Unit: College of Arts and Sciences
Department: Department of Mathematics
Office location and address
141 Cabell DrCharlottesville, Virginia 22904
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
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
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.
Introduces measure and integration theory. Prerequisite: MATH 5310 or equivalent.
Continuation of Probability Theory I. Elements of stochastic processes, including Brownian motion, continuous time martingales, and Markov processes.
This course provides the opportunity to offer a new topic in the subject of mathematics.
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.
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.