BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Pelle Steffens (Technische Universität München) DTSTART:20240326T203000Z DTEND:20240326T220000Z DTSTAMP:20260422T174306Z UID:tandg/17 DESCRIPTION:Title: D ifferential geometric PDE moduli spaces: derived enhancements\, ellipticit y and representability\nby Pelle Steffens (Technische Universität Mü nchen) as part of Topology and Geometry Seminar (Texas\, Kansas)\n\n\nAbst ract\nAll sorts of algebro-geometric moduli spaces (of stable curves\, sta ble sheaves on a CY 3-folds\, flat bundles\, Higgs bundles...) are best un derstood as objects in derived geometry. Derived enhancements of classical moduli spaces give transparent intrinsic meaning to previously ad-hoc str uctures pertaining to\, for instance\, enumerative geometry and are indisp ensable for more advanced constructions\, such as categorification of enum erative invariants and (algebraic) deformation quantization of derived sym plectic structures. I will outline how to construct such enhancements for moduli spaces in global analysis and mathematical physics\, that is\, solu tion spaces of PDEs in the framework of derived ${\\rm C}^\\infty$ geometr y and discuss the elliptic representability theorem\, which guarantees tha t\, for elliptic equations\, these derived moduli stacks are bona fide geo metric objects (Artin stacks at worst). If time permits some applications to enumerative geometry (symplectic Gromov-Witten and Floer theory) and de rived symplectic geometry (the global BV formalism).\n LOCATION:https://researchseminars.org/talk/tandg/17/ END:VEVENT END:VCALENDAR