# Joint IAS-PU Symplectic Geometry Seminar

## Monotone Lagrangians in cotangent bundles

Luis Diogo
Columbia University
October 11, 2016
We show that there is a 1-parameter family of monotone Lagrangian tori in the cotangent bundle of the 3-sphere with the following property: every compact orientable monotone Lagrangian with non-trivial Floer cohomology is not Hamiltonian-displaceable from either the zero-section or one of the tori in the family. The proof involves studying a version of the wrapped Fukaya category of the cotangent bundle which includes monotone Lagrangians. Time permitting, we may also discuss an extension to other cotangent bundles. This is joint work with Mohammed Abouzaid.

## Lagrangian cell complexes and Markov numbers

Jonny Evans
University College London
September 20, 2016
Joint work with Ivan Smith. Let p be a positive integer. Take the quotient of a 2-disc by the equivalence relation which identifies two boundary points if the boundary arc connecting them subtends an angle which is an integer multiple of ($2 \pi / p$). We call the resulting cell complex a '$p$-pinwheel'. We will discuss constraints on Lagrangian embeddings of pinwheels. In particular, we will see that a p-pinwheel admits a Lagrangian embedding in $CP^2$ if and only if $p$ is a Markov number.