Research interests

Stochastic analysis: stochastic processes, stochastic differential equations and differentiable measures on infinite and finite dimensional manifolds, random operators

Global analysis: differential operators on manifolds, operator algebras, L2 invariants, representations of infinite dimensional groups, geometry of infinite dimensional manifolds

Mathematical physics: classical and quantum models of statistical mechanics, Gibbs measures, Glauber dynamics, asymptotic quantization and semi-classical limits

My current research programme is mostly devoted to stochastic analysis on infinite configuration spaces of Riemannian manifolds, and related questions. It is strongly motivated by applications in statistical mechanics, and requires the combination of analytic, probabilistic and algebraic methods. There are currently three directions of research:

• study of the relationship between properties of Gibbs measures on configuration spaces of Riemannian manifolds and geometry and topology of underlying manifolds
• study of the stochastic dynamics associated with concrete models of statistical mechanics (in particular, with Poisson cluster point processes)
• study of the Laplace operators on braided Fock spaces, associated with anyon and plekton models.

Recent Publications

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Teaching

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