Here you can find my major research topics and main publications
(see also Full Publication List):
 Quantum equivariant Ktheory and quantum integrable systems
We investigate the relationship between quantum integrable systems
and enumerative geometry, motivated by the results in the study of
supersymmetric gauge theories.
Peter Koroteev, Anton M. Zeitlin,
"Difference Equations for Ktheoretic Vertex Functions of TypeA Nakajima Varieties",
arXiv:1802.04463.
Peter Koroteev, Petr P. Pushkar, Andrey Smirnov, Anton M. Zeitlin,
"Quantum Ktheory of Quiver Varieties and ManyBody Systems",
arXiv:1705.10419.
Petr P. Pushkar, Andrey Smirnov, Anton M. Zeitlin,
"Baxter Qoperator from quantum Ktheory", arXiv:1612.08723.
 Higher Teichmüller theory
We construct the analogue of Penner coordinates on the N=1 and N=2 superTeichmüller spaces.
Future projects based on this work involve superanalogue of cluster algebras, computations of volumes of supermoduli spaces, quantization of (higher) superTeichmüller spaces.
Ivan C.H. Ip, Robert C. Penner, Anton M. Zeitlin,
"On Ramond Decorations", arXiv:1709.06207.
Ivan C.H. Ip, Robert C. Penner, Anton M. Zeitlin,
"N=2 SuperTeichmüller Theory", arXiv:1605.08094.
R.C. Penner, Anton M. Zeitlin, "Decorated SuperTeichmüller Space",
Journal of Differential Geometry, in press,
arXiv:1509.06302.
 Quantum groups and KacMoody algebras
 Towards the continuous KazhdanLusztig correspondence. ChernSimons theory
for real reductive Lie groups
We attempt to build the braided tensor category of modules for affine
KacMoody algebras, equivalent to the modular double tensor category of
quantum groups. This will lead to the mathematical understanding of WZW
model and ChernSimons theory for real reductive Lie groups.
Anton M. Zeitlin, "On the unitary representations of the affine $ax+b$group, $\widehat{sl}(2,\mathbb{R})$
and their relatives",
Proc. Symp. Pure Math., AMS,
Volume 92 "Lie Algebras, Lie Superalgebras,
Vertex Algebras and Related Topics", pp. 325355, 2016,
arXiv:1509.06072.
Igor B. Frenkel, Anton M. Zeitlin, "On the continuous series for $\widehat{sl}(2,\mathbb{R})$",
Communications in Mathematical Physics, Volume 326, Issue 1, pp. 145165, 2014
(doi: 10.1007/s0022001318329),
arXiv:1210.2135.
Anton M. Zeitlin, "Unitary representations of a loop ax+b group, Wiener measure and Gammafunction",
Journal of Functional Analysis,
Volume 263, Issue 3, pp. 529548, 2012
(doi: 10.1016/j.jfa.2012.05.004),
arXiv:1012.4826.
 Semiinfinite cohomology, quantum groups and noncommutative geometry
We introduce a new approach to quantum groups as semiinfinite cohomology
rings for certain braided vertex algebras. This leads to surprising
realizations of some constructions in noncommutative geometry.
Igor B. Frenkel, Anton M. Zeitlin,
"Quantum Group GL_{q}(2) and Quantum Laplace Operator via Semiinfinite Cohomology",
Journal of Noncommutative Geometry,
Volume 7, Issue 4, pp. 10071026, 2013
(doi: 10.4171/JNCG/142),
arXiv:1110.1696.
Igor B. Frenkel, Anton M. Zeitlin, "Quantum Group as Semiinfinite Cohomology",
Communications in Mathematical Physics, Volume 297, Number 3, pp. 687732, 2010
(doi: 10.1007/s0022001010552),
arXiv:0812.1620.
 Homotopy Gerstenhaber algebras, Einstein equations and Courant algebroids
Using the relation to 2dimensional sigma models, we construct an underlying homotopy Gerstenhaber algebra within Einstein equations with extra fields. Such an algebraic structure is
naturally related to the Courant algebroid.
Anton M. Zeitlin, "BeltramiCourant Differentials and $G_\infty$algebras",
Advances in Theoretical and Mathematical Physics,
Volume 19, Number 6, pp. 12491275, 2015
(doi: 10.4310/ATMP.2015.v19.n6.a3),
arXiv:1404.3069.
Anton M. Zeitlin,
"Quasiclassical LianZuckerman Homotopy Algebras, Courant Algebroid and Gauge Theory",
Communications in Mathematical Physics, Volume 303, Number 2, pp. 331359, 2011
(doi: 10.1007/s0022001112060),
arXiv:0910.3652.
Anton M. Zeitlin, "Betagamma systems and the deformations of the BRST operator",
Journal of Physics A: Mathematical and Theoretical,
Volume 42, Number 35, 355401, 2009
(doi: 10.1088/17518113/42/35/355401),
arXiv:0904.2234.
Anton M. Zeitlin,
"SFTinspired Algebraic Structures in Gauge Theories",
Journal of Mathematical Physics (JMP), 50, Issue 6, 063501, 2009
(doi: 10.1063/1.3142964),
arXiv:0711.3843.
Anton M. Zeitlin,
"Perturbed BetaGamma Systems and Complex Geometry",
Nuclear Physics B,
Volume 794, Issue 3[PM], pp. 381401, 2008
(doi: 10.1016/j.nuclphysb.2007.09.002),
arXiv:0708.0682.
Andrei S. Losev, Andrei Marshakov, Anton M. Zeitlin,
"On First Order Formalism in String Theory",
Physics Letters B, Volume 633/23, pp. 375381, 2006
(doi: 10.1016/j.physletb.2005.12.010),
hepth/0510065.
 Geometric Langlands correspondence for supergroups
We define a counterpart of an oper on a supercurve and study the analogue of Geometric Langlands correspondence in the simplest nontrivial case of OSp(12) supergroup. In the future we plan to extend it to higher rank case.
Anton M. Zeitlin, "Superopers on Supercurves",
Letters in Mathematical Physics, Volume 105, Issue 2, pp. 149167, 2015
(doi: 10.1007/s1100501407359),
arXiv:1311.5997.
 Homotopy algebras of topological conformal field theories
We introduce nonlocal operators in topological conformal field theories using integration over the compactified moduli spaces and study relations between them.
Anton M. Zeitlin, "On higher order Leibniz identities in TCFT",
Contemporary Mathematics, Volume 623, pp. 267280, 2014
(doi: 10.1090/conm/623/12458)
arXiv:1301.6382.
Anton M. Zeitlin, "Homotopy Relations for Topological VOA",
International Journal of Mathematics (IJM), Volume 23, Issue 1, 1250012, 2012
(doi: 10.1142/S0129167X11007550),
arXiv:1104.5038.
 Integrable systems and (super)conformal field theory
We investigate integrable structures in superconformal field theory. In
particular, that involves quantization of supersymmetric models of KdV type.
Ivan ChiHo Ip, Anton M. Zeitlin,
"Qoperator and fusion relations for C_{q}^{(2)}(2)",
Letters in Mathematical Physics, Volume 104, Issue 8, pp. 10191043, 2014
(doi: 10.1007/s1100501407025),
arXiv:1312.4063.
A.M. Zeitlin, "Quantization of N=2 supersymmetric KdV Hierarchy",
Theoretical and Mathematical Physics, v. 147, n. 2, pp. 303314, 2006 (in russian,
(doi: 10.4213/tmf1965),
Engl. transl.: Theoretical and Mathematical Physics v. 147, n. 2, pp. 698708, 2006
(doi: 10.1007/s112320060071z),
hepth/0606129.
Petr P. Kulish, Anton M. Zeitlin, "Quantum supersymmetric TodamKdV hierarchies",
Nuclear Physics B, Volume 720, Issue 3, pp. 289306, 2005
(doi: 10.1016/j.nuclphysb.2005.06.002),
hepth/0506027.
Petr P. Kulish, Anton M. Zeitlin,
"Superconformal field theory and SUSY N=1 KdV hierarchy II: the Qoperator",
Nuclear Physics B, Volume 709, Issue 3, pp. 578591,
2005 (pdf)
(doi: 10.1016/j.nuclphysb.2004.12.031),
hepth/0501019.
Petr P. Kulish, Anton M. Zeitlin,
"Quantum inverse scattering method and (super)conformal field theory",
Theoretical and Mathematical Physics, v. 142, n. 2, pp. 252264, 2005 (in russian,
doi: 10.4213/tmf1779),
Engl. transl.: Theoretical and Mathematical Physics, v. 142, n. 2, pp. 211221, 2005
(pdf),
(doi: 10.1007/s1123200500545),
hepth/0501018.
Petr P. Kulish, Anton M. Zeitlin,
"Superconformal Field Theory and SUSY N=1 KdV Hierarchy I: Vertex
Operators and YangBaxter Equation",
Physics Letters B, Volume 597, Issue 2, pp. 229236, 2004
(doi: 10.1016/j.physletb.2004.07.019),
hepth/0407154.
Petr P. Kulish, Anton M. Zeitlin,
"Integrable Structure of Superconformal
Field Theory and Quantum superKdV Theory",
Physics Letters B, Volume 581, Issues 12, pp. 125132, 2004
(doi: 10.1016/j.physletb.2003.12.008),
hepth/0312159.
Petr P. Kulish, Anton M. Zeitlin,
"Group Theoretical Structure and Inverse Scattering Method for
superKdV Equation", Zapiski Nauchnih Seminarov POMI (Steklov Institute), vol. 291,
185205 (ps.gz),
2002 (in russian);
Engl. transl. :
Journal of Mathematical Sciences (Springer/Kluwer), v. 125, n. 2, pp. 203214, 2005
(doi: 10.1023/B:JOTH.0000049572.41993.9f),
hepth/0312158.
