Seminars and Colloquia by Series

Bridge trisections and minimal genus

Series
Geometry Topology Working Seminar
Time
Friday, January 25, 2019 - 14:00 for 2 hours
Location
Skiles 006
Speaker
Peter Lambert-ColeGeorgia Insitute of Technology
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.

An Oral Exam: Curvature, Contact Topology and Reeb Dynamics

Series
Geometry Topology Working Seminar
Time
Friday, November 30, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Surena HozooriGeorgia Institute of Technology
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.

Holonomic Approximation Theorem I

Series
Geometry Topology Working Seminar
Time
Friday, October 12, 2018 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Sudipta KolayGeorgia Tech
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.

Stein domains and the Oka-Grauert principle

Series
Geometry Topology Working Seminar
Time
Friday, September 21, 2018 - 14:00 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Peter Lambert-ColeGeorgia Insitute of Technology
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.

Stein domains and the Oka-Grauert principle

Series
Geometry Topology Working Seminar
Time
Friday, September 14, 2018 - 13:55 for 1.5 hours (actually 80 minutes)
Location
Skiles 006
Speaker
Peter Lambert-ColeGeorgia Insitute of Technology
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.

Oral Exam: Contact structures on hyperbolic 3-manifolds

Series
Geometry Topology Working Seminar
Time
Wednesday, May 2, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hyunki MinGeorgia Tech
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.

The Alexander module and categorification, part 3

Series
Geometry Topology Working Seminar
Time
Friday, March 16, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jen HomGeorgia Tech
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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