LP

Unit: College of Arts and Sciences

Department: Department of Mathematics

##### Office location and address

141 Cabell Dr

Charlottesville,
Virginia
22904
##### Publications

##### Sponsored Awards

Distributional symmetries in stochastic systems

Source: The Simons Foundation, Inc.

September 01, 2020 – August 31, 2025

FRG: Collaborative Research: Integrable Probability

Source: U.S. National Science Foundation (NSF)

July 01, 2017 – June 30, 2022

##### Courses

Credits: 3

Introduces fundamental ideas of probability, the theory of randomness. Focuses on problem solving and understanding key theoretical ideas. Topics include sample spaces, counting, random variables, classical distributions, expectation, Chebyshev's inequality, independence, central limit theorem, conditional probability, generating functions, joint distributions. Prerequisite: MATH 1320 or equivalent. Strongly recommended: MATH 2310

Credits: 3

Covers functions of a complex variable that are complex differentiable and the unusual and useful properties of such functions. Some topics: Cauchy's integral formula/power series/the residue theorem/Rouché's theorem. Applications include doing real integrals using complex methods and applications to fluid flow in two dimensions. Prerequisite: MATH 2310.

Credits: 3

Introduces measure and integration theory. Prerequisite: MATH 5310 or equivalent.

Credits: 3

Continuation of Probability Theory I. Elements of stochastic processes, including Brownian motion, continuous time martingales, and Markov processes.

Credits: 1–4

This course provides the opportunity to offer a new topic in the subject of mathematics.

Credits: 3

Discusses fundamental problems and results of the theory of random matrices, and their connections to tools of algebra and combinatorics: Wigner's semicircle law, free probability, Gaussian, circular, and beta ensembles of random matrices, bulk and edge asymptotics and universality, Dyson's Brownian motion, determinantal point processes, and discrete analogues of random matrix models. Prerequisite: MATH 7360 or instructor permission.

Credits: 3–9

Independent Research

Credits: 1–12

The Mathematics Colloquium is held weekly, the sessions being devoted to research activities of students and faculty members, and to reports by visiting mathematicians on current work of interest. For doctoral dissertation, taken under the supervision of a dissertation director.