Department of Mathematics
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I graduated from Kiev University and received PhD and Dr Sci degrees at Institute of Mathematics, Kiev. In the 90’s, I was a research associate at the Institute of Applied Mathematics in Bonn. I moved to Nottingham in 2001 and then to York in 2007.
Stochastic analysis: stochastic processes, stochastic differential equations and differentiable measures on infinite dimensional spaces, with applications to the study of complex interacting systems, in particular models of statistical mechanics
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, stochastic dynamics of infinite particle systems
There are currently three directions of research:
Mathematical Finance and Stochastic Analysis
Mathematical Physics and Quantum Information
I can offer several PhD projects in the area of stochastic / functional analysis and its applications to models of statistical mechanics. They will be suitable for students with MSc in Mathematics and background in probability theory and functional analysis. Some projects may have more algebraic flavour.
Below are some examples of possible topics: