Nikolay Grantcharov

About

I am a sixth year graduate student at the University of Chicago working under the supervision of Victor Ginzburg. My research interests are in geometric representation theory. Specifically, I study deformation theory, DAHAs and Cherednik algebras, quantum groups, and D-modules. I also like BunG and co-founded The BunG Seminar devoted to it in January 2023 with Aaron Slipper. My research is supported by the NSF Graduate Research Fellowship.

I am on the postdoc job market in Fall 2024.

Here is a link to my CV. My email is nikolayg at uchicago dot edu.

Publications

• Infinitesimal neighborhoods of BunG in positive characteristic, preprint available at https://arxiv.org/abs/2402.10369.
• On BBW parabolics for simple classical Lie superalgebras (with D. Grantcharov, D. Nakano, J. Wu), Advances in Mathematics, 381 (April 2021), 107647, 44 pages https://arxiv.org/abs/1810.06980.
• Extension quiver for Lie superalgebra q(3) (with V. Serganova), SIGMA 16 (2020), 141, 32 pages https://arxiv.org/abs/2008.10649.

• Selected Notes from The BunG Seminar:
  • Non-abelian poincare duality and Drinfeld's proof of contractibility of rational maps pdf
  • BunG and Higgs bundles pdf
  • Introduction to stacks and BunG pdf
• Soergel's theorems via wall-crossing functors: Topic proposal discussed with V. Ginzburg, February 2021, pdf.
• Galois Representations valued in reductive groups and their centralizers: University of Michigan REU project supervised with T. Kaletha, September 2018, pdf.

Teaching

• University of Chicago
  • Fall 2024, Instructor, Math 133, Calculus III.
  • Winter 2023-Spring 2023, DRP mentor for C. Chang, representation theory of finite groups and Lie algebras.
  • Spring 2022, Instructor, Math 133, Calculus III.
  • Winter 2022, Instructor, Math 132, Calculus II.
  • Fall 2021, Instructor, Math 131, Calculus I.
  • Spring 2021: College fellow, Math 259 Honors Basic Algebra III, taught by F. Calegari.
  • Winter 2021: College fellow, Math 244 Introduction to Algebraic Geometry, taught by S. Filip.
  • Fall 2020: College fellow, Math 254 Basic Algebra I, taught by P. Tosteson.
  • Summer 2020: REU mentor for J. Yang Super five of Ramsey theory and G. Graham The ring of symmetric polynomials.
• AwesomeMath Summer Program (AMSP)
  • Instructor: 2017-- Present. AMSP is a Summer program for gifted high school students training for USAMO and IMO. Taught intermediate (Euclidean) Geometry and Algebra courses. Developed course curriculum and wrote course notes for new Geometry course (2021).
  • TA: 2014 -- 2016. Ran problem sessions, held office hours, graded exams.

Invited Conference Talks

• AMS Sectional, Mobile Alabama, "Infinitesimal neighborhoods of BunG in positive characteristic'', (20 minutes) October 14, 2023
• AMS Sectional, Cincinnati, Ohio, "Infinitesimal neighborhoods of BunG in positive characteristic'', (20 minutes) April 15, 2023
• Canada-Mexico-USA Conference in Representation Theory, Noncommutative Algebra, and Categorification, "On BBW Parabolics for Lie superalgebras" (poster presentation), June 9th-12th, 2022
• Workshop on Supergeometry, Fields Institute, Toronto, Ontario, "Finite-dimensional representations of the queer Lie supergroup Q(n)" (25 minutes), March 21, 2022.Slides Video
• Southeast Lie Theory XII, Charleston, South Carolina, ''BBW parabolics for classical Lie superalgebras" (15 mins), October 16, 2021, Slides.
• Representation Theory and Integrable Systems conference, Zurich, Switzerland, ''Extension quiver for Lie superalgebra q(3)" (15 mins), August 14, 2019, Slides.

Seminar Talks

• Coulomb branch seminar, Northwestern, "Cherednik algebras as Coulomb branches" (90 minutes), March 10, 2025.
• UChicago BunG seminar, ``Geometric realizations of the affine Hecke algebra", (120 minutes) January 15, 2025
• Geometry/Physics Seminar, Northwestern, "Infinitesimal structure of BunG" (60 minutes) December 5, 2024
• Algebra seminar, UGA, ``Infinitesimal structure of BunG'', (60 minutes) November 11, 2024.
• Math Physics seminar, LSU, ``Infinitesimal structure of BunG'', (60 minutes) October 28, 2024.
• UChicago BunG seminar, ``Representation theory for finite W-algebras'', (120 minutes) October 16, 2024, Video Notes
• Math Physics seminar, Perimeter Institute, ``Infinitesimal structure of BunG'', (60 minutes) May 23, 2024, Video, Pretalk notes, Talk notes.
• UChicago BunG seminar, ``The global Hecke action'', (120 minutes) May 1, 2024, Video Notes
• UChicago BunG seminar, ``Non-abelian poincare duality'', (120 minutes) February 14,2024, Video Notes
• UChicago BunG seminar, ``The local and global Hitchin map'', (120 minutes) October 18, 2023, Video
• University of Bath, lecture series on "Cherednik algebras and their representation theory", (4 hours) August 14-15, 2023.
• UChicago BunG seminar, ``Infinitesimal neighborhoods of BunG'', (100 minutes) March 29, 2023, Video
• UChicago student representation theory seminar, ''A compactification of a configuration space for curves'', (60 mins), May 22, 2022.
• UChicago student representation theory seminar, ''Haiman's proof of the n! conjecture, parts I and II'', (90 mins each), October 20 and 27, 2021.
• Columbia University student seminar on category O (online), "Projective Functors" (90 mins), April 2, 2021.
• Columbia University student seminar on category O (online), "Parabolic Category O" (90 mins), February 12, 2021.
• Superalgebra Theory and Representations seminar (online), Weizmann institute, "Finite-dimensional representation theory of the queer Lie superalgebra q(n)" (75 mins), December 2, 2020.
• Columbia University student seminar on category O (online), "Translation functors for BGG category O'' (90 mins), September 18, 2020, Notes.
• Math Monday undergraduate seminar, U. C. Berkeley, ''Symmetric Polynomials and Representation Theory" (60 mins), April 22, 2019, Slides.
• Global Langlands over function fields seminar, U. C. Berkeley, ''Excursion operators" (90 mins), April 4, 2019.

Travel

• Quantized symplectic singularities and applications to Lie theory, MIT, Cambridge, MA, June 13-17, 2022.
• Workshop on Supergeometry and Bracket Structures, Fields Institute, Toronto, Ontario, March 21-25, 2022
• Lie Theory and Poisson Geometry, CIRM, Marseilles, France, January 10-14, 2022.
• Springest in honor of Vera Serganova , online, April 25-May 13, 2021.
• Graduate Summer School on Geometry and Modular Representation Theory of Algebraic Groups, Stony Brook, NY, August 19-23, 2019.
• Representation Theory and Integrable Systems, Zurich, Switzerland, August 12-16, 2019.
• Michigan Representation Stability Week, Ann Arbor, MI, August 13-17, 2018.
• Representation Theory Day in Quebec City, Quebec City, Quebec, July 29, 2017
• Mathematical Congress of the Americas, Montreal, Quebec, July 24-28, 2017.

A guide for making good espresso.