[Geom.,Alg.&Phys.] The Rising Sea for Enumerative Mirror Symmetry
ABSTRACT
Enumerative Mirror Symmetry predicts that each Calabi-Yau variety X admits a mirror-dual Calabi-Yau variety Y, so that the symplectic Gromov-Witten (GW) invariants of X are computed from period integrals on Y. Mirror Symmetry inspired calculations of GW invariants have been achieved in several large families of cases yielding lots of data, yet we are still lacking a general approach. The rising sea is a metaphor introduced by Grothendieck to describe a mathematical framework that is set up in a way so that major results of the theory are an almost automatic consequence of the definitions.
Comes in Intrinsic Mirror Symmetry (Gross-Siebert, 2022), which provides a general construction of Y from X. I will talk about an ongoing joint project with Siebert, where we show that the generating function of GW invariants of X equals the expansion of an intrinsic period integral on the Intrinsic Mirror Y of X. This project is motivated by building a Rising Sea framework for Enumerative Mirror Symmetry. (https://sites.google.com/view/gapkias)
