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College of Arts & Sciences

Analysis Research

Marcel Bischoff

  • Operator Algebras, in particular Subfactors
  • Algebraic Quantum Field Theory, in particular Conformal Field Theory
  • Tensor Categories

Jeffery Connor

  • Sequence spaces and summability theory, wavelets

Adam Fuller

  • Operator Algebras
  • Multivariate Operator Theory

Archil Gulisashvili

Financial Mathematics

  • General stochastic asset price models; classical stochastic volatility models (Hull-White, Stein-Stein, Heston); Gaussian Volterra type stochastic volatility models; fractional and rough models; scaling properties of stochastic volatility models; models with jumps; option pricing theory; asymptotic behavior of stock price distribution densities, option pricing functions, and the implied volatility; moment explosions, geometrical methods in financial mathematics; Heston geometry, large and moderate deviation principles; the G\"{a}rtner-Ellis theorem. 

Stochastic Processes 

  • Non-homogeneous Markov processes, time-reversal and duality theory for Markov processes, applications of Markov processes to parabolic initial and final value problems. 

Semigroup Theory and Propagator Theory

  • Schroedinger semigroups and Feynman-Kac propagators; non-autonomous Kato classes of functions and measures; smoothing properties of Schroedinger semigroups.

Tatiana Savin

  • Applied analysis, analytic continuation of solutions to elliptic differential equations

Vladimir Uspenskiy

  • Functional analysis, and other related areas.

Departmental Social Media

College of Arts & Sciences