Christopher Ryba

I am a Morrey Visiting Assistant Professor in the mathematics department at UC Berkeley. I completed my PhD in 2020 at MIT, advised by Pavel Etingof. My primary research interests are representation theory and algebraic combinatorics.

I can be reached via email at the following address:


"Stable Centres of Iwahori-Hecke Algebras of type A". Algebr. Represent. Theory (2022). journal link arXiv link.

(with Nate Harman) "A Tensor-Cube Version of the Saxl Conjecture". To Appear: Algebraic Combin. arXiv link.

(with Arun S. Kannan) "Stable Centres II: Finite Classical Groups". Submitted for publication. arXiv link.

"Kronecker Comultiplication of Stable Characters and Restriction From S_{mn} to S_{m}×S_{n}". Submitted for publication. arXiv link.

"Stable Centres I: Wreath Products". To Appear: Algebraic Combin. arXiv link.

(with Zhengwei Liu) "The Grothendieck Ring of a Family of Spherical Categories". To Appear: Commun. Math. Phys. arXiv link.

(with Christian Gaetz) "Stable characters from permutation patterns". Selecta Math. (N.S.) 27 (2021) 70, journal link arXiv link.

"Littlewood complexes for symmetric groups". Represent. Theory 25 (2021) 594-605, journal link arXiv link.

"Indecomposable Objects of Rep(GL_t) in Terms of Exterior Powers of the Tautological Object and its Dual". J. Algebra 557 (2020) 165-171, journal link arXiv link.

"A Permutation Module Deligne Category and Stable Patterns of Kronecker Coefficients". Transform. Groups 27 (2022) 1069-1109, journal link arXiv link.

(with S. Nyobe Likeng and A. Savage) Appendix to "Embedding Deligne's category Rep(S_t) in the Heisenberg category", by S. Nyobe Likeng and A. Savage. Quantum Topol. 12 (2021) 211-242, journal link arXiv link.

"Resolving Irreducible \mathbb{C}S_n-Modules by Modules Restricted from GL_n(\mathbb{C})". Represent. Theory 24 (2020) 229-234, journal link arXiv link.

"The Structure of Grothendieck Rings of Wreath Product Deligne Categories and their Generalisations". Int. Math. Res. Not. 16 (2021) 12420-12462, journal link arXiv link.

"Stable Grothendieck Rings of Wreath Product Categories". J. Algebr. Comb. 49 (2019) 267-307, journal link arXiv link.

Other Mathematical Work:

In 2017, I mentored a PRIMES-USA project by Mihir Singhal, titled "Generalizations of Hall-Littlewood Polynomials". Mihir was a Regeneron TST 2018 Scholar.

An Answer to a Question of Zeilberger and Zeilberger about Fractional Counting of Partitions: arXiv link.

Notes, Slides, and Software:

Here are notes for some seminar talks I have given:

Notes (323 kB) on Macdonald Polynomials and Double Affine Hecke Algebras at the MIT-Northeastern Graduate seminar on Double Affine Hecke algebras and Elliptic Hall algebras, Spring 2017,
Notes (252 kB) on tensoring with finite-dimensional modules in category O at the MIT-Northeastern Graduate seminar on category O and Soergel bimodules, Fall 2017,
Notes (handwritten, 12 MB) on blocks of Rep(S_t) at the MIT Deligne Categories and Representation Stability seminar, Fall 2016.

Here are slides for some presentations I have given:

Deligne Categories (368 kB),
Symmetric Tensor Categories (232 kB).
Stable Character Polynomials for Symmetric Groups (302 kB).
Stable characters from permutation patterns (474 kB).

I have written some Python programs for calculating quantities related to representations of symmetric groups:

Characters of Symmetric Groups,
Littlewood-Richardson Coefficients.


Here is script I wrote for making (hopefully pretty) pictures: Scribble. It should work on both mobile and desktop versions of Firefox, Chrome, and Safari (intended for a full-size browser window).