Seminars and Colloquia by Series

Friday, January 25, 2019 - 14:00 , Location: Skiles 006 , Peter Lambert-Cole , Georgia Insitute of Technology , Organizer: Peter Lambert-Cole
The classical degree-genus formula computes the genus of a nonsingular algebraic curve in the complex projective plane. The well-known Thom conjecture posits that this is a lower bound on the genus of smoothly embedded, oriented and connected surface in CP^2.  The conjecture was first proved twenty-five years ago by Kronheimer and Mrowka, using Seiberg-Witten invariants.  In this talk, we will describe a new proof of the conjecture that combines contact geometry with the novel theory of bridge trisections of knotted surfaces.  Notably, the proof completely avoids any gauge theory or pseudoholomorphic curve techniques.
Friday, November 30, 2018 - 14:00 , Location: Skiles 006 , Surena Hozoori , Georgia Institute of Technology , shozoori3@gatech.edu , Organizer: Surena Hozoori
In post-geometrization low dimensional topology, we expect to be able to relate any topological theory of 3-manifolds to the Riemannian geometry of those manifolds.  On the other hand, originated from reformalization of classical mechanics, the study of contact structures has become a central topic in low dimensional topology, thanks to the works of Eliashberg, Giroux, Etnyre and Taubes, to name a few. Yet we know very little about how Riemannian geometry fits into the theory.In my oral exam, I will talk about "Ricci-Reeb realization problem" which asks which functions can be prescribed as the Ricci curvature of a "Reeb vector field" associated to a contact manifold. Finally motivated by Ricci-Reeb realization problem and using the previous study of contact dynamics by Hofer-Wysocki-Zehnder, I will prove new topological results using compatible geometry of contact manifolds. The generalization of these results in higher dimensions is the first known results achieving tightness based on curvature conditions.
Friday, November 16, 2018 - 14:00 , Location: Skiles 006 , None , None , Organizer: John Etnyre
Friday, October 19, 2018 - 14:00 , Location: Skiles 006 , Sudipta Kolay , Georgia Tech , Organizer: Sudipta Kolay
I will discuss some applications of the holonomic approximation theorem to questions about immersions, embeddings, and singularities.
Friday, October 12, 2018 - 14:00 , Location: Skiles 006 , Sudipta Kolay , Georgia Tech , Organizer: Sudipta Kolay
One of the general methods of proving h-principle is holonomic aprroximation. In this series of talks, I will give a proof of holonomic approximation theorem, and talk about some of its applications.
Friday, September 28, 2018 - 14:00 , Location: Skiles 006 , None , None , Organizer: John Etnyre
Friday, September 21, 2018 - 14:00 , Location: Skiles 006 , Peter Lambert-Cole , Georgia Insitute of Technology , Organizer: Peter Lambert-Cole
The Oka-Grauert principle is one of the first examples of an h-principle.  It states that for a Stein domain X and a complex Lie group G, the topological and holomorphic classifications of principal G-bundles over X agree.  In particular, a complex vector bundle over X has a holomorphic trivialization if and only if it has a continuous trivialization.  In these talks, we will discuss the complex geometry of Stein domains, including various characterizations of Stein domains, the classical Theorems A and B, and the Oka-Grauert principle.
Friday, September 14, 2018 - 13:55 , Location: Skiles 006 , Peter Lambert-Cole , Georgia Insitute of Technology , Organizer: Peter Lambert-Cole
The Oka-Grauert principle is one of the first examples of an h-principle.  It states that for a Stein domain X and a complex Lie group G, the topological and holomorphic classifications of principal G-bundles over X agree.  In particular, a complex vector bundle over X has a holomorphic trivialization if and only if it has a continuous trivialization.  In these talks, we will discuss the complex geometry of Stein domains, including various characterizations of Stein domains, the classical Theorems A and B, and the Oka-Grauert principle.
Wednesday, May 2, 2018 - 14:00 , Location: Skiles 006 , Hyunki Min , Georgia Tech , hmin38@gatech.edu , Organizer: Hyun Ki Min
Understanding contact structures on hyperbolic 3-manifolds is one of the major open problems in the area of contact topology. As a first step, we try to classify tight contact structures on a specific hyperbolic 3-manifold. In this talk, we will review the previous classification results and classify tight contact structures on the Weeks manifold, which has the smallest hyperbolic volume. Finally, we will discuss how to generalize this method to classify tight contact structures on some other hyperbolic 3-manifolds.
Friday, March 16, 2018 - 14:00 , Location: Skiles 006 , Jen Hom , Georgia Tech , Organizer: Jennifer Hom
In this series of talks, we will study the relationship between the Alexander module and the bordered Floer homology of the Seifert surface complement. In particular, we will show that bordered Floer categorifies Donaldson's TQFT description of the Alexander module. 

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