Notes

These are the notes I think are worth sharing. I don't claim any originality for this work, my contributions usually amount to provide full proofs to claims that I found non-trivial when learning the subject.

• Non-squeezing theorem in Symplectic Geometry : Here are the notes of a seminar about the famous Non-Squeezing theorem. I closely followed a presentation given by J. Pardon in Princenton in June 2018. This is a nice introduction to the main tools of Gromov-Witten theory.
• Refined Seiberg-Witten invariants: Here are the notes of a seminar about the cohomotopy refinement of the Seiberg-Witten invariants due to S. Bauer and M. Furuta
• Taubes's constraints on symplectic 4-manifolds: These are the notes of a seminar about Taubes's constraints on symplcetic four-manifolds. They contain a (very) concise overview to Seiberg-Witten invariants and Spin^c-structures of four-manifolds.
• Generalized orientation and characteristic classes : These are some notes for a seminar I originally held in Bonn and succesively for a summer class here in UT Austin. They are also available on the nLab.