**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 research interests are in the field of homotopy theory and algebraic
topology. They branch out in many other fields of pure mathematics: homological
and homotopical algebra, algebraic and differential geometry, and category
theory, to name just a few. It is also related to, and draws motivation from,
aspects of theoretical physics, specifically quantum field theory.

More specifically and narrowly, my recent research deals with homotopy theory of differential graded algebras and
categories, derived categories and higher phenomena. It has applications in
rational homotopy theory, theory of operads and operadic algebras,
algebraic topology and pure algebra.

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;**
**Homotopy**** theory of differential
graded categories**

** **

Recent papers

**Lecture notes**

__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)