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:20210416T160000Z DTEND:20210416T170000Z DTSTAMP:20260423T021401Z UID:TQFT/36 DESCRIPTION:Title: Qu antum differential equations\, qKZ difference equations\, and helices\ nby Giordano Cotti (Grupo de Física Matemática\, Universidade de Lisboa) as part of Topological Quantum Field Theory Club (IST\, Lisbon)\n\n\nAbst ract\nQuantum differential equations (qDEs) are a rich object attached to complex smooth projective varieties. They encode information on their enum erative geometry\, topology and (conjecturally) on their algebraic geometr y. In occasion of the 1998 ICM in Berlin\, B.Dubrovin conjectured an intri guing connection between the enumerative geometry of a Fano manifold $X$ w ith algebro-geometric properties of exceptional collections in the derived category $D_b(X)$. Under the assumption of semisimplicity of the quantum cohomology of $X$\, the conjecture prescribes an explicit form for local i nvariants of $QH^*(X)$\, the so-called “monodromy data”\, in terms of Gram matrices and characteristic classes of objects of exceptional collect ions. In this talk I will discuss an equivariant analog of these relations \, focusing on the example of projective spaces. The study of the equivari ant quantum differential equations for partial flag varieties has been ini tiated by V.Tarasov and A.Varchenko in 2017. They discovered the existence of a system of compatible qKZ difference equations\, which have made the study of the quantum differential equations easier than in the non-equivar iant case. I will establish relations between the monodromy data of the jo int system of the equivariant qDE and qKZ equations for $\\mathbb{P}^n$ an d characteristic classes of objects of the derived category of T-equivaria nt coherent sheaves on $\\mathbb{P}^n$.\n\nBased on joint works with B.Dub rovin\, D.Guzzetti and A.Varchenko.\n LOCATION:https://researchseminars.org/talk/TQFT/36/ END:VEVENT END:VCALENDAR