Anton Alekseev (mathematician)

Anton Yurevich Alekseev (Антон Юрьевич Алексеев, born 9 August 1967) is a Russian mathematician.

Alekseev was a student of Ludvig Faddeev. Alekseev worked at the Steklov Institute in Saint Petersburg and at the beginning of the 1990s at Uppsala University. He is now a professor ordinarius at the University of Geneva.^[1]

Alekseev does research on representation theory of Lie groups and algebras, moment theory, symplectic geometry and mathematical physics.^[1]

In 2006 he, with Eckhard Meinrenken, published in Inventiones Mathematicae a proof of the Kashiwara-Vergne conjecture.^[2] In 2008 he gave a new proof with Charles Torossian.^[3]

In 2014 Alekseev was an invited speaker with talk Three lives of the Gelfand-Zeitlin integrable system at the International Congress of Mathematicians in Seoul.

In 2020 Alekseev received the Medal of the Erwin Schrödinger International Institute for Mathematics and Physics.^[4]

Selected publications

• as editor with A. Hietamäki, K. Huitu, A. Morozov, Antti Juhani Niemi: Integrable Models and Strings, Proceedings of the 3rd Baltic Rim Student Seminar Held at Helsinki, Finland, 13.–17. September 1993, Springer, Lecture Notes in Physics, 1994; abstract doi:10.1007/3-540-58453-6
  • within the Proceedings by Anton Alekseev and A. Malkin: Symplectic geometry and the Chern-Simons theory, pp. 59–97 preprint
• with Eckhard Meinrenken: The non commutative Weil Algebra, Inventiones Mathematicae, vol. 139, 2000, pp. 135–172, Arxiv
• with Eckhard Meinrenken: Poisson geometry and the Kashiwara-Vergne conjecture, C. R. Acad. Sci., 335, 2003, pp. 723–728, Arxiv
• with Eckhard Meinrenken: Clifford algebras and the classical dynamical Yang-Baxter-Equations, Math.Res.Lett., vol. 10, 2003, pp. 253–268, Arxiv
• with Eckhard Meinrenken: On the Kashiwara-Vergne conjecture, Inventiones Mathematicae 164, 2006, 615–634, Arxiv
• with Carlo A. Rossi, Charles Torossian, Thomas Willwacher: Logarithms and Deformation Quantization, Inventiones Mathematicae, vol. 206, 2016, pp. 1–26, Arxiv
• with C. Torossian: The Kashiwara-Vergne Conjecture and Drinfeld's associators, Annals of Mathematics, vol. 175, 2012, pp. 415–463, Arxiv
• with C. Torossian: On triviality of the Kashiwara-Vergne problem for quadratic Lie algebras, C. R. Math. Acad. Sci. Paris, vol. 347, 2009, pp. 21–22, 1231–1236. Arxiv
• with C. Torossian: Kontsevich deformation quantization and flat connections, Comm. Math. Phys., vol. 300, 2010, pp. 47–64, Arxiv
• with B. Enriquez, C. Torossian: Drinfeld associators, braid groups and explicit solutions of the Kashiwara-Vergne equations, Publ. Math. Inst. Hautes Études Sci., Band 112, 2010, S. 143–189, Arxiv
• with Arkady Berenstein, Benjamin Hoffman, Yanpeng Li: Langlands Duality and Poisson-Lie Duality via Cluster Theory and Tropicalization, Arxiv 2018

References

1. . Section of Mathematics, University of Geneva. 2007-10-03. Archived from the original on 2020-09-22. Retrieved 2019-11-20.
2. Alekseev, A.; Meinrenken, E. (2006). "On the Kashiwara–Vergne conjecture". Inventiones Mathematicae. 164 (3): 615–634. arXiv:math/0506499. Bibcode:2006InMat.164..615A. doi:10.1007/s00222-005-0486-4. ISSN 0020-9910. S2CID 119682533. arXiv preprint
3. Alekseev, Anton; Torossian, Charles (2008). "The Kashiwara-Vergne conjecture and Drinfeld's associators". arXiv:0802.4300 [math.QA].
4. "Medal Ceremony and Award Lecture of ESI Medal 2020".

External links

• mathnet.ru
• "ICM2014 VideoSeries IL11.1: Anton Alekseev on Aug15Fri". YouTube. Seoul ICM VOD.
• "Anton Alekseev: Logarithms and deformation quantization". YouTube. Centre International de Rencontres Mathématiques. 7 August 2015.
• "Anton Alekseev - The Kashiwara-Vergne theory and 2-dimensional topology". YouTube. Institut des Hautes Études Scientifiques (IHÉS). 12 June 2017.
• "Poisson Geometry in Mathematics and Physics - Anton Alekseev". YouTube. Instituto de Matemática Pura e Aplicada. 29 May 2018.