Geometry and Topology seminar
Speaker: Dr. Gorapada Bera, Simons Center for Geometry and Physics, Stony Brook University
Host: Sandip Singh
Title: Associative submanifolds of G₂-manifolds and adiabatic limits
Time, day and date: 11:30:00 AM - 12:30:00 PM, Monday, March 16
Venue: Online (Google Meet: https://meet.google.com/jzy-kqch-nzy)
Abstract: G₂-manifolds are 7-dimensional Riemannian manifolds with special holonomy, analogous to Calabi–Yau 3-folds, and associative submanifolds are a special class of volume-minimizing 3-dimensional submanifolds, analogous to holomorphic curves or special Lagrangians. Inspired by the counting of holomorphic curves or special Lagrangians in Calabi–Yau 3-folds, Joyce, Doan, and Walpuski have proposals about defining enumerative invariants of G₂-manifolds by counting closed associative submanifolds. In this talk, I will focus on three topics connected to this enumerative theory. First, I will discuss a key ingredient of these proposals: the appearance of conically singular associative submanifolds and their desingularizations. Afterwards, I will describe a method for constructing associative submanifolds in a class of G₂-manifolds known as twisted connected sums. Finally, I will discuss Donaldson’s program on the adiabatic limit of K3-fibered G₂-manifolds, along with conjectures regarding associative submanifolds and potential directions for future research.