Leon A. Takhtajan

Professor, Department of Mathematics

Office: Math. Tower 5-111 (631) 632-8287; Fax 632-7631; e-mail: leontak@math.sunysb.edu

Secretary : Lynne Barnett, Math 5-116, 632-8290

Research interests: Mathematical physics, in particular applications of quantum field theory to geometry, algebra and analysis.

Teaching schedule:

  • MAT 536 Complex Analysis I MW 10:00am-11:20am in Physics P127.

    Office hours: W 2:00pm-3:30pm and Th 1:30pm-3:00pm in Math Tower 5-111.

    Former graduate students:

    Recent Papers:

    1. Quantum field theories on an algebraic curve Lett. Math. Phys. 52 (2000), 79-91.
    2. Deformation quantization on Kähler manifolds (with N. Reshetikhin),  Amer. Math. Soc. Transl. (2) 201 (2000), 257-276.
    3. Free bosons and tau-functions for compact Riemann surfaces and closed Jordan curves. Current correlation functions Lett. Math. Phys. 56 (2001), 181-228.
    4. Generating functional in CFT on Riemann surfaces II: Homological aspects  (with E. Aldrovandi), Commun. Math. Phys. 227 (2002), 303-348; Part I Generating functional in CFT and effective action for two-dimensional quantum gravity on higher genus Riemann surfaces  (with E. Aldrovandi), Commun. Math. Phys. 188 (1997), 29-67.
    5. Hyperbolic 2-spheres with conical singularities, accessory parameters and Kähler meitrics on M _{0,n} (with P. Zograf), Trans. Amer. Math. Soc. 355 (2003), 1857-1867, Erratum.
    6. Liouville action and Weil-Petersson metric on deformation spaces, global Kleinian reciprocity and holography (with L.-P. Teo), Commun. Math. Phys. 239 (2003), 183-240.
    7. Weil-Petersson metric on the universal Teichmuller space I: Curvature properties and Chern forms (with L.-P. Teo), arXiv: math.CV/0312172 (2003).
    8. Weil-Petersson metric on the universal Teichmuller space II: Kahler potential and period mapping (with L.-P. Teo), arXiv: math.CV/0406408 (2004).
    9. Weil-Petersson geometry of the universal Teichmuller space (with L.-P. Teo), Progress in Math. 237 (2005), 219-227.
    10. Holomorphic factorization of determinants of laplacians on Riemann surfaces and a higher genus generalization of Kronecker's first limit formula (with A. McIntyre), Geom. and Funct. Analysis, 16 (2006), 1291-1323.
    11. Quantum Liouville theory in the background field formalism I. Compact Riemann surfaces (with L.-P. Teo), Commun. Math. Phys. 268 (2006), 135-197.
    12. Weil-Petersson Metric on the Universal Teichmuller Space (with L.-P. Teo) Memoirs of the Amer. Math. Soc. 183 No. 861 (2006), vii + 119 pp.
    13. Hamiltonian Methods in the Theory of Solitons (with L.D. Faddeev) Springer "Classics in Mathematics" 2007, xiv + 592 pp, reprint of 1987 original; review in Zentralblatt MATH.
    14. Normal matrix models, dbar-problem, and orthogonal polynomials on the complex plane (with A. Its), arXiv:0708.3867 (2007).
    15. The first Chern form on moduli of parabolic bundles (with P. Zograf), Math. Annalen 341 (2008), 113-135, Addendum.
    16. Quantum Mechanics for Mathematicians Amer. Math. Soc. "Graduate Studies in Mathematics" vol. 95, 2008, xv + 387 pp; Additional Material and Errata; review in Zentralblatt MATH.
    17. Quantum Mechanics for Mathematicians Russian translation, 2011, 496 pp.
    18. Spectrum of the density matrix of a large block of spins of the XY model in one dimension (with F. Franchini, A. R. Its and V. E. Korepin), Quantum Inf. Process. 10 (2011), 325-341.
    19. Hamiltonian Methods in the Theory of Solitons (with L.D. Faddeev) Japanese translation 2012, two volumes.
    20. Quantum field theories on algebraic curves. I. Additive bosons Izvestiya RAN: Ser. Mat. 77:2 (2013), 165-196; English translation in Izvestiya: Mathematics 2013, 77:2, 378-406.
    21. On Bott-Chern forms and their applications (with V. Pingali), Math. Annalen 360:1-2 (2014), 519-546.
    22. On real projective connections, V.I. Smirnov's approach, and black hole type solutions of the Liouville equation Teoret. Mat. Fiz. 181:1 (2014), 206-217; English translation in Theor. and Math. Physics 181:1 (2014), 1307-1316.
    23. Logarithmic connections, WZNW action, and moduli of parabolic bundles on the sphere arXiv:1407.6752 (2014) (with C. Meneses).
    24. The spectral theory of a functional-difference operator in conformal field theory (with L. Faddeev), Izvestiya RAN: Ser. Mat. 79:2 (2015), 181-204; English translation in Izvestiya: Mathematics 2015, 79:2, 388-410.
    25. Explicit computation of the Chern character forms Geom Dedicata 181:1 (2016), 223-237.
    26. Weyl type asymptotics and bounds for the eigenvalues of functional-difference operators for mirror curves (with A. Laptev and L. Schimmer) Geometric and Functional Analysis (GAFA), 26:1 (2016), 288-305.
    27. Potentials and Chern forms for Weil-Petersson and Takhtajan-Zograf metrics on moduli spaces Adv in Math 305 (2017), 856-894 (with J. Park and L.-P. Teo).
    28. Remarkable lives an legacy of Sofia Kovalevskaya and Emmy Noether ICTS Public Lecture Bangalore, India (2017).
    29. Ludwig Faddeev (1934-2017): His work and legacy Newsletter of the European Mathematical Society, June 2017, issue 4, 35-41 (with I. Aref’eva and M. Semenov-Tian-Shansky); Ludwig D. Faddeev (March 23, 1934 - February 26, 2017) IAMP News Bulletin, October 2017 (with N. Reshetikhin and M. Semenov-Tian-Shansky); Ludwig Dmitrievich Faddeev (obituary) Uspekhi Mat. Nauk 72:6 (2017) 191-196; English translation in Russian Math. Surveys 72:6 (2017), 1157-1163 (with I.Ya. Aref’eva, V.E. Zakharov, V.V. Kozlov, I.M. Krichever, V.P. Maslov, S.P. Novikov, A.M. Polyakov, N.Yu. Reshetikhin, M.A. Semenov-Tian-Shansky, E.K. Sklyanin, F.A. Smirnov, and S.L. Shatashvili).
    30. Scientific heritage of L. D. Faddeev. Survey of papers Uspekhi Mat. Nauk 72:6 (2017) 3-112; English translation in Russian Math. Surveys 72:6 (2017) 977-1081 (with A. Yu. Alekseev, I. Ya. Aref’eva, M. A. Semenov-Tian-Shansky, E. K. Sklyanin, F. A. Smirnov, and S. L. Shatashvili).
    31. Unravelling nonlinearity - Exactly Interview with BhAvanA magazine, vol. 1, issue 3 (2017).
    32. On Kawai theorem for orbifold Riemann surfaces Mathematische Annalen, Published online: 07 August, 2018.
    33. Local index theorem for orbifold Riemann surfaces Letters in Mathematical Physics, Published online: 12 December, 2018 (with P. Zograf).