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Local compactified Jacobians of planar curve singularities and harmonic analysis
Algebraic Geometry and Number Theory| Speaker: | Cheng-Chiang Tsai, Stanford University |
| Related Webpage: | https://mathematics.stanford.edu/people/department-directory/name/cheng-chiang-tsai/ |
| Location: | 2112 MSB |
| Start time: | Wed, Oct 17 2018, 1:10PM |
In this talk, we study the weight polynomial of the local compactified Jacobian of a planar curve singularity, or equivalent counting $\mathbb{F}_q$-points on such Jacobians. The problem will be translated to questions about $p$-adic integrals, and tackled with methods in harmonic analysis of p-adic groups. If time permits, we will also discuss possible interaction of the method with knot (or rather braid) invariants.