# Videos and slides

Several of my talks are available online. Here are some:

The Simplicity Conjecture is a talk I gave about my joint work resolving the longstanding Simplicity Conjecture. (See also this very nice article.)

PFH spectral invariants and the large-scale geometry of Hofer's metric is a talk I gave about my joint work resolving the Kapovich-Polterovich question.

The Quasimorphism Question is a talk I gave about my joint work resolving the "Quasimorphism question".

Obstructing infinite staircases is a talk about my joint work about the ``staircase obstruction".

“An introduction to embedded contact homology” is an expository talk which could be of interest to researchers wanting to know more about embedded contact homology.

“Volume in Seiberg-Witten theory and the existence of two Reeb orbits”

is a talk on my joint work about the ECH Weyl Law and the existence of two Reeb orbits.

“Symplectic embeddings from concave toric domains into convex ones” is a talk I gave on my work on symplectic embeddings of toric domains.

“Symplectic embeddings of products” is a talk on my joint work on higher dimensional symplectic embedding problems.

“From symplectic geometry to combinatorics and back” is a talk on an irrational version of Ehrhart theory that naturally arises in symplectic embedding problems

“From one Reeb orbit to two” is a short talk I gave about some problems in three-dimensional Reeb dynamics.

“Two or infinity” is a talk I gave about my work showing that in many cases there are either two or infinitely many Reeb orbits on closed three-manifolds.

Here are some slides from powerpoint presentations that I’ve given (many of these are for the talks above):

Current Developments in Mathematics (Harvard/MIT, 2024)

Notes: hybrid (in-person) talk, these are just the slides; the beautiful picture of the Calabi invariant is due to Ghys. Colloquium @ Brown: simplicity conjecture + symplectic packings Brown University colloquium talk

Notes: hybrid (in-person) talk, these are just the slides; the beautiful picture of the Calabi invariant is due to Ghys. Closing lemma @ Brown (slightly revised since talk) Closing lemma @ Brown

Subleading asymptootics @ Tel Aviv Subleading asymptotics of the ECH spectrum

PFH spectral invariants @ NCSGS PFH spectral invariants and applications

Obstructing Infinite Staircases @ Ellipsoid day! ellipsoid_day

Simplicity Conjecture @ PU/IAS/Montreal simplicity_conjecture

“Symplectic embeddings of concave toric domains into convex ones”

“Reeb dynamics in dimension 3”

“What can symplectic geometry tell us about Hamiltonian dynamics?” (University of Colorado applied math seminar)