Probability theory is the mathematical description of random phenomena. Probability plays an increasingly important role in almost all areas of engineering and science. Probability research in ORFE ranges from theoretical to applied, with particular emphasis on stochastic analysis and its applications in various areas including financial mathematics, stochastic networks and queueing, signal and image processing, and stochastic control.

## Research Area Faculty

**Research Interests:** Stochastic analysis (SPDEs, BSDEs, FBSDEs, stochastic control and large stochastic differential games such as mean field games), high frequency markets, energy and commodity markets, environmental finance and financial mathematics models.

**Research Interests:** Machine learning - theory of neural networks: approximation power, statistical physics of initialization, guarantees for optimization, and generalization Probability - mathematical physics, random matrix theory, Gaussian processes arising in spectral theory/quantum mechanics, and random polynomial

**Research Interests:** Stochastic control and games, including in particular mean-field games and continuous-time principal-agent problems, using recently introduced and state of the art tools in stochastic control such as second-order backward SDEs. Research motivated by applications to energy management, epidemiology,…

**Research Interests:** Stochastic networks and queueing theory, performance models for service systems, dynamic optimal control and pricing for service systems, stochastic analysis and asymptotics, stochastic dominance on partially ordered spaces, theory of dynamic rate queues, special functions; communications, healthcare

**Research Interests:** High-dimensional probability, randomized algorithms, numerical linear algebra, matrix and tensor methods, mathematics of data, robust and interpretable learning, non-asymptotic random matrix theory

**Research Interests:** Financial mathematics (stochastic portfolio theory, optimal investment, systemic risk), probability theory (interacting particle systems, random matrix theory, and their applications to finance, neuroscience, and physics), partial differential equations (parabolic PDEs/SPDEs, free boundary problems,…

**Research Interests:** Financial mathematics (risk management, model uncertainty, optimal investment); Stochastic analysis (stochastic control, SDEs, BSDEs, FBSDEs, probabilistic representations of parabolic/elliptic PDEs); Probability theory (optimal transportation, functional inequalities)

**Research Interests:** Probability theory, stochastic analysis, Markov processes, ergodic theory, mathematical statistics, information theory, nonlinear filtering, mathematical physics, applied mathematics

**Research Interests:** Interior-point methods for linear, convex, nonconvex, semidefinite optimization, robust optimization, the parametric simplex method, and constraint matrix sparsification (e.g. fast Fourier optimization). Applications include high-contrast imaging (to design a NASA space telescope), finding new stable…