March 19, 2024
Title: Study GEMS through LSD
Speaker: Michel van Garrel (Birmingham)
In this joint work in progress with Helge Ruddat and Bernd Siebert, we employ a particular type of Log Smooth Degeneration (LSD) to study the Geometry of Enumerative Mirror Symmetry (GEMS).
Mirror Symmetry is a broad conjecture that predicts that symplectic invariants of a Kähler manifold correspond to algebro-geometric invariants of a mirror-dual complex algebraic variety. This is generally proven by computing both sides.
In this work, we take the first steps towards a full enumerative correspondence that canonically identifies the invariants of both sides. To do so, we employ the Intrinsic Mirror Construction of Gross-Siebert. Then the enumerative correspondence passes through an intermediary tropical manifold and tropical invariants thereof.