Nonabelian DT theory from abelian DT theory

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 sheaves on X.

I will describe ongoing work with Soheyla Feyzbakhsh with the eventual aim of writing the generalised DT invariants in any rank r in terms of rank 1 invariants. By the MNOP conjecture the latter are determined by the GW invariants of X.

Along the way we express rank r DT invariants in terms of rank 0 invariants counting D4-D2-D0 branes. These invariants are predicted by S-duality to be governed by (vector-valued mock) modular forms.

Based partly on arXiv:2007.03037 and arXiv:2103.02915 .

differential geometrymetric geometry

Audience: researchers in the discipline

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Western Hemisphere colloquium on geometry and physics

Series comments: Description: Biweekly colloquium of geometers and physicists

This weekly online colloquium features geometers and physicists presenting current research on a wide range of topics in the interface of the two fields. The talks are aimed at a broad audience. They will take place via Zoom on alternate Mondays at 3pm Eastern, noon Pacific, 4pm BRT. Each session features a 60 minute talk, followed by 15 minutes for questions and discussion. You may join the meeting 15 minutes in advance. Questions and comments may be submitted to the moderator via the chat interface during the talk, or presented in person during the Q&A session. These colloquia will be recorded and will be available (linked from the website) asap after the event.

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