Jul 22 2020

### Singularities of solutions of the Hamilton-Jacobi equation. A toy model: distance to a closed subset.

Speaker: Albert Fathi

5:30pm | Remote Access Only
This is a joint work with Piermarco Cannarsa and Wei Cheng.
Most of the lecture is about the distance function to a closed subset in Euclidean subset, at the level of a beginning graduate student.
If $A$ is a closed subset of the Euclidean space $\mathbb R^k$,...

Jul 15 2020

### On the cap-set problem and the slice rank polynomial method

Speaker: Lisa Sauermann

5:30pm | Remote Access Only
In 2016, Ellenberg and Gijswijt made a breakthrough on the famous cap-set problem, which asks about the maximum size of a subset of \mathbb{F}_3^n not containing a three-term arithmetic progression. Ellenberg and Gijswijt proved that any such set has size at most 2.756^n....

Jul 08 2020

### Weyl laws and dense periodic orbits

Speaker: Michael Hutchings

5:30pm | Remote Access Only
We review a "Weyl law" in embedded contact homology, relating periods of orbits of the Reeb vector field on a contact three-manifold to volume. (This was also mentioned in the talk by Dan Cristofaro-Gardiner.) We explain a clever argument by Kei Irie which deduces from this that a generic...

Jul 01 2020

### The reversibility paradox: 130 years after Loschmidt and Zermelo

Speaker: Laure Saint-Reymond

5:30pm | Remote Access Only
The reversibility paradox is the objection that it should not be possible to deduce an irreversible process from time-symmetric dynamics. A first result reconciling the fundamental microscopic physical processes (with time reversal symmetry) and macroscopic models (satisfying the second law of...

Jun 24 2020

### Knot concordance and 4-manifolds

Speaker: Lisa Piccirillo

5:30pm | Remote Access Only
There is a rich interplay between the fields of knot theory and 3- and 4-manifold topology. In this talk, I will describe a weak notion of equivalence for knots called concordance, and highlight some historical and recent connections between knot concordance and the study of 4-manifolds, with a...

Jun 17 2020

### Infinite dimensional Hamiltonian systems: when hard problems become harder

Speaker: Gigliola Staffilani

5:30pm | Remote Access Only
In this talk I will first recall three classical theorems in the theory of finite dimensional Hamiltonian systems, then I will use the periodic nonlinear Schrodinger equation as an example of an infinite dimensional Hamiltonian system and I will report on the extension of those three...

Jun 03 2020

### Mathematics formalization for mathematicians

Speaker: Patrick Massot

5:30pm | Remote Access Only
A growing number of mathematicians are having fun explaining mathematics to computers using proof assistant softwares. This process is called formalization. For instance, together with Kevin Buzzard and Johan Commelin, I recently formalized enough topology and algebra to define Scholze's...

May 27 2020

### Emerging symmetries in statistical physics systems

Speaker: Hugo Duminil-Copin

5:30pm | Remote Access Only
A great achievement of physics in the second half of the twentieth century has been the prediction of conformal symmetry of the scaling limit of critical statistical physics systems. Around the turn of the millenium, the mathematical understanding of this fact has progressed tremendously...