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 and string theory to complex and algebraic analysis. These applications include quantum field theories on algebraic curves and reciprocity laws, Kähler geometry of the universal Teichmüller space and  univalent maps, two-dimensional quantum gravity and Weil-Petersson geometry of moduli spaces, trace formulas.

Teaching schedule:

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

MAT 560 Mathematical Physics I, TuTh 1:00pm-2:20pm in Earth & Space 181

Office hours: Tu 3:00pm-4:00pm and Wed 2:30pm-3:30pm in 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.
  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).