Friday, July 20, 2018 - 13:00 , Location: Skiles 006 , Kashyap Rajeevsarathy , IISER Bhopal , Organizer: Dan Margalit
Let Mod(Sg) denote the mapping class group of the closed orientable surface Sg of genus g ≥ 2. Given a finite subgroup H < Mod(Sg), let Fix(H) denote the set of fixed points induced by the action of H on the Teichmuller space Teich(Sg). In this talk, we give an explicit description of Fix(H), when H is cyclic, thereby providing a complete solution to the Modular Nielsen Realization Problem for this case. Among other applications of these realizations, we derive an intriguing correlation between finite order maps and the filling systems of surfaces. Finally, we will briefly discuss some examples of realizations of two-generator finite abelian actions.
Wednesday, May 23, 2018 - 14:00 , Location: Skiles 006 , Bulent Tosun , University of Alabama , Organizer: John Etnyre
This will be a 90 minute seminar
It is well known that all contact 3-manifolds can be obtained from the standard contact structure on the 3-sphere by contact surgery on a Legendrian link. Hence, an interesting and much studied question asks what properties are preserved under various types of contact surgeries. The case for the negative contact surgeries is fairly well understood. In this talk, we will discuss some new results about positive contact surgeries and in particular completely characterize when contact r surgery is symplectically/Stein fillable when r is in (0,1]. This is joint work with James Conway and John Etnyre.
Monday, April 30, 2018 - 14:00 , Location: Skiles 006 , Michael Harrison , Lehigh University , email@example.com , Organizer: Mohammad Ghomi
The h-principle is a powerful tool in differential topology which is used to study spaces of functionswith certain distinguished properties (immersions, submersions, k-mersions, embeddings, free maps, etc.). Iwill discuss some examples of the h-principle and give a neat proof of a special case of the Smale-HirschTheorem, using the "removal of singularities" h-principle technique due to Eliashberg and Gromov. Finally, I willdefine and discuss totally convex immersions and discuss some h-principle statements in this context.
Monday, April 23, 2018 - 14:00 , Location: Skiles 006 , Hong Van Le , Institute of Mathematics CAS, Praha, Czech Republic , firstname.lastname@example.org , Organizer: Thang Le
Novikov homology was introduced by Novikov in the early 1980s motivated by problems in hydrodynamics. The Novikov inequalities in the Novikov homology theory give lower bounds for the number of critical points of a Morse closed 1-form on a compact differentiable manifold M. In the first part of my talk I shall survey the Novikov homology theory in finite dimensional setting and its further developments in infinite dimensional setting with applications in the theory of symplectic fixed points and Lagrangian intersection/embedding problems. In the second part of my talk I shall report on my recent joint work with Jean-Francois Barraud and Agnes Gadbled on construction of the Novikov fundamental group associated to a cohomology class of a closed 1-form on M and its application to obtaining new lower bounds for the number of critical points of a Morse 1-form.
Monday, April 2, 2018 - 14:00 , Location: Skiles 006 , Linh Truong , Columbia University , Organizer: Jennifer Hom
Heegaard Floer homology has proven to be a useful tool in the study of knot concordance. Ozsvath and Szabo first constructed the tau invariant using the hat version of Heegaard Floer homology and showed it provides a lower bound on the slice genus. Later, Hom and Wu constructed a concordance invariant using the plus version of Heegaard Floer homology; this provides an even better lower-bound on the slice genus. In this talk, I discuss a sequence of concordance invariants that are derived from the truncated version of Heegaard Floer homology. These truncated Floer concordance invariants generalize the Ozsvath-Szabo and Hom-Wu invariants.