Pavel Mnev

Pavel Mnev is an Associate Professor in the Department of Mathematics at the University of Notre Dame. His research focuses on mathematical physics, particularly the interplay between quantum field theory, topology, homological algebra, and supergeometry. He specializes in the Batalin-Vilkovisky (BV) formalism for quantizing gauge theories, including topological field theories, and their discretizations using CW complexes. His work explores topics like exact discretizations of topological field theories, perturbative/non-perturbative comparisons, and extensions to manifolds with corners. He has also contributed to studies on renormalization flows, Igusa-Klein torsions, and the BV-BFV framework for field theories on manifolds with boundaries.

Education: Ph.D. in Mathematical Physics (Russian Academy of Sciences, 2008), M.S. (2005) and B.S. (2002) in Physics from St. Petersburg State University.

Research Interests: Mathematical Physics, Topological Quantum Field Theories, BV Formalism, Homological Algebra, Quantum Gravity Models, and Exact Discretizations.

Publications: Over 40 peer-reviewed articles, including works on simplicial BF theory, Chern-Simons theory, Poisson sigma models, and BV-BFV quantization. Recent contributions address heat kernel gluing, combinatorial QFT on graphs, and holographic correspondences in BV-BFV settings.

Teaching: Regular courses on calculus, linear algebra, differential equations, and advanced topics in topology/geometry at Notre Dame. Taught specialized graduate courses on Batalin-Vilkovisky formalism, conformal field theory, and topological quantum mechanics.