Christopher Ryba


I am a fifth year mathematics PhD student at MIT, advised by Pavel Etingof. My primary research interests are representation theory and algebraic combinatorics.

My CV is here and my research statement is here. I can be reached via email at the following address: ryba@mit.edu


Publications:

"Stable Grothendieck Rings of Wreath Product Categories". Journal of Algebraic Combinatorics (2019) 49: 267, arXiv link.

"The Structure of Grothendieck Rings of Wreath Product Deligne Categories and their Generalisations". IMRN (to appear), arXiv link.

"Resolving Irreducible \mathbb{C}S_n-Modules by Modules Restricted from GL_n(\mathbb{C})". Representation Theory, accepted for publication. 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 Topology, accepted for publication. arXiv link.

"A Permutation Module Deligne Category and Stable Patterns of Kronecker Coefficients". Submitted for publication. arXiv link.

"Indecomposable Objects of Rep(GL_t) in Terms of Exterior Powers of the Tautological Object and its Dual". Submitted for publication. 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 (13 slides, 368 kB),
Symmetric Tensor Categories (12 slides, 232 kB).

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

Characters of Symmetric Groups,
Littlewood-Richardson Coefficients.

Other:

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).