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Student Cluster Algebra Seminar: Compactifications of cluster varieties and dualities between them

Event Type
Seminar/Symposium
Sponsor
n/a
Virtual
wifi event
Date
Feb 17, 2022   2:00 pm  
Speaker
Man-Wai Cheung
Contact
Elizabeth Kelley
E-Mail
kelleye@illinois.edu
Views
18

Abstract: Cluster varieties are log Calabi-Yau varieties which are unions of algebraic tori glued by birational "mutation" maps. In particular, they are blowups of toric varieties. We will show how to generalize the polytope construction of toric varieties to cluster varieties. As an application, we will see that the non-integral vertex in the Newton-Okounkov body of the Grassmannian comes from the so-called broken line convexity. We will also discuss mirror dualities of cluster varieties from the symplectic perspective. This talk will be based on a series of joint works with Bardwell-Evans, Bossinger, Hong, Lin, Magee, and Najera-Chavez.

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