# Finite Energy Instantons on $\Sigma \times \mathbb{C}$

-
Max Lipyanskiy , Columbia University
Fine Hall 314

We will outline a proof of a conjecture by Jardim-Biquard on the asymptotic decay of instantons on $\Sigma \times \mathbb{C}$. In the case $\Sigma$ is a torus, coupled with the results of Jardim-Biquard, this establishes a correspondence between finite energy instantons and (stable) holomorphic bundles on $\Sigma \times P^1$. Our techniques are based on the Gromov-Uhlenbeck compactness estimates developed for the Atiyah-Floer Conjecture.