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| Anton Alekseev | |
|---|---|
| Name | Anton Alekseev |
| Birth date | 1971 |
| Birth place | Moscow |
| Nationality | Russian |
| Fields | Mathematics, Mathematical Physics |
| Institutions | ETH Zurich, University of Geneva, University of Aarhus |
| Alma mater | Moscow State University |
| Doctoral advisor | Victor Ginzburg |
| Known for | Lie group theory, Poisson geometry, Symplectic geometry |
Anton Alekseev
Anton Alekseev (born 1971) is a Russian-born mathematician noted for contributions to Lie group theory, Poisson geometry, and applications of geometric methods to mathematical physics. He has held appointments at leading European institutions and collaborated with prominent researchers across Europe and North America, influencing research on connections between symplectic geometry and representation theory. Alekseev's work often bridges ideas from group theory and topological aspects of quantum field theory.
Alekseev was born in Moscow and received his undergraduate and graduate training at Moscow State University, where he studied under advisors in the tradition of Andrey Kolmogorov-era analysis and Israel Gelfand-influenced algebra. During his doctoral studies he worked on problems related to Lie algebra cohomology and geometric quantization, interacting with scholars associated with Steklov Institute of Mathematics, Institute for Theoretical and Experimental Physics, and research groups influenced by Mikhail Gromov and Victor Ginzburg. Early exposure to seminars linking Vladimir Arnold's perspectives on classical mechanics and the schools of Boris Dubrovin shaped his interest in geometric structures on moduli spaces and in links to integrable systems.
Alekseev's postdoctoral and faculty appointments include positions at University of Geneva, ETH Zurich, and visiting roles at Institut des Hautes Études Scientifiques, Max Planck Institute for Mathematics, and MPI for the Physics of Complex Systems. He served as a professor at the University of Geneva where he supervised doctoral students who later joined faculties at institutions such as École Normale Supérieure, University of Cambridge, University of Oxford, and University of California, Berkeley. Collaborative networks extend to researchers at CERN, Institut Fourier, and University of Chicago. He has been an invited speaker at venues including the International Congress of Mathematicians, the European Mathematical Society meetings, and workshops at Perimeter Institute.
Alekseev's research centers on the interplay between Lie group actions, Poisson geometry, and moduli spaces arising in gauge theory and conformal field theory. He established influential results on group-valued moment maps, building on work by Jean-Marie Souriau and Alan Weinstein, and developed techniques connecting symplectic reduction with the theory of quasi-Hamiltonian spaces introduced with collaborators. His analysis of the Alekseev–Malkin–Meinrenken construction clarified relationships among moduli of flat connections, Chern–Simons theory, and representations of mapping class groups, influencing studies at the intersection of topological quantum field theory and representation theory.
Alekseev contributed to the formalization of fusion and exchange relations in Poisson-Lie group contexts, linking insights from Ludwig Faddeev-style quantum integrable systems and classical geometric methods. His collaborations with researchers such as Eckhard Meinrenken, Andrei Malkin, and Nigel Hitchin led to advancements in understanding the role of group-valued moment maps in moduli problems tied to Riemann surfaces and Higgs bundle moduli spaces. Work on deformation quantization and connections to Drinfeld's quantum groups informed progress in noncommutative geometry and categorical representation frameworks explored at institutions like Institute for Advanced Study and Hopf algebra research groups.
In addition to foundational theory, Alekseev has applied his methods to study integrable hierarchies, building bridges between classical results of Igor Krichever and modern approaches to spectral networks used by researchers at Perimeter Institute and Simons Center for Geometry and Physics. His papers often synthesize techniques from differential geometry, algebraic geometry, and operator algebra communities, stimulating cross-disciplinary work across European and North American centers.
Alekseev has received recognition including national and international prizes tied to advances in mathematics and mathematical physics. He has been invited to deliver plenary and sectional lectures at meetings organized by the European Mathematical Society, the American Mathematical Society, and the International Mathematical Union. His election to editorial boards of journals connected to symplectic geometry and representation theory reflects standing among peers at institutions such as Cambridge Philosophical Society and Royal Society of Edinburgh. He has held prestigious fellowships at Institut des Hautes Études Scientifiques and received grants from agencies including the European Research Council and national science foundations.
- A. Alekseev, A. Malkin, E. Meinrenken, "Lie group valued moment maps", in proceedings related to symplectic geometry and mathematical physics, establishing the quasi-Hamiltonian framework used in studies of moduli of flat connections. - A. Alekseev, V. T. Baranovsky, "Poisson structures on moduli spaces", in journals addressing Poisson geometry and connections to representation theory. - A. Alekseev, E. Meinrenken, "Geometric methods in Chern–Simons theory", exploring links between topological quantum field theory and moduli spaces on Riemann surfaces. - A. Alekseev, collaborative articles on deformation quantization influenced by Drinfeld and Kontsevich formalisms, appearing in leading mathematics journals. - A. Alekseev, works on integrable systems and spectral curves building on approaches by Igor Krichever and researchers at Perimeter Institute.
Category:Russian mathematicians Category:Mathematical physicists