For more information about this meeting, contact Nigel Higson, Ping Xu, Mathieu Stienon.
| Title: | Singularities of admissible normal functions |
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| Seminar: | GAP Seminar |
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| Speaker: | Zhaohu Nie, PSU-Altoona |
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| Abstract: |
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| The first proof of the Lefschetz (1,1) theorem was given by
Poincare and Lefschetz using normal functions for a Lefschetz pencil.
The hope to generalize this method to higher codimensional Hodge
conjecture was blocked by the failure of Jacobian inversion. In another
direction, one can hope for an inductive proof of the Hodge conjecture
if for any primitive Hodge class one can find a, necessarily singular,
hypersurface to "capture part of it". Recently Green and Griffiths
introduced the notion of extended normal functions over higher
dimensional bases such that their singular loci corresponds to such
hypersurfaces. In this talk, we will present how to understand
singularities using the viewpoint of admissible normal functions, and
how the Hodge conjecture is then equivalent to the existence of
singularities. This is joint work with P. Brosnan, H. Fang and G.
Pearlstein. |
Room Reservation Information
| Room Number: | MB106 |
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| Date: | 11 / 10 / 2009 |
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| Time: | 02:30pm - 03:30pm |
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