Leon A. Takhtajan
Distinguished Professor
Department of
Mathematics
Office: Math. Tower 5111 (631) 6328287; Fax
6327631; email: leontak@math.stonybrook.edu
Department Administrator: Anne Duffy, Math 5116,
6328290
Research interests: Mathematical physics,
in particular applications of quantum field theory to geometry,
algebra and analysis.
Teaching schedule:
MAT 538 Riemann surfaces MW 2:30pm3:50pm in Physics 129.
Office hours:
Tu 2:00pm4:00pm in Math Tower 5111 and by appointment.
Former graduate students:
 Joseph Schaefer
 Carlos Florentino
 Rukmini Dey
 LeePeng Teo
 Andrew McIntyre
 Joshua Friedman
 Daniel An
 Ki Song
 Joseph Walsh
 Vamsi Pingali
 Claudio Meneses

Jun Wen
Recent Papers:
 Quantum
field
theories on an algebraic curve Lett. Math. Phys. 52 (2000),
7991.
 Deformation
quantization on Kähler manifolds (with N.
Reshetikhin),
Amer. Math. Soc. Transl. (2) 201 (2000), 257276.
 Free
bosons
and taufunctions for compact Riemann surfaces and closed Jordan
curves.
Current correlation functions Lett. Math. Phys. 56 (2001),
181228.
 Generating
functional
in CFT on Riemann surfaces II: Homological aspects (with
E. Aldrovandi), Commun. Math. Phys. 227 (2002), 303348; Part I
Generating
functional in CFT and effective action for twodimensional quantum
gravity on higher genus Riemann surfaces (with
E. Aldrovandi), Commun. Math. Phys. 188 (1997), 2967.
 Hyperbolic
2spheres
with conical singularities, accessory parameters and Kähler
meitrics
on M _{0,n} (with P. Zograf), Trans. Amer. Math. Soc. 355 (2003),
18571867, Erratum.
 Liouville
action and WeilPetersson metric on deformation spaces, global Kleinian
reciprocity and holography (with L.P. Teo), Commun. Math. Phys. 239
(2003), 183240.
 WeilPetersson
metric on the universal Teichmuller space I: Curvature properties and
Chern forms (with L.P. Teo), arXiv: math.CV/0312172 (2003).
 WeilPetersson
metric on the universal Teichmuller space II: Kahler potential and
period mapping (with L.P. Teo), arXiv: math.CV/0406408 (2004).
 WeilPetersson
geometry of the universal Teichmuller space (with L.P. Teo),
Progress in Math. 237 (2005), 219227.
 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), 12911323.

Quantum Liouville theory in the background field formalism I. Compact Riemann surfaces
(with L.P. Teo), Commun. Math. Phys. 268 (2006), 135197.

WeilPetersson Metric on the Universal
Teichmuller Space (with L.P. Teo) Memoirs of the Amer. Math. Soc. 183 No. 861 (2006), vii + 119 pp.
 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.

Normal matrix models, dbarproblem, and orthogonal polynomials on the complex plane
(with A. Its), arXiv:0708.3867 (2007).

The first Chern form on moduli of parabolic bundles (with P. Zograf),
Math. Annalen 341 (2008), 113135, Addendum.
 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.

Quantum Mechanics for Mathematicians
Russian translation, 2011, 496 pp.
 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), 325341.
 Hamiltonian Methods in the Theory of Solitons
(with L.D. Faddeev) Japanese translation 2012, two volumes.
 Quantum field
theories on algebraic curves. I. Additive bosons Izvestiya
RAN: Ser. Mat. 77:2 (2013), 165196 (in Russian); English translation in Izvestiya: Mathematics 2013, 77:2, 378406.
 On
BottChern forms and their applications (with V. Pingali),
Math. Annalen 360:12 (2014), 519546.
 On real projective
connections, V.I. Smirnov's approach, and black hole type solutions of
the Liouville equation Teoret. Mat. Fiz. 181:1 (2014),
206217 (in Russian); English translation in Theor. and Math. Physics
181:1 (2014), 13071316.
 The spectral theory of
a functionaldifference operator in conformal field
theory (with L. Faddeev),
Izvestiya RAN: Ser. Mat. 79:2 (2015), 181204 (in Russian); English
translation in Izvestiya: Mathematics 2015, 79:2, 388410.
 Explicit
computation of the Chern character forms Geom Dedicata
181:1 (2016), 223237.
 Weyl type asymptotics and
bounds for the eigenvalues of functionaldifference operators for
mirror curves (with A. Laptev and L. Schimmer),
Geometric and Functional Analysis
(GAFA), 26:1 (2016), 288305.
 Potentials
and Chern forms for WeilPetersson and TakhtajanZograf metrics on
moduli spaces (with
J. Park and L.P. Teo), Adv in Math 305 (2017), 856894.
 Remarkable lives an legacy
of Sofia Kovalevskaya and Emmy Noether ICTS Public Lecture
Bangalore, India (2017).
 Ludwig Faddeev
(19342017): His work and legacy Newsletter of the European
Mathematical Society, June 2017, issue 4, 3541 (with I. Aref’eva and
M. SemenovTianShansky); Ludwig D. Faddeev
(March 23, 1934  February 26, 2017) IAMP News Bulletin,
October 2017 (with N. Reshetikhin and
M. SemenovTianShansky); Ludwig
Dmitrievich Faddeev (obituary) Uspekhi Mat. Nauk 72:6
(2017) 191196 (in Russian); English translation in
Russian Math. Surveys 72:6
(2017), 11571163 (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. SemenovTianShansky, E.K. Sklyanin,
F.A. Smirnov, and S.L. Shatashvili).
 Scientific
heritage of L. D. Faddeev. Survey of papers Uspekhi Mat. Nauk
72:6 (2017) 3112 (in Russian); English translation in Russian
Math. Surveys 72:6 (2017) 9771081 (with A. Yu. Alekseev,
I. Ya. Aref’eva, M. A. SemenovTianShansky, E. K. Sklyanin, F. A. Smirnov, and S. L. Shatashvili).
 Unravelling
nonlinearity  Exactly Interview with BhAvanA magazine, vol. 1, issue 3 (2017).
 Local
index theorem for orbifold Riemann surfaces (with P. Zograf), Lett.
Math. Phys. 109:5 (2019), 11191143.
 Weyl asymptotics for perturbed functional
difference operators (with A. Laptev and L. Schimmer), J. Math. Phys. 60, 103505 (2019).
 On
Kawai theorem for orbifold Riemann surfaces Math.
Annalen, 375:3 (2019), 923947.
 Etudes of the
resolvent Uspekhi Mat. Nauk, 75:1(451) (2020), 155194 (in
Russian); English translation: Russian
Math. Surveys, 75:1 (2020), 147186.
 Trace formulas
for the modified Mathieu equation in " Partial Differential
Equations, Spectral Theory and Mathematical Physics, The Ari Laptev
Anniversary Volume" (Eds. P. Exner et al), Published by
EMS Press; 427442, 2021.
 Logarithmic connections, WZNW action, and moduli
of parabolic bundles on the sphere (with C. Meneses) Commun. Math. Phys.,
387:2 (2021), 649680.
 Supersymmetry
and trace formulas I. Compact Lie groups (with C. Choi)
arXiv:2112.07942 (2021).
 Goldman form,
flat connections and stable vector
bundles Enseign. Math. 68 (2022), no. 3/4, 409–440;
arXiv version (2021).
 Ludwig
Dmitrievich Faddeev Biographical Memoirs of Fellows of the
Royal Society, published online 24 August 2022 (pdf file).
 Berezin
quantization, conformal welding and the BottVirasoro group
(with A. Alekseev and S. Shatashvili)
arXiv:2212.04822 (2022).
 Supersymmetry
and trace formulas II. Selberg trace formula (with C. Choi)
arXiv:2306.13636 (2023).
 Algebraic de
Rham theorem and BakerAkhiezer function (with I. Krichever)
arXiv:2311.04440 (2023).