Ron Cherny

Published Work

1. Matthew Satriano, Ron Cherny, and Yohan Song. On the Algebra Generated by Three Commuting Matrices: Combinatorial Cases. The Electronic Journal of Combinatorics, Volume 31, Issue 4 (2024). PDF

In Progress

1. Describing gluing of arbitrary rank web diagrams; Jungle Tableaux with Oliver Pechenik Stephan Pfannerer.
2. Combinatorial instance of the Gerstehaber problem with Matthew Satriano and Tam An Le Quang.

Projects

• I am currently working under the supervision of Matthew Kennedy, exploring applications of the non-commutative convexity framework in arithmetic dynamics
• I have also been supervised by Oliver Pechenik together with Stephan Pfannerer, investigating the structure of promotion permutations. These permutations arise naturally from recording row indices during the promotion process on rectangular Young tableaux. We are interested in these permutations because they appear to encode combinatorial data underlying a correspondence between rectangular Young tableaux and web diagrams.
• I collaborated with Yohan Song under the supervision of Matthew Satriano on a combinatorial instance of the Gerstenhaber problem. The problem asks whether, given three commuting $n \times n$ matrices, the dimension of the algebra they generate is always bounded by $n$. We proved that this bound holds for a broad class of matrices generated from certain combinatorial structures.

Talks

1. I gave a talk on extending the framework of the first rotation-invariant $U_q(sl_4)$ web basis to higher rank, by studying promotion permutations and extracting structural information about the webs. This talk was presented at CanaDAM 2025 in the Web Graphs session. Slides
2. I presented a talk on the Gerstenhaber problem in the Algebraic and Enumerative Combinatorics Seminar at the University of Waterloo, focusing on whether the dimension of the algebra generated by three commuting $n \times n$ matrices is less than $n$. Slides