BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Adrián Andrada (Universidad Nacional de Córdoba) DTSTART:20260909T140000Z DTEND:20260909T150000Z DTSTAMP:20260914T071149Z UID:VSGS/138 DESCRIPTION:Title: F rom integer polynomials to complex and hypercomplex manifolds\nby Adri án Andrada (Universidad Nacional de Córdoba) as part of Virtual seminar on geometry with symmetries\n\n\nAbstract\nWe say that a polynomial $p\\in \\mathbb{Z}[x]$ belongs to $\\Delta_n$ if it is monic of degree $n$\, all its roots are positive and distinct\, and the product of its roots is 1. F or $p\\in \\Delta_n$\, we show how to construct a $(2n+2)$-dimensional sol vmanifold equipped with an invariant complex structure\, and a $(4n+4)$-di mensional solvmanifold equipped with an invariant hypercomplex structure. These solvmanifolds are completely solvable\, therefore their de Rham coho mology can be computed using invariant differential forms. Imposing certai n restrictions on $p$ (namely\, the "full rank" or "quasi-full rank" condi tions)\, we obtain explicit expressions for their Betti numbers. In the co mplex case\, we show that these solvmanifolds are generalized Nakamura man ifolds (as defined by Cattaneo and Tomassini) and\, under the same conditi ons on $p$ plus an extra condition on the lattice\, we determine their Hod ge numbers.\n\nThis talk is based on joint work with María Laura Barberis and Valentina Chaves (Córdoba).\n LOCATION:https://researchseminars.org/talk/VSGS/138/ END:VEVENT END:VCALENDAR