# Dennis Eriksson: Refined Riemann–Roch for degenerations of Calabi–Yau manifolds and a mirror symmetry-conjecture

**Time: **
Tue 2021-11-30 13.15 - 14.15

**Location: **
Institut Mittag-Leffler, Seminar Hall Kuskvillan (alt. Zoom, meeting ID: 921 756 1880)

**Lecturer: **
Dennis Eriksson (Chalmers/University of Gothenburg)

**Abstract:** In recent joint work (w. Gerard Freixas and Christophe Mourougane) we proved a mirror symmetry-statement for genus one Gromov–Witten invariants of Calabi–Yau hypersurfaces in projective space. The original conjecture was formulated by string theorists. A central tool was a reformulation of the conjecture, using an metric version of the Riemann–Roch. In this talk I will focus on a formulation of a more mathematical version of the conjecture, together with a list of examples where it is verified. There are two main ingredients, namely the limit Hodge structure of a maximally degenerate family, and a lifting of the (codimension 1)-version of the Grothendieck–Riemann–Roch theorem to the level of line bundles. The latter ingredient is ongoing joint work Gerard Freixas.