**2024년 09월 QSMS Monthly Seminar**

**Date:**Sept 20th (Fri) 14:00 ~ 17:00**Place:**27-220**Contents:**

**Speaker: **김명호 (오후2시)

**TiTle: **Braid varieties and cluster algebras

**Abstract: **

Braid varieties are generalization of several varieties such as half-decorated Double Bott-Samelson varieties, open Richardson varieties, and so on.

We will review the definition of braid varieties and cluster algebra structures on their coordinate rings, following the paper "Cluster structures on braid varieties" by R. Casals, E. Grosky, M. Gorsky, I. Le, L. Shen and J. Simental.

**Speaker: **김유식 (오후4시)

**Title: **Symplectic geometry of Markov-type Diophantine equations

**Abstract:**

The Markov Diophantine equation a^2 +b^2 +c^2 =3abc has appeared in various areas of mathematics, particularly in relation to the geometry of the complex projective plane. In this talk, I will explore the connection between this equation and the symplectic geometry of the projective plane. I will then discuss how it can be generalized to higher dimensions by examining the relationship between Markov-type Diophantine equations and the symplectic geometry of Fano varieties.