Tsymbaliuk Oleksandr (Sasha)
Simons Center for Geometry and Physics E-mail:
otsymbaliuk@scgp.stonybrook.edu
Stony Brook University
Webpage: http://mysbfiles.stonybrook.edu/~otsymbaliuk/
John S. Toll Dr
Born:
May 21, 1987, Kharkiv, Ukraine
Stony Brook, NY 11794
Citizenship:
Ukraine citizen
Research interests
• Representation theory.
Employment
• Research Assistant Professor
Simons Center for Geometry and Physics
at Stony Brook University.
Education
• Ph.D. in Mathematics, Massachusetts Institute of Technology
Thesis: “The affine Yangian of gl1 and
the Infinitesimal Cherednik algebras”.
Advisor: P. I. Etingof.
April 2014
• Diploma, Mathematics (cum laude), Moscow State University
Thesis: “Heisenberg action in the equivariant K-theory
of Hilbert schemes via shuffle algebra”.
Advisor: E. B. Vinberg.
June 2009
• Diploma, Mathematics, Independent University of Moscow
Thesis: “Quantum affine Gelfand-Tsetlin bases and quantum
toroidal algebra via K-theory of affine Laumon spaces”.
Advisor: B. L. Feigin.
May 2009
• NSF grant DMS-1502497
2015–2018
Grants,
fellowships, and
distinctions
Sept. 2014–Aug. 2017
• Japan Society for the Promotion of Science
Postdoctoral Fellowship for Foreign Researchers
• Akamai Presidential Fellowship, MIT
Teaching
experience
Winter 2015
2009–2010
• Dobrushin Fellowship, Independent Moscow University
Fall 2008
• Dobrushin Fellowship, Independent Moscow University
Fall 2007
• Silver Medalist at International Mathematics Olympiad
July 2004
• Lecturer for Calculus (at SBU)
Fall 2015
• Teaching assistant for Calculus IV with Applications (at SBU)
Fall 2014
• Teaching assistant for Real Analysis (at MIT)
Spring 2014
• Mentor in the MIT Directed reading program
IAP 2014
• Recitation leader for Multivariable Calculus (at MIT)
Fall 2012
• Mentor in the MIT program “PRIMES”
• Grader for the following courses at MIT:
Real and Functional Analysis, Calculus, Commutative Algebra,
Introduction to Arithmetic Geometry, Algebraic Groups
2011–2013
Publications
• Homomorphisms between different quantum toroidal and affine Yangian algebras,
joint with M. Bershtein.
Preprint, arXiv:1512.09109.
b n ) via shuffle algebras, joint with B. Feigin.
• Bethe subalgebras of Uq (gl
to appear in Selecta Math., DOI: 10.1007/s00029-015-0212-z.; arXiv:1504.01696.
• The affine Yangian of gl1 revisited.
Preprint, arXiv:1404.5240.
• Infinitesimal Hecke algebras of soN .
J. Pure Appl. Algebra 219 (2015), 2046–2061; arXiv:1306.1514.
• Infinitesimal Cherednik algebras as W –algebras, joint with I. Losev.
Transf. Groups 19 (2014), no. 2, 495–526; arXiv:1305.6873.
• Representations of infinitesimal Cherednik algebras, joint with F. Ding.
Represent. Theory (electronic) 17 (2013), 557–583; arXiv:1210.4833.
• Equivariant K-theory of Hilbert schemes via shuffle algebra, joint with B. Feigin.
Kyoto J. Math. 51 (2011), no. 4, 831–854; arXiv:0904.1679.
• Quantum affine Gelfand–Tsetlin bases and quantum
toroidal algebra via K-theory of affine Laumon spaces.
Selecta Math. 16 (2010), no. 2, 173–200; arXiv:0903.0917.
Talks
• SCGP, “Geometric representation theory” Program
Homomorphisms between different quantum toroidal
and affine Yangian algebras.
• Temple University, Algebra seminar
Relation between quantum toroidal algebras of sln and
affine Yangians of sln for different values of n.
• Yale University, Representation theory seminar
b n ).
Shuffle realization of Üq,d (sln ) and Bethe subalgebras of Uq (gl
January 2016
November 2015
April 2015
• Tokyo University, Infinite analysis seminar
Continuous and infinitesimal Hecke algebras.
January 2015
• CUNY (New York), Representation theory seminar
Quantum toroidal and affine Yangian of gl1 and sln .
October 2014
• Northeastern University, Graduate student seminar
The affine Yangian and the quantum toroidal of gl1 .
April 2014
• MIT-NEU, Graduate student seminar on
Quantum cohomology and Representation theory
Geometric representation theory of the Hilbert schemes.
February 2014
• ETH Zurich, Talks in theoretical sciences
November 2013
Trigonometric q-deformations of shift of the argument algebras.
• Northeastern University, Graduate student seminar
Continuous and infinitesimal Hecke algebras.
April 2013
• Harvard-MIT, Representation theory seminar
Introduction to quantum groups: tensor category approach.
April 2012
• Harvard-MIT, Representation theory seminar
Category O at the negative level.
September 2011
• Harvard-MIT, Graduate student seminar
Chiral version of Wakimoto modules.
April 2011
• Harvard-MIT, Graduate student seminar
Algebraic origin of Wakimoto modules.
February 2011
• Hebrew University, Graduate student seminar
Whittaker functions from the geometrical viewpoint.
October 2010
• Boston University, Geometry seminar
Laumon spaces and their role in representation theory.
April 2010
• MIT, Infinite-dimensional algebra seminar
Ding-Iohara algebras and their action on the
K-theory of the Hilbert scheme.
March 2010
• Clay Institute, Workshop “Macdonald polynomials and geometry” March 2010
Gelfand-Tsetlin bases via Laumon spaces.
Schools and
workshops
• Research Program of the 25th Annual PCMI Summer Session
Park City, Utah.
July 2015
• Workshop “RIMS Project 2014 Geometric Representation Theory”
Research Institute for Mathematical Sciences, Kyoto, Japan.
July 2014
• Workshop “Yangians and Quantum Loop Algebras”
Austin, TX.
May 2014
• Summer school “Symplectic reflection algebras”
Moscow region, Russia.
July 2013
• Spring school “Algebraic microlocal analysis”
Northwestern University, Evanston, IL.
May 2012
• Summer school “Quantization and representation theory”
Notre Dame University, IN.
June 2011
• Semester in “Geometric Langlands and representation theory”
Hebrew University, Jerusalem.
• Winter school “Representation theory”
Kyoto University, Japan.
Research Visits
Fall 2010
January 2009
• Research visit
Institut des Hautes Études Scientifiques, France.
June–July 2017
• Research visit
Max Planck Institute for Mathematics, Bonn, Germany.
June–July 2016
• Research visit
Max Planck Institute for Mathematics, Bonn, Germany.
June 2015
• JSPS postdoctoral research program
Research Institute for Mathematical Sciences, Kyoto, Japan.
January 2015
Professional
activities
• Journals
Referee for: IMRN, Journal of Algebra, Selecta Mathematica, SIGMA.
• Seminars
Organizer of: Postdoc Seminar at SCGP (2015–2016).
• Grant Reviews
In 2016 I have reviewed grant applications for NSF.