Alexei Daletskii

Profile

Biography

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. 

Departmental roles

• Maths and Economics / Finance combined degree executive committee.

Research

Overview

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:

• study of equilibrium states (Gibbs measures) of random interacting  particle systems, in particular questions of their uniqueness / multiplicity (phase transitions)
• study of the stochastic dynamics associated with concrete models of statistical mechanics,  in particular  with marked point processes describing systems of particles with internal parameter
• study of representations of Q-deformed commutation relations and the corresponding Laplace operators on braided Fock spaces, in particular associated with anyon and plekton models of quantum mechanics.

Research group(s)

Mathematical Finance and Stochastic Analysis

Mathematical Physics and Quantum Information

Available PhD research projects

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:

• existence and uniqueness / multiplicity (phase transitions) of Gibbs measures on configuration spaces / random graphs
• construction and study of deterministic and stochastic infinite systems of differential and stochastic differential equations with random coefficients and dynamics of infinite particle systems
• representations of diffeomorphism groups associated with marked Gibbs measures 

Supervision

Current Research Students

• Asma Alalyani - aasa525@york.ac.uk