This project is maintained by ysykimura
2021年7月2日(金) 15:00~16:30
Zoom
桑垣樹氏(大阪大学理学研究科)
Sheaf quantization and cluster structure
Cluster structures on wild character varieties have been studied from various different perspectives. Shende—Treumann—Williams—Zaslow studied them by regarding the varieties as moduli of constructible sheaves. Via the Nadler–Zaslow equivalence, we can also consider them as moduli spaces of Lagrangian branes. Then the cluster variables are identified with local systems on Lagrangian branes. On the other hand, in Gaiotto–Moore–Neitzke (or its mathematical realization by Iwaki–Nakanishi), the cluster variables are identified with local systems on spectral curves. These two perspectives are similar, but the latter has a bit more information than the former and the latter can be described using sheaf quantizations (constructible sheaves living on +1-dimensional space). Recently, we (I and T. Ishibashi) observed how moduli of decorated sheaf quantizations are related to (X, A, principal) cluster varieties. In this talk, I will report these topics.