Motivic Donaldson–Thomas theory


Time and place

Summer semester 2020
Fridays 14-16, M 103


The Donaldson–Thomas invariants of a Calabi–Yau threefold X are certain virtual curve counts produced using the moduli stack of stable sheaves on X. The MNOP conjecture, recently proven for most Calabi–Yau threefolds by Pandharipande and Pixton, predicts a tight relationship between Donaldson–Thomas and Gromov–Witten invariants. In this course, we will give an introduction to Donaldson–Thomas theory and discuss a refinement that produces invariants of motivic nature. To achieve this, we will study and apply the following tools: the local structure of quasi-smooth derived stacks with (-1)–shifted symplectic structure, the formalism of motivic vanishing cycles, and microlocal geometry.

Prerequisites: Algebraic geometry. Familiarity with homotopical algebra / infinity-categories, and mixed motives or ℓ-adic sheaves, is recommended.



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  • [BJM] V. Bussi, D. Joyce, S. Meinhardt, On motivic vanishing cycles of critical loci, J. Algebraic Geom. 28 (2019), no. 3, 405--438, DOI.