Gromov-Witten invariants of the Hilbert scheme of points of a K3
surface (and more)
-- Georg Oberdieck, November 20, 2015

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A theorem of Maulik-Pandharipande-Thomas asserts that the
Gromov-Witten theory of K3 surfaces is governed by quasi-modular
forms.  In this talk I will discuss a generalization of their result
to the Hilbert scheme of 2 points of a K3 surface, the analog of a K3
surface in dimension 4, namely: The genus 0 Gromov Witten theory of
Hilb<sub>2</sub>(K3) (in primitive classes) is governed by
quasi-Jacobi forms. If time permits, I will explain how this leads to
new curve-counting formulas on the K3 surface itself.