From curve counting on Calabi-Yau 4-folds to quasimaps for quivers with potentials

Abstract

I will start by reviewing an old joint work with Davesh Maulik and Yukinobu Toda on relating Gromov-Witten, Gopakumar-Vafa and stable pair invariants on compact Calabi-Yau 4-folds. For non-compact CY4 like local curves, similar invariants can be studied via the perspective of quasimaps to quivers with potentials. In a joint work in progress with Gufang Zhao, we define a virtual count for such quasimaps and prove a gluing formula. Computations of examples will also be discussed.

About the speaker

I am a mathematician doing research on algebraic geometry, differential geometry and mathematical physics. I am particularly interested in understanding Yang-Mills theory on Calabi-Yau 4-folds and how it is interacted with enumerative geometry. I am eager to understand how such theory could lead to unexpected relations with other areas. It is my great pleasure to join RIKEN iTHEMS and I am looking forward to having exciting discussions with you.

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https://ithems.riken.jp/en/members/yalong-cao