|Title:||Descendent series for Hilbert schemes of points (Postdoc Colloquium)|
|Date (JST):||Fri, Sep 24, 2021, 11:30 - 12:00|
Among the most fundamental moduli spaces appearing in algebraic geometry are Hilbert schemes of points, which parametrize finite configurations of points in varieties. Interesting structure emerges when the underlying variety is fixed, but the number of points being parametrized is allowed to vary.
For example, one can consider descendent integrals over Hilbert schemes. These are integrals of characteristic classes of naturally occurring vector bundles, which may carry enumerative information. Generating series formed from compiling these integrals as the number of points varies often enjoy nice properties. For example, such series may be Laurent expansions of rational functions.
I will survey some results and conjectures on descendent series (and their K-theoretic analogs) for Hilbert schemes of points on curves, surfaces, and fourfolds, including some known results in search of geometric explanations.
|Remarks:||IPMU Postdoc Colloquium Series
Registration necessary from here: https://ipmu.zoom.us/webinar/register/WN_VTTp-bOdQY6GHCMDQrFVIg