On isolated hypersurface singularities: algebra-geometric and symplectic aspects

TL;DR

This paper explores the interplay between algebraic geometry and symplectic geometry in understanding isolated hypersurface singularities, focusing on recent advances in symplectic cohomology of Milnor fibers.

Contribution

It provides an accessible explanation of recent work connecting singularity theory with symplectic cohomology, highlighting interdisciplinary methods and insights.

Findings

Clarifies the role of algebraic geometry in symplectic cohomology

Explains the symplectic structure of Milnor fibers for isolated singularities

Bridges concepts from singularity theory and symplectic geometry

Abstract

These notes are based on a seminar which took place in the autumn of 2022 at the Mathematical Institute of the University of Leiden. Its goal was to understand the recent work of J. Evans and Y. Lekili on the symplectic cohomology of the Milnor fiber for specific classes of isolated singularities. This work uses inputs from several fields, notably from algebraic geometry, in particular singularity theory, and from symplectic geometry. The main aim of the notes is to make the work of J. Evans and Y. Lekili more accessible by explaining the main ideas from these fields and indicate how these play a role in this work.