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Current Colloquia & Seminars

  1. Bowen Lecture Series -3- Birational geometry in characteristic p>0.

    Location: UC Berkeley - 60 Evans Hall
    Speakers: Christopher Hacon (University of Utah)

    After recent spectacular progress in the classification of varieties over an algebraic closed field of characteristic 0 (e.g. the solution set of a system of polynomial equations defined by p1,...,prp1,...,pr in C[x1,...,xn]C[x1,...,xn]) it is natural to try and understand the geometry of varieties defined over an algebraically closed field of characteristic p>0p>0. Many technical difficulties arise in this context. Nevertheless, there has been much progress recently. In particular, the MMP was established for 3-folds in characteristic p>5p>5 by work of Birkar, Hacon, Xu and others. In this talk, we will explain some of the challenges and the recent progress in this active area of research.

    Updated on Feb 11, 2019 10:16 AM PST
  2. DAG Seminar: Motivic cohomology and the derived Hecke algebra for dihedral weight one forms

    Location: MSRI: Simons Auditorium
    Speakers: Michael Harris (Columbia University)

    This is a report on joint work in progress with Darmon, Rotger, and Venkatesh.    In a series of papers, Venkatesh and his collaborators have proposed a conjectural framework that incorporates the action of motivic cohomology groups on the cohomology of locally symmetric spaces.  The simplest case concerns the cohomology of the special fiber in characteristic p of the modular curve with coefficients in the sheaf of weight 1 forms. There the conjecture relates the action of derived Hecke operators, which only exist over coefficient rings in positive characteristic, to the (discrete) logarithms of certain units in the number fields cut out by two-dimensional complex representations of the absolute Galois group of Q.  Our main result is a proof of this conjecture as it pertains to weight one forms whose associated Galois representations are induced from Dirichlet characters of quadratic fields.  The proof is based on classical constructions in the theory of modular forms. If time permits, there will be a discussion of how Venkatesh's conjectures might fit into a (highly speculative) derived version of the Langlands program.

    Updated on Feb 14, 2019 09:34 AM PST