From Knots to Symplectic Geometry and Algebra

Explore the fascinating connections between knots, symplectic geometry, and algebra in this 56-minute AMS Invited Address given by Peter Ozsvath from Princeton University at the 2019 Joint Mathematics Meetings in Baltimore, MD. Delve into topics such as nonfloor homology, unknotting sequences, and the Alexander polynomial. Examine Kaufman states, black graphs, and Knopfler homology through illustrative examples and pictures. Investigate tunnel homology, knot homology, and Hagar diagrams, while learning about pseudo holomorphic disks and chain complex symbols. Conclude with an exploration of curved modules, tensor products, and the underlying algebra that ties these concepts together.

Introduction
Nonfloor homology
Unknotting sequences
Unique invariant
Alexander polynomial
Kaufman states
Black graph
Alexander contributions
Knopfler homology
Pictures
Examples
Not Flow homology
Tunnel homology
Knot homology
Hagar diagram
Pseudo holomorphic disks
Chain complex symbols
Example
Algebra
Curved Modules
Tensor Product
The Algebra