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Probability

Graduate Courses

The Department of Mathematics at the University of Illinois has historically had a strong reputation in probability, both through its faculty and through the many postdoctoral visitors who have been here. The document Graduate Study in Probability Theory outlines the general areas of probability theory studied here and describes the advanced undergraduate and graduate courses that are offered regularly.

Graduate Courses in Applied Probability

Faculty Members in Probability

Partha Dey — Ph.D. UC-Berkeley, 2010. Mathematical physics, Probability, Stein’s method, Random networks.

Runhuan Feng — Ph.D. University of Waterloo, 2008. Actuarial science, Mathematical finance, Applied stochastic processes, Applied analysis.

Kay Kirkpatrick — Ph.D. UC-Berkeley, 2007. Statistical mechanics, probability, differential equations, and applications to physics and biology.

Shu Li — Ph.D. University of Waterloo, 2015. Actuarial science, applied stochastic processes, quantitative risk management.

Renming Song — Ph.D. Florida, 1993. Stochastic analysis, Markov processes, mathematical physics, mathematical finance.

Richard B. Sowers — Ph.D. Maryland, 1991. Applied stochastic processes, asymptotics of stochastic processes, randomly-perturbed dynamical systems, and stochastic PDE's.

Postdocs

Janna Lierl — Ph.D. Cornell, 2012. Probability, geometric analysis; fractals, heat kernel, Dirichlet forms.

Zoran Vondraček — Ph.D. University of Florida 1990. Stochastic processes, Markov processes, Probabilistic potential theory.

Jing Wang — Ph.D. Purdue University 2014. Fields probability, analysis, and sub-Riemannian geometry. In particular diffusion semigroups on sub-Riemannian manifolds and the related functional inequalities with geometric contents; small time estimations of transition densities of strongly hypoelliptic diffusion processes.

Faculty Members in Related Areas

Philippe Di Francesco — Ph.D. Universite Paris 6, 1989. Mathematical Physics, Enumerative and Algebraic Combinatorics, Integrable models of Statistical Physics, Cluster Algebra, Matrix models, Quantum (Conformal) Field Theory.

Burak Erdogan — Ph.D. Caltech, 2001. Harmonic analysis on Euclidean spaces and PDEs.

Lee DeVille — Ph.D. Boston University, 2001. Stochastic analysis, differential equations, dynamical systems .

Zoltan Furedi — Ph.D. 1981, D.Sc. Mathematics Institute of the Hungarian Academy of Sciences, 1990. Theory of finite sets with applications in geometry, designs, and computer science.

Eduard Kirr — Ph.D., Michigan, 2002. Existence and stability of coherent structures in equations from mathematical physics, their coupling with radiation under perturbations, theory and numerical simulation of waves in homogeneous and random media.

Jang-Mei Wu — Ph.D. Illinois, 1974. Potential theory, conformal mapping, exceptional sets, complex function theory.

Emeriti Faculty

Lester Helms — Ph.D. Purdue, 1956. Probability theory, diffusion equations, second-order elliptic partial differential equations, heat equation, stochastic processes.

Robert Kaufman — Ph.D. Yale, 1965. Classical analysis, complex function theory, Hausdorff measure, analytic sets.

Peter Loeb — Ph.D. Stanford, 1964. Nonstandard analysis, potential theory, covering theorems, integration theory.

Joseph Rosenblatt — Ph.D. Washington, 1972. Harmonic analysis, ergodic theory, functional analysis.