Organizers
Corina Calinescu (ccalinescu@citytech.cuny.edu)
Bob Donley — in memoriam
Andrew Douglas (adouglas@citytech.cuny.edu)
Rishi Nath (rnath@york.cuny.edu)
The CUNY Representation Theory Seminar features both research and expository talks in representation theory, broadly interpreted. Talks will, as much as possible, be accessible to a wide audience, including graduate students, faculty from other specialties, and experts in representation theory. Applications of representation theory in physics will also be addressed.
The seminar is held on most Fridays from 9:30 AM to 10:30 AM, both in person and via Zoom.
In-Person Location:
CUNY Graduate Center
365 Fifth Avenue
New York, NY 10016
Room: 6417
Zoom Link for Talks: Zoom links for talks are posted separtely below.
Fall 2026 Talks
September 18
Joshua Sussan
MEC, CUNY
Title: Tilting colored Khovanov homology
Abstract: We will review the representation theory of the distribution algebra for SL(2) in characteristic p. We will apply this machinery to construct a homology theory of links whose components are colored by tilting modules. This is joint work with Y. Qi, L.H. Robert, and E. Wagner.
October 16
Benjamin Steinberg
CCNY, CUNY
Title: TBA
Abstract: TBA
October 30
David C. Luo
University of Minnesota
Title: On the Local Converse Theorem for p-adic GL(n)
Abstract: In this talk, we briefly introduce twisted gamma factors, analytic invariants that, through the Local Converse Theorem, determine supercuspidal representations of p-adic general linear groups up to isomorphism. We then review the history of the Local Converse Theorem and discuss recent improvements to its bounds. This is joint work with Shaun Stevens.
November 13
Hyun Kyu Kim
Korea Institute for Advanced Study
Title: Canonical bases of skein algebras, and categorification by Coulomb branch
Abstract: For an oriented surface S, the Kauffman bracket skein algebra of S is an algebra generated by isotopy classes of framed links in the thickened surface S x (-1,1) modulo skein relations, and it quantizes the SL2 character variety of S. I will review various vector space bases of the skein algebra, and discuss the problem on the positivity of structure constants. I will spend enough time to give an elementary introduction, and I will mention recently known results, from quantum cluster algebras and mirror symmetry, from foams, and from Braverman-Finkelberg-Nakajima's quantized K-theoretic Coulomb branches for quiver gauge theories. I hope to focus more on the last one, which is based on my joint work 2505.13332 with Dylan Allegretti and Peng Shan, which gives a monoidal categorification of the skein algebra of a genus zero punctured surface.
Spring 2026 Talks
February 20
Robert W. Donley, Jr.
QCC, CUNY
Title: Methods for Validation of Adinkra Models in Supersymmetry
Abstract:
In a series of papers from 2020, the definition of the Adynkra as a graph-theoretic model for computations in supersymmetry was given by S. J. Gates, Jr., Y. Hu, and S.-N. H. Mak, with the construction based on Young tableaux and branching rules. In this talk, we validate the constructions found there using alternative methods, which include character decompositions and spreadsheet models. This work is joint with S. James Gates, Jr., Tristan Hubsch, and Rishi Nath.
Recording: https://www.youtube.com/watch?v=xMm524L50wM
March 6
Sultan Catto
CUNY Graduate Center
Title: The Role of 8-Dimensional Quadratic Normed Division Algebras in Nature and in Mathematics. Nouvelle Algebras Imitating Octonions.
Abstract: The last of the Hurwitz algebras, octonions, and their various applications in hadronic physics are exploited. We point to relations of new algebras, labelled by R appearing in Galois theory, and those marked by the script l that appear in superstring theories, closely related to split-octonion algebra, which are utilized in the description of dynamical hadronic supersymmetry. If time permits, we shall further elaborate on Jordan algebras, magic squares, seven spheres, and supergravity, pointing to the existence of a larger theory with a 27-dimensional lattice and unifying all known superstring theories.
Zoom Link: https://us02web.zoom.us/j/83196056340?pwd=MBGg0SxOiHR11cxzpGNptDIF9iXbMn.1 (Passcode: 613032)
Rishi Nath
York College, CUNY
Title: Scopes classes via a Weyl group action
Abstract: Let p be a prime and let D be a finite p-group. The Donovan conjecture says that there are finitely many Morita equivalence classes of blocks with defect group D. In 1991, J. Scopes proved this for the symmetric groups by providing Morita equivalences between pairs of blocks in the symmetric groups and obtaining bounds on the number of equivalence classes. Using a Weyl group action on abaci (first discovered by A. Lascoux), we recover known results and go further, parametrizing the set of so-called Scopes classes that are finite, as well as those that are infinite, and computing their number. This is joint work with O. Brunat (Paris).
Zoom Link: https://us02web.zoom.us/j/84339451196?pwd=tAJjXz9AGaMQSDaTxVg6OiktbVJdJI.1 (Passcode: 683337)
Karol Koziol
Baruch College, CUNY
Title: (Derived) Hecke algebras in the representation theory of p-adic groups
Abstract: I'll give an overview of how various flavors of (derived) Hecke algebras arise in the representation theory of p-adic groups. Time permitting, I'll also mention connections to Galois representations via the mod-p Langlands program.
Zoom Link: https://us02web.zoom.us/j/85171659775?pwd=144Sk8v2IcKZoebnGidZtRgZpisRwN.1
Passcode: 013725
Miodrag Iovanov
Yeshiva University
Title: A global (categorical) solution to the Wild Problem
Abstract: The wild problem is the question of finding a "canonical" simultaneous form for an n-tuple of matrices up to conjugation. This is equivalent to asking to classify the finite dimensional representations of the non-commutative polynomial algebra K<x_1,...x_n> in n variables, and is tightly related to classifying the representations of the free group on n letters.
We take a categorical approach and show that the category of finite dimensional representations of K<x_1,...x_n> is hereditary after completion with colimits, and hence it is completely determined up to equivalence by its Ext quiver. We precisely describe this quiver Q_n, and show that many other free quantum groups, including the free group on n letters, have the same representation theory, equivalent to locally nilpotent representations of Q_n.
Time permitting, we discuss the problem to what extent the above "free representation theory" determines the algebra. We conjecture that a group which has such a representation theory must itself be free, and we give some evidence for this. Part of this work is joint with a R. Bianconni.
Zoom Link: https://us02web.zoom.us/j/84034718657?pwd=TKSjHpLkqRxMsm7p2W6Lzy9qAVC0f5.1
Passcode: 607633
University of Trento, Italy
Title: The Orbits of Spin(7,7)
Abstract: The orbits of the complex group Spin(14,C) were classified first by Popov and then by Kac and Vinberg. In this talk we show how to classify the orbits of its real form Spin(7,7). Following Kac and Vinberg we embed the group Spin(14,C) into a Vinberg theta-group. Then the real form Spin(7,7) is embedded in the same group. The main technical difficulty is to determine the stabilizers of the orbits of Spin(14,C). Then the orbits of Spin(7,7) can be determined with Galois cohomology. This is joint work with Emanuel Di Bella.
Zoom Link: https://us02web.zoom.us/j/88292226533?pwd=oCxEvlM74EKVRoxz9Vxcugv5BWWylq.1
Passcode: 070462