Research Seminars @ Illinois

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Tailored for undergraduate researchers, this calendar is a curated list of research seminars at the University of Illinois. Explore the diverse world of research and expand your knowledge through engaging sessions designed to inspire and enlighten.

To have your events added or removed from this calendar, please contact OUR at ugresearch@illinois.edu

Integrability & Representation Theory (IRT) Seminar

Event Type

Seminar/Symposium

Sponsor

IRT

Location

Altgeld 343

Date

Apr 17, 2025 1:00 pm

Speaker

Esther Banaian

Contact

Trung Vu

Originating Calendar

General Events - Department of Mathematics

Title: A cluster-theoretic perspective on Markov Numbers and Cohn Matrices

Abstract: Markov numbers, i.e. numbers which appear in solution triples to x^2 + y^2 + z^2 = 3xyz, first appeared in the context of Diophantine approximation. Cohn exhibited a connection between Markov numbers and the lengths of closed simple geodesics on the punctured torus. A byproduct is the family of Cohn matrices, which can be seen as a matrixization of Markov numbers. It is known that Markov numbers can be viewed as specializations of cluster variables in the cluster algebra from a once-punctured torus. We give a cluster-algebraic interpretation to Cohn matrices, using poset-theoretic formulas from Kantarcı Oguz-Yıldırım and Pilaud-Reading-Schroll. We also discuss variations of the Markov equation and cluster Cohn matrices, inspired by generalized cluster algebras in the sense of Chekhov-Shapiro. This is based on joint works with Yasuaki Gyoda and with Archan Sen.

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