# Richard Thomas: Nonabelian DT theory from abelian DT theory

**Time: **
Tue 2021-09-07 14.30 - 15.30

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan (alt. Zoom, meeting ID: 921 756 1880)

**Lecturer: **
Richard Thomas (Imperial College London, online)

**Abstract: **Fix a Calabi–Yau 3-fold *X*. Its DT invariants count stable bundles and sheaves on *X*. Joyce's generalised DT invariants 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 the latter are determined by the GW invariants of *X*. Along the way we also express rank *r* DT invariants in terms of rank 0 invariants counting sheaves supported on surfaces in *X*. These invariants are predicted by S-duality to be governed by (vector-valued mock) modular forms.