BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Okke van Garderen (Max-Planck Institute) DTSTART:20220317T090000Z DTEND:20220317T100000Z DTSTAMP:20260404T111007Z UID:HubEG/1 DESCRIPTION:Title: Symmetry & vanishing in the DT theory of cDV singularities\nby Ok ke van Garderen (Max-Planck Institute) as part of Events Hub: Enumerative geometry\n\n\nAbstract\nDonaldson–Thomas theory was conceived as a metho d of counting certain sheaves in Calabi-Yau threefolds\, which are suppose d to encode ‘BPS numbers’ in string theory. More recent developments h ave led to broader\, refined versions of this theory\, which produce motiv ic or cohomological invariants from moduli spaces of semistable objects in the derived category. In this talk I will focus on DT theory for crepant resolutions of compound Du-Val singularities\, which include threefold flo ps\, as well as some divisor-to-curve contractions and quotient singularit ies. I will explain how one can determine the moduli of semistable objects in this setting via a tilting method that is governed by Dynkin diagram c ombinatorics. Using this\, I will show that the motivic incarnations of th e BPS numbers vanish for K-theory classes outside an associated root latti ce\, and exhibit additional symmetries among these invariants. To make thi s explicit\, I will use the example of a dihedral quotient singularity\, f or which the invariants can be fully calculated.\n\nZoom: 941 5513 6832 Co de: YMSC\n LOCATION:https://stable.researchseminars.org/talk/HubEG/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Henry Liu (Oxford) DTSTART:20220331T090000Z DTEND:20220331T100000Z DTSTAMP:20260404T111007Z UID:HubEG/2 DESCRIPTION:Title: Quasimaps and stable pairs\nby Henry Liu (Oxford) as part of Even ts Hub: Enumerative geometry\n\n\nAbstract\nQuasimaps to Hilbert schemes o f surfaces S resemble the Donaldson-Thomas theory of S times a curve. This correspondence can be made precise for the appropriate DT stability chamb er\, namely the so-called Bryan-Steinberg stable pairs. I will explain why BS pairs and quasimaps are equivalent whenever they are comparable. Quasi maps have been used recently to study 3d mirror symmetry\, which when push ed through this equivalence has implications for some aspects of sheaf-cou nting theories\, including the (DT) crepant resolution conjecture.\n\nZoom : 849 963 1368 Code: YMSC\n LOCATION:https://stable.researchseminars.org/talk/HubEG/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Carl Lian DTSTART:20220407T090000Z DTEND:20220407T100000Z DTSTAMP:20260404T111007Z UID:HubEG/3 DESCRIPTION:Title: Curve-counting with fixed domain (“Tevelev degrees”)\nby Carl Lian as part of Events Hub: Enumerative geometry\n\n\nAbstract\nWe will c onsider the following problem: if (C\,x_1\,...\,x_n) is a fixed general po inted curve\, and X is a fixed target variety with general points y_1\,... \,y_n\, then how many maps f:C -> X in a given homology class are there\, such that f(x_i)=y_i? When considered virtually in Gromov-Witten theory\, the answer may be expressed in terms of the quantum cohomology of X\, lead ing to explicit formulas in some cases (Buch-Pandharipande). The geometric question is more subtle\, though in the presence of sufficient positivity \, it is expected that the virtual answers are enumerative. I will give an overview of recent progress on various aspects of this problem\, includin g joint work with Farkas\, Pandharipande\, and Cela\, as well as work of o ther authors.\n\nZoom: 849 963 1368 Code: YMSC\n LOCATION:https://stable.researchseminars.org/talk/HubEG/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Yalong Cao DTSTART:20220519T080000Z DTEND:20220519T090000Z DTSTAMP:20260404T111007Z UID:HubEG/4 DESCRIPTION:Title: Gopakumar-Vafa type invariants of holomorphic symplectic 4-folds\ nby Yalong Cao as part of Events Hub: Enumerative geometry\n\n\nAbstract\n Abstract: Gromov-Witten invariants of holomorphic symplectic 4-folds vanis h and one can consider the corresponding reduced theory. In this talk\, we will explain a definition of Gopakumar-Vafa type invariants for such a re duced theory. These invariants are conjectured to be integers and have alt ernative interpretations using sheaf theoretic moduli spaces. Our conjectu re is proved for the product of two K3 surfaces\, which naturally leads to a closed formula of Fujiki constants of Chern classes of tangent bundles of Hilbert schemes of points on K3 surfaces. On a very general holomorphic symplectic 4-folds of K3^[2] type\, our conjecture provides a Yau-Zaslow type formula for the number of isolated genus 2 curves of minimal degree. Based on joint works with Georg Oberdieck and Yukinobu Toda.\n\nZoom Meeti ng ID: 271 534 5558\nPasscode: YMSC\n LOCATION:https://stable.researchseminars.org/talk/HubEG/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Miguel Moreira (ETH Zürich) DTSTART:20220526T080000Z DTEND:20220526T090000Z DTSTAMP:20260404T111007Z UID:HubEG/5 DESCRIPTION:Title: Weyl symmetry for curve counting invariants via spherical twists\ nby Miguel Moreira (ETH Zürich) as part of Events Hub: Enumerative geomet ry\n\n\nAbstract\nAbstract: Let X be a Calabi-Yau 3-fold containing a rule d surface W and let B be the homology class of the lines in the ruling. Ph ysics suggests that curve counting on X should satisfy some symmetry relat ing curves in classes β and β’=β+(W.β)B. In this talk I’ll explain how to make such a symmetry precise with a new rationality result for the Pandharipande-Thomas invariants of X. Mathematically\, the symmetry is ex plained by a certain involution of the derived category of X constructed using a particular spherical functor\; our proof is an instance of the gen eral principle that automorphisms of the derived category should constrain enumerative invariants. This is joint work with Tim Buelles and it is hig hly inspired in the proof of rationality for the PT generating series of a n orbifold by Beentjes-Calabrese-Rennemo.\n\nZoom Meeting ID: 271 534 5558 Passcode: YMSC\n LOCATION:https://stable.researchseminars.org/talk/HubEG/5/ END:VEVENT END:VCALENDAR