# Topology

## Khovanov homology

Lecture notes on Khovanov homology.

## Duality Notes

These are notes for the Duality talk presented as part of the West Coast Algebraic Toplogy Summer School.

## Verlinde Algebra

Lecture Notes on Verlinde Algebra

## WCATSS Problem Set 5

This is the third problem of the West Coast Algebraic Topology Summer School (WCATSS)

## WCATSS Problem Set 4

This is the third problem of the West Coast Algebraic Topology Summer School (WCATSS)

## WCATSS Problem Set 3

This is the third problem of the West Coast Algebraic Topology Summer School (WCATSS)

## WCATSS Problem Set 2

This is the second problem of the West Coast Algebraic Topology Summer School (WCATSS)

## WCATSS Problem Set 1

This is the first problem of the West Coast Algebraic Topology Summer School (WCATSS)

## Algebraic Topology- Methods, Computation and Science 6

## A short elementary survey of Symplectic Topology

Symplectic topology can be thought as the mathematical versant of String theory: they were born independently at the same time, the second one as a fantastic enterprise to unify large-scale and low-scale physics, and the first one to solve classical dynamical problems on periodic orbits of physical problems, the famous Arnold conjectures. In the 80's, Gromov's revolutionary work opened a new perspective by presenting symplectic topology as an almost Kähler geometry (a concept that he defined), and constructing the corresponding theory which is entirely covariant (whereas algebraic geometry is entirely contravariant). A few years later, Floer and Hofer established the bridge between the two interpretations of Symplectic topology, the one as a dynamical theory and the one as a Kähler theory. This bridge was confirmed for the first time by Lalonde-McDuff who related explicitly the first theory to the second by showing that Gromov's Non-Squeezing Theorem is equivalent to Hofer's energy-capacity inequality.

Nowadays, Symplectic Topology is a very vibrant subject, and there is perhaps no other subject that produces new and deep moduli spaces at such a pace ! More recent results will also be presented.