### Spring 2021

### Math GR8210 – Partial Differential Equations

**Instructor**: Richard Hamilton

**Day/Time**: TR 2:40 – 3:55 PM

**Title**: TBD

**Abstract**: TBD

### Math GR9904 – Seminar in Algebraic Geometry

**Instructor**: Mohammed Abouzaid

**Day/Time**: TBD (preliminary meeting Friday Jan 14, 3:15 pm)

**Title**: Manifolds and K-theory

**Abstract**: We will study Waldhausen’s work relating stable pseudo-isotopy spaces to algebraic K-theory. The focus will be on understanding the geometric part of the construction, following Waldhausen’s paper “Algebraic $K$-theory of spaces, a manifold approach.”

### Mats GR8260 – Topics in Stochastic Analysis

**Instructor**: Julien Dubedat

**Day**/Time: MW 2:40 – 3:55 PM

**Title**: High-dimensional probability

**Abstract**: A common theme in probability, statistics, computer science, and cognate fields is the study of quantities that depend in a complex (non-linear) way on a large number of random inputs. Basic questions include concentration, normality of fluctuations, and non-asymptotic estimates on deviations. The aim of the course is to introduce ideas and techniques that have proved relevant in a variety of situations. Topics may include: concentration of measure; martingale inequalities; isoperimetry; Markov semigroups, mixing times; hypercontractivity; influences; suprema of random fields; generic chaining; entropy and combinatorial dimensions; selected applications.

References:

Probability in High Dimension, Ramon van Handel.

High-dimensional probability, Roman Vershynin, Cambridge University Press.

Concentration inequalities. A nonasymptotic theory of independence, Stéphane Boucheron, Gábor Lugosi, and Pascal Massart. Oxford University Press.