Algebra, Differential Geometry, Topology, and Mathematical Physics Much of what I do is related with supermanifolds and their applications. Among topics I have worked on are: integration on supermanifolds, geometry of brackets (even and odd Poisson structures, Lie algebroids and their generalizations, homotopy algebras, etc.), quantization and Atiyah-Singer index theorem, super Darboux transformations, and superanalog of cluster algebras.
So far my most influential work has been on "higher derived brackets", and after it, the works on super de Rham theory. As a single recent achievement I value most, I can name the idea of "microformal geometry", in which ordinary maps of (super)manifolds are generalized to "thick morphisms" [a notion I introduced] that induce non-linear, in general, pullbacks of functions. These non-linear pullbacks can be characterized algebraically as "non-linear ring homomorphisms", that is, such non-linear, in general, maps of algebras that their differentials at every point are ring homomorphisms. (This construction is motivated by application to homotopy analogs of Poisson brackets and seems to give the correct notion of P-infinity and S-infinity morphisms.)
Publications
- Recent publications.
- Publications on MathSciNet (access required). arXiv preprints. On Google Scholar. On ResearchGate. A list as a PDF file
Meetings and activities:
- Symmetry, Discrete Geometry, and Mathematical Physics, Scalea, Italy, June 2025
- "Cohomological Aspects of Quantum Field Theory", thematic program at Institut Mittag-Leffler, Stockholm, February-March 2025
- "Gauge invariance: quantization and geometry", Mons, Belgium, September 2024
- "Gone Fishing" Poisson geometry conference, Northwestern, April 2024
- SuperGeometry and SuperModuli: Simons Center, Stony Brook, March 27-May 19, 2023
- "Gone Fishing" Poisson geometry conference, Amherst, March 2023
- Workshop on Supergeometry and Bracket Structures in Mathematics and Physics, The Fields Institute, Toronto, March 21-25, 2022
- Diffieties, Cohomological Physics, and Other Animals: Alexandre Vinogradov Memorial Conference, MCCME, Independent University of Moscow, 13-17 December 2021
- Geometry for Higher Spin Gravity: Conformal Structures, PDEs, and $Q$-manifolds, ESI, Vienna, August 2021
- ESI Thematic Programme: Higher Structures and Field Theory, ESI, Vienna, August 3 - September 25, 2020
- Workshop "Emergent Geometries from Strings and Quantum Fields", Galileo Galilei Institute, Florence, March 30 - May 8, 2020
- Supergeometry, supersymmetry and quantization, University of Luxembourg, December 16-19, 2019
- AMS Fall Central Sectional Meeting: Special Session on Supergeometry, Poisson Brackets, and Homotopy Structures, U of Wisconsin-Madison, September 14-15, 2019
- Conference on "Integrability, Geometry and Moduli", MPIM Bonn, July 29 - August 2, 2019
- The Art of Quantization (commemorating life and legacy of Ludwig Faddeev), Euler Institute and St.Petersburg Department of the Steklov Institute, May 27-June 1, 2019
- LMS-EPSRC Durham Symposium: Higher Structures in M-Theory, Durham, 12-18 August 2018
- Algebraic Topology, Combinatorics, and Mathematical Physics - a conference on occasion of Victor Buchstaber's 75th birthday, Moscow, May 24-30, 2018
- Higher Structures 2 - A conference honoring Murray Gerstenhaber's 90th and Jim Stasheff's 80th birthday, UPenn, March 5-8, 2018
- GEOQUANT 2017, Aarhus University, Denmark, 7-11 August 2017
- "Gone Fishing" Poisson Geometry Conference, U of Notre Dame, 4-7 May 2017
- 14th GAP: Geometry and Physics --- Séminaire itinérant, Sheffield, UK, 8-12 August 2016
- Differential Geometry and its Applications. Brno, Czech Republic, 11 to 15 July 2015.
- Torus Actions in Geometry, Topology, and Applications, Skoltech, Moscow, February 2015
- Geometry, Topology and Integrability, Skoltech, Moscow, October 2014
- Homological Methods in Algebra, Geometry and Physics, London, July 2014
- Belgian Bracket and Quantisation Workshop, Brussels, Belgium, April 2014
- Algebraic Topology and Abelian Functions (In honour of Victor Buchstaber), Moscow, June 2013
- ESI program on Higher Structures in Mathematics and Physics, Vienna, 1 September - 7 November 2010.
- Gauge Theories, Supersymmetry, and Mathematical Physics, Lyon, 6-10 April 2010.
The Białowieża meetings. The annual Workshop on Geometric Methods in Physics has been traditionally held (since 1981) approximately in the first week of July (dates vary) in the small town of Białowieża, Poland, in the heart of the Białowieża National Park, which is a part of the last remaining primordial forest in Europe. Each year it brings in a unique combination of mathematicians and physicists from around the globe. (See also the article : "Bialowieza: 30 years of success and inspiration" in European Mathematical Society Newsletter, issue 75, March 2010, p. 10.)
Last modified: 18 September (1 October) 2025 Ted Voronov