BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Giordano Cotti (FCUL\, Lisbon) DTSTART:20201216T140000Z DTEND:20201216T150000Z DTSTAMP:20260423T010637Z UID:GPL/3 DESCRIPTION:Title: Quan tum differential equations\, isomonodromic deformations\, and derived cate gories\nby Giordano Cotti (FCUL\, Lisbon) as part of Geometry and Phys ics @ Lisbon\n\n\nAbstract\nThe quantum differential equation (qDE) is a r ich object attached to a smooth projective variety X. It is an ordinary di fferential equation in the complex domain which encodes information of the enumerative geometry of X\, more precisely its Gromov-Witten theory. Furt hermore\, the asymptotic and monodromy of its solutions conjecturally rule s also the topology and complex geometry of X. \n\nThese differential equa tions were introduced in the middle of the creative impetus for mathematic ally rigorous foundations of Topological Field Theories\, Supersymmetric Q uantum Field Theories and related Mirror Symmetry phenomena. Special menti on has to be given to the relation between qDE's and Dubrovin-Frobenius ma nifolds\, the latter being identifiable with the space of isomonodromic de formation parameters of the former. \n\nThe study of qDE’s represents a challenging active area in both contemporary geometry and mathematical ph ysics: it is continuously inspiring the introduction of new mathematical t ools\, ranging from algebraic geometry\, the realm of integrable systems\, the analysis of ODE’s\, to the theory of integral transforms and specia l functions.\n\nThis talk will be a gentle introduction to the analytical study of qDE’s\, their relationship with derived categories of coherent sheaves (in both non-equivariant and equivariant settings)\, and a theory of integral representations for its solutions. The talk will be a survey o f the results of the speaker in this research area.\n LOCATION:https://researchseminars.org/talk/GPL/3/ END:VEVENT END:VCALENDAR