in time? Well, I don’t know. But if you ask instead about an operator that picks out the worst possible behavior of a function, we sometimes know how to control it. We’ll mention some classical...

Feb 21 2018

### Dimension and support of the harmonic measure or What do Brownian travelers see?

Speaker: Svitlana Mayboroda

6:00pm | Dilworth Room
Harmonic measure of a portion of the boundary is the probability that a Brownian traveler starting inside the domain exits through this portion of the boundary. It is also a simplest building block of any harmonic function in a domain. Some questions pertaining to the...

Feb 14 2018

### The ubiquity of matrix tuples across mathematics

Speaker: Avi Wigderson

6:00pm | Dilworth Room
Our object of interest will be tuples matrices over a field.
I will explain how different views of this object by diverse fields of mathematics give rise to important questions in these areas, which turn out to be surprisingly tightly connected. These areas include...

Feb 07 2018

### An Introduction to Univalent Foundations

Speaker: Daniel Grayson

6:00pm | Dilworth Room
The Univalent Foundations of Voevodsky offer not only a formal language for use in computer verification of proofs, but also a foundation of mathematics alternative to set theory, in which propositions and their proofs are mathematical objects, and which offers a hierarchy...

Jan 31 2018

### Randomness to Structure

Speaker: Alex Kontorovich

6:00pm | Dilworth Room
We will describe several situations in number theory and geometry in which one recovers a sought-after structure by first constructing a “random” approximation to it.