Professor Andrey Lazarev

Professor of Pure Mathematics

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.

Derived localisation of algebras and modules
Braun, C., Chuang, J., Lazarev, A. 13/04/2018 In: Advances in Mathematics. 328, p. 555-622. 68 p.
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Cocommutative algebras: homotopy theory and Koszul duality
Chuang, J., Lazarev, A., Mannan, W.H. 11/2016 In: Homology, Homotopy and Applications. 18, 2, p. 303-336. 34 p.
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Koszul-Morita duality
Chuang, J., Lazarev, A., Mannan, W. 2016 In: Journal of Noncommutative Geometry. 10, 4, p. 1541-1557. 17 p.
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Unimodular homotopy algebras and Chern-Simons theory
Braun, C., Lazarev, A. 11/2015 In: Journal of Pure and Applied Algebra. 219, 11, p. 5158-5194. 37 p.
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Disconnected rational homotopy theory
Lazarev, A., Markl, M. 1/10/2015 In: Advances in Mathematics. 283, p. 303-361. 59 p.
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Models for classifying spaces and derived deformation theory
Lazarev, A. 4/02/2014 In: Proceedings of the London Mathematical Society. 109, 1, p. 40-64. 25 p.
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Maurer–Cartan moduli and models for function spaces
Lazarev, A. 1/03/2013 In: Advances in Mathematics. 235, p. 296-320. 25 p.
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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.
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Homotopy BV algebras in Poisson geometry
Braun, C., Lazarev, A. 2013 In: Transactions of Moscow Mathematical Society. 74, 2, p. 217-227. 11 p.
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Curved infinity-algebras and their characteristic classes
Lazarev, A., Schedler, T. 2012 In: Journal of Topology. 5, 3, p. 503-528. 26 p.
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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.
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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.

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.
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