**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 homological algebra, broadly
understood. It branches out in many other fields of pure mathematics: algebraic
topology, algebraic and differential geometry, abstract homotopy
theory 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__

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__Graduate lectures on Algebraic Topology__

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

Mathematical foundations of physics (handwritten
notes)