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Seminar
FIELD Mathematics
DATE December 08 (Tue), 2020
TIME 16:30-17:30
PLACE Online
SPEAKER Kool, Martijn
HOST Oh, Jeongseok
INSTITUTE Universiteit Utrecht
TITLE Virtual invariants of projective surfaces
ABSTRACT Moduli spaces of stable sheaves on general type surfaces are typically singular. However, they carry a virtual class which can be used to define intersection numbers such as virtual Euler and Segre numbers. The former are part of SU(r) Vafa-Witten invariants. I give an overview of these invariants highlighting recent developments, such as a mathematical definition of SU(r)/Z_r Vafa-Witten invariants in terms of twisted sheaves, a new formula for SU(5) Vafa-Witten invariants in terms of the Rogers-Ramanujan continued fraction, and a virtual Segre-Verlinde correspondence. Joint works with Goettsche, Goettsche-Laarakker, and Jiang.
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