108, College House ,
University of Leicester,
Leicester LE1 7RHOffice:
108, College House
Tel:+44 (0)116 252 3892
My current research interests lie at the junction between different areas of Pure Mathematics and Mathematical Physics: Algebraic Topology, Homological Algebra and Deformation Theory, Noncommutative Geometry and Conformal Field Theory.
The projects I am presently working on aim to apply ideas and methods of quantum field theory (Feynman path integrals) to classical problems of algebra and geometry, such as the study of moduli spaces.
Closely related to this circle of ideas is the study of homotopy algebras and operads, which were originally invented by topologists in order to study H-spaces.
My research is also concerned with the more traditional areas of algebraic topology, such as generalized homology theories, particularly those related to complex cobordisms and associated formal and p-divisible groups.
The following is a sample list of PhD projects which I am prepared to supervise. Prospective postgraduate students are recommended to have a look at the lectures on operads and TCFT's (below) to get some familiarity with basic ideas and notions.
Graph cohomology and noncommutative geometry;
Homotopy theory of algebras over operads and modular operads;
Deformation theory of algebraic and geometric structures;
Moduli spaces and topological field theories;
Operads and formal Frobenius manifolds.
TeachingGraduate lectures on operads and topological field theories