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I started my research in Moscow at the seminar of I.M.Gelfand on Representation Theory. In 1991 I obtained PhD in Mathematics from the Moscow State University, supervised by A.A.Kirillov and G.I.Olshanski. In 1990 I was appointed as Assistant Professor of Mathematics at the Moscow State University. Between 1992-1993 I spent time at the Research Institute for Mathematical Sciences in Kyoto as JSPS Postdoctoral Fellow. In 1993 I obtained from the University of Wales a Research Fellowship to work in Swansea for two years. In 1995 I was awarded an EPSRC Advanced Research Fellowship. In 1996 I moved to the University of York, where in 2000 I became a Lecturer.
I gave a Morning Talk at the British Mathematical Colloquium in 2000, and an Invited Talk at the International Congress of Mathematicians in 2002. In 2003 I was awarded a Whitehead Prize by the London Mathematical Society. In 2003 I was appointed as Reader in Mathematics at the University of York. In 2006 I was promoted to Professor.
Member of the University Senate (Aug 2015-Jul 2018)
Member of the Faculty Promotions Advisory Panel (2017, 2018, 2019)
Member of the University Special Cases Committee (Oct 2019-Jul 2022)
I work on the algebraic and combinatorial aspects of the representation theory of quantum affine algebras, including applications to quantum integrable systems. Most of my works on the subject can be found here.
Many people delight in the formal elegance the symmetry can bring to a design. Less well known is the 19th century mathematical discovery that symmetry forms the framework for Geometry. Later, 20th century physicists discovered that these same ideas lie at the heart of our understanding of the Universe. There is a special branch of Mathematics, called Representation Theory, which studies symmetries revealed (or sometimes concealed) by objects and phenomena in Mathematics and other fields of Science including Biology, Chemistry and Physics. That branch is the area of my research.
The aim of my current project is to study particular objects, called Cherednik algebras or double affine Hecke algebras. They appeared about 20 years ago as a result of blending ideas from the branch of modern Theoretical Physics called Conformal Field Theory, and from a more traditional branch of Mathematics, called the Theory of Special Functions. Since then the Cherednik algebras were found to play major roles in several other branches of Mathematics. The aim is to advance the theory of these algebras, and to find more links between Mathematics and Theoretical Physics.