Seminars & Events for Algebraic Geometry Seminar

April 19, 2016
4:30pm - 5:30pm
Intersection numbers and higher derivatives of L-functions for functions fields, I

In joint work with Wei Zhang, we prove a higher derivative analogue of the Waldspurger formula and the Gross-Zagier formula in the function field setting under the assumption that the relevant objects are everywhere unramified. Our formula relates the self-intersection number of certain cycles on the moduli of Shtukas for GL(2) to higher derivatives of automorphic L-functions for GL(2). In this first talk, I will explain the geometric construction behind the formula.

Speaker: Zhiwei Yun , Stanford University
Location:
Fine Hall 322
April 26, 2016
4:30pm - 5:30pm
Hodge ideals

I will present joint work with M. Mustata, in which we study a sequence of ideals arising naturally from M. Saito's Hodge filtration on the localization along a hypersurface. The multiplier ideal of the hypersurface appears as the first step in this sequence, which as a whole provides a more refined measure of singularities. We give applications to the comparison between the Hodge filtration and the pole order filtration, adjunction, and the singularities of hypersurfaces in projective space and theta divisors on abelian varieties.

Speaker: Mihnea Popa , Northwestern University
Location:
Fine Hall 322
April 27, 2016
2:30pm - 3:30pm
Mirror symmetry, elliptic fibrations, and Jacobi forms

Please note special day (Wednesday).  We conjecture, with evidence, that the all-genus Gromov-Witten generating function of an elliptically fibered Calabi-Yau threefold is expressed as a quotient of weak Jacobi forms with a universal denominator. For the Calabi-Yau Weierstrass fibration over the projective plane, the conjecture allows the GW invariants for any curve class to be computed algorithmically up to genus 189, while the GW invariants for curve classes which project to a plane curve of degree at most 20 can be computed algorithmically to arbitrarily high genus. This talk is based on joint work with Min-xin Huang and Albrecht Klemm.

Speaker: Sheldon Katz, University of Illinois at Urbana-Champaign
Location:
Fine Hall 322

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