BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Giordano Cotti (Grupo de Física Matemática\, Universidade de Lis boa) DTSTART:20240130T160000Z DTEND:20240130T170000Z DTSTAMP:20260423T022624Z UID:Geolis/143 DESCRIPTION:Title: Gromov-Witten theory\, quantum differential equations\, and derived categ ories\nby Giordano Cotti (Grupo de Física Matemática\, Universidade de Lisboa) as part of Geometria em Lisboa (IST)\n\n\nAbstract\nEnumerative geometry sinks its roots many centuries back in time. In the last decades \, ideas coming from physics brought innovation to this research area\, wi th both new techniques and the emergence of new rich geometrical structure s. As an example\, Gromov--Witten theory\, focusing on symplectic invarian ts defined as counting numbers of curves on a target space\, led to the no tion of quantum cohomology and quantum differential equations (qDEs).\n\nT he qDEs define a class of ordinary differential equations in the complex d omain\, whose study represents a challenging active area in both contempor ary geometry and mathematical physics. The qDEs define rich invariants att ached to smooth projective varieties. These equations\, indeed\, encapsula te information not only about the enumerative geometry of varieties but ev en (conjecturally) of their topology and complex geometry. The way to disc lose such a huge amount of data is through the study of the asymptotics an d monodromy of their solutions. This talk will be a gentle introduction to the study of qDE's\, their relationship with derived categories of cohere nt sheaves (in both non-equivariant and equivariant settings)\, and a theo ry of integral representations for its solutions. Overall\, the talk will be a survey of the results of the speaker in this research area.\n LOCATION:https://researchseminars.org/talk/Geolis/143/ END:VEVENT END:VCALENDAR