Dyck paths combinatorics for wall-crossings

Time：Mon., 15:30-16:30, Sept. 8, 2025

Venue：B627, Shuangqing Complex Building A

Organizer：/

Speaker：Lang Mou

Speaker

报告人

牟浪（University of California，Davis）

Time

时间

Mon., 15:30-16:30, Sept. 8, 2025

Venue

地点

B627, Shuangqing Complex Building A

Abstract

摘要

I will present a manifestly positive formula computing any wall-function in a rank-2 scattering diagram generated by two initial lines. The coefficients of these wall-functions enumerate partial tilings of the region above certain Dyck paths. By lifting the rank-2 positivity to higher ranks, we obtain a proof of the positivity conjecture for Chekhov-Shapiro's generalized cluster algebras. This is joint work with Amanda Burcroff and Kyungyong Lee.

DATESeptember 4, 2025

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