Professor Andrey Lazarev

Head of Department, Professor

Research Overview

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. I am also interested in algebraic topology, rational homotopy theory and deformation theory.

Maurer–Cartan moduli and models for function spaces
Lazarev, A. 1/03/2013 In: Advances in Mathematics. 235, p. 296-320. 25 p.
Journal article

Formal geometry and combinatorics of the Maurer-Cartan equation
Chuang, J., Lazarev, A. 2013 In: Letters in Mathematical Physics. 103, 1, p. 79–112. 34 p.
Journal article

Curved infinity-algebras and their characteristic classes
Lazarev, A., Schedler, T. 2012 In: Journal of Topology. 5, 3, p. 503-528. 26 p.
Journal article

L -infinity maps and twistings
Chuang, J., Lazarev, A. 2011 In: Homology, Homotopy and Applications . 13, 2, p. 175-195. 21 p.
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Feynman diagrams and minimal models for operadic algebras.
Chuang, J., Lazarev, A. 04/2010 In: Journal of the London Mathematical Society. 81, 2, p. 317-337. 21 p.
Journal article

Graph cohomology classes in the Batalin-Vilkovisky formalism
Hamilton, A., Lazarev, A. 05/2009 In: Journal of Geometry and Physics. 59, 5, p. 555-575. 21 p.
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Abstract Hodge decomposition and minimal models for cyclic algebras
Chuang, J., Lazarev, A. 2009 In: Letters in Mathematical Physics. 89, 1, p. 33-49. 17 p.
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Cohomology theories for homotopy algebras and noncommutative geometry
Hamilton, A., Lazarev, A. 2009 In: Algebraic and Geometric Topology . 9, 3, p. 1503-1583. 81 p.
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Characteristic classes of $\ai$-algebras
Hamilton, A., Lazarev, A. 2008 In: Journal of Homotopy and Related Structures. 3, 1, p. 65-111. 47 p.
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Graph homology: Koszul and Verdier duality
Lazarev, A., Voronov, A. 2008 In: Advances in Mathematics. 218, 6, p. 1878-1894. 17 p.
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Symplectic A ∞ -algebras and string topology operations.
Hamilton, A., Lazarev, A. 2008 In: Geometry, topology, and mathematical physics . Providence, R.I. : American Mathematical Society p. 147–157. 11 p.
Paper

Symplectic C ∞ -algebras.
Hamilton, A., Lazarev, A. 2008 In: Moscow Mathematical Journal. 8, 3
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The Stasheff model of a simply-connected manifold and the string bracket.
Lazarev, A. 2008 In: Proceedings of the American Mathematical Society. 136, 2, p. 735-745. 11 p.
Journal article