We meet on Friday at 16:00 on Sugimoto Campus of Osaka Metropolitan University.

The venue is Room E408 in Science Building E. We also broadcast the seminar via Zoom.

Organizers: Yohsuke Matsuzawa, Ryo Kanda, Takamichi Sano, Hiroyuki Minamoto

Next Talk

Friday, May 22, 2026, 16:00-17:00
Venue: Room E408 in Science Building E

Toshiya Yurikusa (Osaka Metropolitan University)
Title: Intersection vectors on triangulated surfaces with applications to cluster algebras and tau-tilting theory
Abstract: In various areas of representation theory and cluster algebras, one associates vectors to algebraic or combinatorial objects, such as dimension vectors of modules or f-vectors of cluster monomials. A natural question is whether these vectors uniquely determine the corresponding objects.

In this talk, we focus on cluster algebras and Jacobian algebras arising from triangulated surfaces. We study this problem from a combinatorial viewpoint via triangulated surfaces. In particular, we use intersection numbers of curves on a triangulated surface and the associated vectors (called intersection vectors), which give rise to algebraic invariants such as f-vectors and dimension vectors.

We show that this perspective allows us to characterize when different multisets of compatible curves are uniquely determined by their intersection vectors. As applications, we obtain results in this setting on when f-vectors of cluster monomials and dimension vectors of tau-rigid and support tau-tilting modules are uniquely determined.

Schedule

Friday, June 19, 2026
Venue: Room F215 in Science Building F

Francesc Castella (University of California, Santa Barbara)

Friday, June 26, 2026
Venue: Room E408 in Science Building E

Shou Yoshikawa (Institute of Science Tokyo)

Support (FY 2025)

Sugimoto Algebra Seminars are supported by:

• JSPS KAKENHI Grant Number JP24K06693

• Osaka Central Advanced Mathematical Institute (MEXT Promotion of Distinctive Joint Research Center Program JPMXP0723833165), Osaka Metropolitan University