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TITLE: [HG_AG] Computing Vafa-Witten invariants of surface with elliptic fibrations

ABSTRACT: By applying Nesterov's theory on surface with elliptic fibrations, we compute Vafa-Witten invariants via some assumption on surface invariant, in following two cases: 1) S = C x E / G, G is a finite group acting on curve C and elliptic curve E freely. 2) S -> P^1 is an elliptic surface, whose fibers are irreducible elliptic curves, at most have nodal singularity. We will also give conjectures on VW invariants for elliptic surfaces whose fibers are elliptic curves(not necessarily irreducible), at most have nodal singularity. The contents of the talk is based on a joint work with Yaoxiong Wen.