Fall 2019
MATH GR8210 – PARTIAL DIFFERENTIAL EQUATIONS
Instructor: Richard Hamilton
Abstract: TBD
Day & Time: TR 2:40pm3:55pm
Location: 507 Mathematics Building
MATH GR8255 – PDE IN GEOMETRY
Instructor: Simon Brendle
Title: “Geometry of submanifolds”
Abstract: “In this course will discuss analytical questions that arise in submanifold geometry. In particular, we will focus on the minimal surface equation, and its parabolic counterpart, the mean curvature flow. We will also discuss the main techniques used in the study of these equations: this includes the basic monotonicity formulae, the MichaelSimon Sobolev inequality, and arguments based on the maximum principle.”
Day & Time: TR 10:10am11:25am
Location: 622 Mathematics Building
MATH GR8480 – GROMOVWITTEN THEORY
Instructor: ChiuChu Liu
Abstract:

 Introduction to GromovWitten theory: moduli of curves, moduli of stable maps, GromovWitten invariants, quantum cohomology, Frobenius manifolds
 Genus zero mirror theorems for complete intersections in projective spaces
 Stable maps with fields, NmixedSpinP fields, and higher genus GromovWitten invariants of quintic CalabiYau threefolds
Day & Time: MW 2:40pm3:55pm
Location: 507 Mathematics Building
MATH GR8674 – TOPICS IN NUMBER THEORY
Instructor: Eric Urban
Topic: Eisenstein congruences, Euler systems, and the padic Langlands Correspondance
Abstract: The goal of this course is to introduce the strategy and some of the ingredients that are used in a new construction of Euler systems for Galois representations attached to pordinary cuspidal representations of symplectic groups or unitary groups. These Euler systems are constructed out of congruences between Eisenstein series and cuspidal forms of all level and weights. The theory of Eigenvarieties allows to see that such non trivial congruences exist, and therefore provides non trivial norm compatible Galois cohomology classes. The integrality of these classes follows from deeper arguments using, among other things, the localglobal compatibility in the padic Langlands correspondance for GL2(Qp). As usual, the first meeting will be devoted to a more detailed presentation and to explain the motivations, the main ideas and the strategy of this construction. I will also give a schedule for the next lectures and a list of useful references.
Day & Time: TR 11:40am12:55pm
Location: 507 Mathematics Building
MATS GR8260 – TOPICS IN STOCHASTIC ANALYSIS
Instructor: Konstantin Matetski
Abstract: The goal of the course is to study several classical and modern topics on stochastic partial differential equations (SPDEs). These equations can be used to describe various processes in Statistical Mechanics, Fluid Mechanics, Quantum Field Theory, Mathematical Biology and so on. Depending on properties of SPDEs, they require different approaches to define solutions and to study their properties. Recent breakthroughs in nonlinear SPDEs, which includes the theory of regularity structures by M. Hairer and the theory of paracontrolled distributions by M. Gubinelli, P. Imkeller and N. Perkowski, have opened new prospects in the field.
The course will cover the following topics:

 Elements of Gaussian measures, including the CameronMartin space, white noise and Wiener integral;
 Linear SPDEs: notions of solutions, existence and uniqueness of solutions, and their properties;
 Elements of rough paths and their usage for nonlinear SPDEs;
 The theory of regularity structures with applications to rough SPDEs, including the KardarParisiZhang (KPZ) and Stochastic Quantization equations.
Day & Time: TR 1:10pm2:25pm
Location: 622 Mathematics Building
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