References
Professor Yakov Eliashberg (Advisor)
Professor Eleny Ionel
Professor Soren Galatius
Professor Mark Meckes (Teaching)

Contact Information
Department of Mathematics
450 Serra Mall, Bldg 380
Stanford, CA 94305

Office: 380S
e-mail: milin@math.stanford.edu
 

 
• Orderability and Nonsqueezing in Contact Geometry
  

  Slides from a talk I gave at Columbia Symplectic Geometry and Gauge Theory Seminar.
  

• Orderability of Contactomorphism Groups of Lens Spaces (coming soon)

  A contact isotopy of a compact contact manifold is positive if during the isotopy each point of the manifold moves in a positively transverse direction to the contact structure. The question of whether this natural notion induces a partial order on the universal cover of the contactomorphism group turns out to be sensitive to the topology of the contact manifold, and is related to nonsqueezing phenomena in contact geometry, as studied by Eliashberg, Kim and Polterovich. In this paper, we introduce an equivariant version of cylindrical contact homology for domains which is then used to detect contact nonsqueezing phenomena leading to a proof of orderability in the case of standard contact lens spaces. This result should be contrasted with the case of the standard contact sphere, where the answer to orderability question is negative.