Andrey Lazarev

Professor of Pure Mathematics

photoContact 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.

 

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)