Math GR8210 – Partial Differential Equations
Instructor: Richard Hamilton
Day/Time: TR 2:40 – 3:55 PM
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.
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.