Math 191 Spring 2020

Section 1 - Topics in Minimal Surfaces (Wang)

This course concerns basic properties of minimal surfaces, in particular, the existence and regularity problems. 

Section 2 - Topics in Combinatorics:  Extremal graph theory (Tyomkyn)

Extremal graph theory studies how various graph properties influence each other, for instance, what conditions enforce the existence of certain subgraphs. The course will begin with a revision of classical theorems of Ramsey, Turan and Erdos-Stone, and will proceed to more advanced topics such as Szemeredi's regularity lemma and its applications. 

There will be no problem sets; to get credit the participants will be asked to give a 1.5 hour presentation. 

Pre-requisites: basic knowledge of graph theory (e.g. through 6a/b or 121a/b),  discrete probability and linear algebra.

Section 3 - Topics in p-adic cohomology theories (Xu)

The goal of this course is to study prismatic cohomology following Bhatt-Scholze and to explain its relationship with other p-adic cohomology theories: crystalline cohomology, étale cohomology, etc.

Section 4 - Approximation, Interpolation and Quadrature (Demirel-Frank)

We give an introduction to the problems of Approximation, Interpolation and Quadrature. This course is aimed at undergraduate level.