BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Albrecht Klemm (Bonn) DTSTART:20210125T200000Z DTEND:20210125T210000Z DTSTAMP:20260423T021445Z UID:WHCGP/25 DESCRIPTION:Title: C alabi-Yau modularity and Feynman graphs\nby Albrecht Klemm (Bonn) as p art of Western Hemisphere colloquium on geometry and physics\n\n\nAbstract \nUsing the GKZ system for the primitive cohomology of an infinite series of complete intersection Calabi-Yau manifolds\, whose dimension is the loo p order minus one\, we completely clarify the analytic structure of all ba nana integrals with arbitrary masses. In particular\, we find that the lea ding logarithmic structure in the high energy regime\, which corresponds t o the point of maximal unipotent monodromy\, is determined by a novel \\ha t b-class evaluation in the ambient spaces of the mirror\, while the imagi nary part of the amplitude in this regime is determined by the Γb-clas s of the mirror Calabi-Yau manifold itself. We provide simple closed all l oop formulas for the former as well as for the Frobenius κ-constants\, which determine the behaviour of the amplitudes\, when the momentum square equals the sum of the masses squared\, in terms of zeta values. We find t he exact differential equation for the graph integrals with arbitrary valu e for the dimensional regularisation (d-\\epsilon) parameter and extend ou r previous work from three to four loops by providing for the latter case a complete set of (inhomogenous) Picard-Fuchs differential ideal for arbit rary masses. Using a recent p-adic analysis of the periods we determine th e value of the maximal cut equal mass four-loop amplitude at the attractor points in terms of periods of modular weight two and four Hecke eigenform s and the quasiperiods of their meromorphic cousins.\n LOCATION:https://researchseminars.org/talk/WHCGP/25/ END:VEVENT END:VCALENDAR