讲座提要：

Fix a Calabi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. The generalised DT invariants of Joyce-Song count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP conjecture these rank 1 “abelian” invariants are determined by the GW invariants of X. Along the way we also express rank r DT invariants in terms of invariants counting “D4-D2-D0 branes”: rank 0 sheaves supported on surfaces in X. These invariants are predicted by physicists’ S-duality to be governed by (vector-valued, mock) modular forms

讲座人介绍：

His research interests include algebraic geometry, mirror symmetry and Calabi-Yau manifolds, moduli problems and invariants derived from them.

Richard Thomas' personal webpage can be found at http://www.ma.ic.ac.uk/~rpwt/