Leon Takhtajan

Leon Armenovich Takhtajan (Armenian: Լևոն Թախտաջյան; Russian: Леон Арменович Тахтаджян, born 1 October 1950, Yerevan) is a Soviet mathematical physicist of Armenian descent, currently a professor of mathematics at the Stony Brook University, Stony Brook, NY, and a leading researcher at the Euler International Mathematical Institute, Saint Petersburg, Russia.

Takhtajan, son of the Armenian Soviet botanist Armen Takhtajan, received in 1975 his Ph.D. (Russian candidate degree) from the Steklov Institute under Ludvig Faddeev with thesis Complete Integrability of the Equation ${\displaystyle u_{tt}+u_{xx}+\sin(u)=0}$. He was then employed at the Steklov Institute and in 1982 received his D.S. degree (doctor of science, 2nd degree in Russia) with thesis Completely integrable models of field theory and statistical mechanics. Since 1992 he is professor at Stony Brook University and was the chair of the mathematics department in 2009–2013.

His research is on integrable systems of mathematical physics (such as the theory of solitons) and applications of quantum field theories and models of string theory to algebraic geometry and complex analysis and includes quantum field theories on algebraic curves and associated reciprocity laws, two-dimensional quantum gravity and Weil–Petersson geometry of moduli spaces, the Kähler geometry of universal Teichmüller space, and trace formulas. His major contributions are in theory of classical and quantum integrable systems, quantum groups and Weil–Petersson geometry of moduli spaces. Together with Ludvig Faddeev and Evgeny Sklyanin he formulated the algebraic Bethe Ansatz and quantum inverse scattering method. Together with Ludvig Faddeev and Nicolai Reshetikhin he proposed a method of quantization of Lie groups and algebras, the FRT construction. In 1983 he was an invited speaker at the International Congress of Mathematicians in Warsaw and gave a talk Integrable models in classical and quantum field theory.

Articles

• Sklyanin, E. K.; Takhtadzhyan, L. A.; Faddeev, L. D. (1980). "Quantum inverse problem method I". Theoretical and Mathematical Physics. 40 (2): 688. Bibcode:1979TMP....40..688S. doi:10.1007/BF01018718.
• Takhtadzhan, L. A.; Faddeev, Lyudvig D. (1979). "The quantum inverse problem method and the XYZ Heisenberg model". Russian Mathematical Surveys. 34 (5): 11. Bibcode:1979RuMaS..34...11T. doi:10.1070/RM1979v034n05ABEH003909.
• Faddeev, L. D.; Reshetikhin, N. Yu.; Takhtajan, L. A. (1990). Quantization of Lie Groups and Lie Algebras. Leningrad Mathematical Journal. 1. pp. 193–225. Bibcode:1990ASMP...10..299F. doi:10.1142/9789812798336_0016. ISBN 9781483268026. translation of Квантование групп Ли и алгебр Ли. 1989.
• Takhtajan, Leon (1994). "On foundation of the generalized Nambu mechanics". Communications in Mathematical Physics. 160 (2): 295–315. arXiv:hep-th/9301111. Bibcode:1994CMaPh.160..295T. doi:10.1007/BF02103278.
• Zograf, P. G.; Takhtadzhyan, L. A. (1988). "On uniformization of Riemann surfaces and the Weil–Petersson metric on Teichmüller and Schottky spaces". Mathematics of the USSR-Sbornik. 60 (2): 297. Bibcode:1988SbMat..60..297Z. doi:10.1070/SM1988v060n02ABEH003170.

Books

• Faddeev, Ludwig; Takhtajan, Leon (2007) [First published 1987]. Hamiltonian methods in the theory of solitons (2nd ed.). Springer Verlag. ISBN 9783540699699.
• Weil–Petersson Metric on the Universal Teichmuller Space. 183. Memoirs of the Amer. Math. Soc. 2006. MR 2251887.
• Quantum mechanics for mathematicians. American Mathematical Society. 2008. MR 2433906.