2021年度
第2回
日時:2021年7月2日(金) 15:00~16:30
場所:Zoom
講演者:桑垣樹氏(大阪大学理学研究科)
タイトル:Sheaf quantization and cluster structure
アブストラクト: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.
第1回
日時:2021年4月23日(金) 15:00~16:30
場所:Zoom
講演者:塚本真由氏(山口大学理学部 数理科学科)
タイトル:Intervals of s-torsion pairs in extriangulated categories with negative first extensions
アブストラクト:In a triangulated category, Happel, Reiten and Smalo provided a construction of new t-structures through torsion pairs in the heart of a given t-structure. This construction induces a bijection between the set of certain t-structures and the set of torsion pairs in the heart. On the other hand, Asai--Pfeifer and Tattar established a bijection for torsion pairs in an abelian category, which is related to tau-tilting theory. In this talk, we introduce the notion of s-torsion pairs in an extriangulated category as a common generalization of t-structures and torsion pairs (in abelian/exact categories). Moreover, we establish a bijection for s-torsion pairs in an extriangulated category which unifies two bijections above. This talk is based on a joint work with Takahide Adachi and Haruhisa Enomoto.