BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Tyler Kelly (University of Birmingham) DTSTART:20221124T233000Z DTEND:20221125T003000Z DTSTAMP:20260422T054234Z UID:SFUQNTAG/78 DESCRIPTION:Title: Open Mirror Symmetry for Landau-Ginzburg models\nby Tyler Kelly (Uni versity of Birmingham) as part of SFU NT-AG seminar\n\nLecture held in K-9 509.\n\nAbstract\nA Landau-Ginzburg (LG) model is a triplet of data (X\, W \, G) consisting of a regular function $W:X\\to\\mathbb{C}$ from a quasi-p rojective variety $X$ with a group $G$ acting on $X$ leaving $W$ invariant . One can build an analogue of Hodge theory and period integrals associate d to an LG model when $G$ is trivial. This involves oscillatory integrals on certain cycles in\n$X$ (fear not: this is actually cute and will be don e in examples!). Mirror symmetry states that period integrals often encode enumerative geometry and this is also the case here. An\nenumerative theo ry developed by Fan\, Jarvis\, and Ruan gives FJRW invariants\, the analog ue of Gromov-Witten invariants for LG models. These invariants are now cal led FJRW invariants. A problem is that finding the right deformation perio d integrals is hard. We define and use a new open enumerative theory for c ertain Landau-Ginzburg LG models to solve this problem in low dimension. \ n\nRoughly speaking\, this involves computing specific integrals on certai n moduli of disks with boundary and interior marked points. One can then c onstruct a mirror Landau-Ginzburg model to a Landau-Ginzburg model using t hese invariants that gives you the right deformation for free. This allows us to prove a mirror symmetry result analogous to that established by Cho -Oh\, Fukaya-Oh-Ohta-Ono\, and Gross for mirror symmetry for toric Fano ma nifolds. This is joint work with Mark Gross and Ran Tessler.\n LOCATION:https://researchseminars.org/talk/SFUQNTAG/78/ END:VEVENT END:VCALENDAR