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 341 Applied Real Analysis, TuTh 10:00am-11:20am in Library E4320

  • MAT 560 Mathematical Physics I, TuTh 2:30pm-3:50pm in Earth & Space 177

    Office hours: Tu 4:00pm-5:30pm, W 2:00pm-3:30pm in 5-111, and by appointment.

    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. Singular 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. Local index theorem for orbifold Riemann surfaces arXiv:1701.00771 (2017) (with P. Zograf).
    29. On Kawai theorem for orbifold Riemann surfaces arXiv:1708.09052 (2017).