Michel van Garrel (Birmingham) - Study GEMS through LSD
Abstract:
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.
I will start by briefly describing the string theory origins of mirror symmetry (Candelas-de la Ossa-Green-Parkes) followed by a brief description of the computational solution to the physics prediction (Givental Mirror Symmetry). Then I will outline our program which puts the physics intuition on firm ground and takes the first steps towards showing that Enumerative Mirror Symmetry follows from the geometric dualities of the Intrinsic Mirror Construction.
Published Feb. 9, 2024 2:38 PM
- Last modified Feb. 9, 2024 2:55 PM