**Andrey**** Lazarev**

### Professor of Pure Mathematics

### Contact details:

Address: Fylde College,

University of Lancaster,

Lancaster, LA1 4YF

*Office:* 7B,
Fylde College

Tel +44(0)1524 592156

Email:
a.lazarev@lancaster.ac.uk

** **

**Research **

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 rational homotopy theory and 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.**

Recent papers

**Teaching**

__Graduate lectures on operads and topological field theories__

__ __

__Graduate lectures on Algebraic Topology__

__ __

Galois Theory (joint with J. Chuang and A. Vishik)

Mathematical foundations of physics (handwritten notes)

**
**

**Mathematics Publishers**

· AMS

· MAA

· Springer

· Elsevier

· Walter de Gruyter

· Wiley

· World
Scientific Publishing Co

· Cambridge University Press

· Oxford
University Press

· Princeton University Press

· International Press

· SIAM