Wall-crossing and vertex algebras, in cohomology, K-theory, and beyond

主讲人 / Speaker

Henry Liu 刘华昕 (IPMU)

时间 / Time

Every Tuesday from April 1st to 29th, 3:30-5:30 pm

地点 / Venue

C654, Shuangqing Complex Building A

Wall-crossing and vertex algebras, in cohomology, K-theory, and beyond

课程介绍 / Description

Variations of stability conditions, and geometric methods relating different (semi)stable loci in moduli spaces, are powerful techniques in enumerative geometry and related areas. In particular, one can sometimes obtain "wall-crossing" formulas for enumerative invariants of such loci, in any cohomology theory of Borel-Moore type, via various so-called "master spaces". I will explain some remarkable algebraic structures and properties that appear in the general study of such wall-crossing formulas, e.g. for elliptic genus. The main case of interest, and also the most sophisticated, is Joyce's recent discovery that that, for a wide class of linear categories like categories of coherent sheaves, cohomological wall-crossing formulas are controlled by a vertex algebra. This may be refined to equivariant K-theory, and leads to rich interactions with geometric representation theory. I will conclude by explaining some joint work, with Nikolas Kuhn and Felix Thimm, on applications of all these ideas to enumerative problems of 3-Calabi-Yau type, notably various flavors of Donaldson-Thomas theory.