Roy Joshua Ohio State University Title: Equivariant Algebraic Ktheory and Derived completion II: the case of equivariant homotopy Ktheory and applications
Abstract : This is a report on work in progress with Gunnar Carlsson and Pablo Pelaez. Derived completion is a technique that originated slightly over 20 years ago. In the first part of this work, we proved
a derived completion theorem for equivariant Gtheory, extending the work of Atiyah and Segal in the topological case and that of Thomason for equivariant Gtheory with finite coefficients and with the Bottelement inverted. In the present work we extend these results to equivariant homotopy Ktheory and discuss applications to equivariant RiemannRoch problems.
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Gregory Pearlstein  University of Pisa
Title: Infinitesimal Torelli and rigidity results for a remarkable class of elliptic surfaces
Abstract: I will discuss joint work with Chris Peters which extends rigidity results of Arakalov, Faltings and Peters to period maps arising from families of complex algebraic varieties which are nonnecessarily proper or smooth. Inspired by recent work with P. Gallardo, L. Schaffler, Z. Zhang, I will discuss two classes of elliptic surfaces which can be presented as hypersurfaces in weighted projective spaces which have a unique canonical curve. In each case, we will show that infinitesimal Torelli fails for H^2 of the compact surface, but is restored when one considers the period map for the complement of the canonical curve.
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Ursula Whitcher  American Math Society
Title: Highly symmetric CalabiYau Grassmannian hypersurfaces
Abstract:We use computational techniques based on work of Fatighenti and Mongardi
to study the Hodge structure of families of CalabiYau varieties
realized as quotients of Grassmannian hypersurfaces by abelian groups.
We show that, in contrast to a proposal of Coates, Doran, and
Kalashnikov, these families do not yield a direct generalization of the
classical GreenePlesser mirror construction, but they do provide a new
perspective on the CalabiYau landscape.
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Pablo Pelaez  UNAM, Mexico
Title: Incidence equivalence and the BlochBeilinson filtration
Abstract: We will present an approach to the BlochBeilinson filtration via Voevodsky’s triangulated category of motives, and show that the second step of the filtration is given by cycles incident equivalent to zero.
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