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 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.

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