Seminars and Colloquia by Series

0-Concordance of 2-Knots

Series
Geometry Topology Student Seminar
Time
Wednesday, September 4, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anubhav Mukherjee

 A 2-knot is a smooth embedding of S^2 in S^4, and a 0-concordance of 2-knots is a concordance with the property that every regular level set of the concordance is just a collection of S^2's. In his thesis, Paul Melvin proved that if two 2-knots are 0-concordant, then a Gluck twist along one will result in the same smooth 4-manifold as a Gluck twist on the other. He asked the following question: Are all 2-knots 0-slice (i.e. 0-concordant to the unknot)? I will explain all relevant definitions, and mostly follow the paper by Nathan Sunukjian on this topic.

Swindles in Mathematics

Series
Geometry Topology Student Seminar
Time
Wednesday, April 17, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sudipta Kolay – Georgia Tech

We will see some instances of swindles in mathematics, primarily focusing on some in geometric topology due to Barry Mazur.

Definition of Casson Invariant

Series
Geometry Topology Student Seminar
Time
Wednesday, April 10, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hongyi Zhou – Georgia Institute of Technology –

Casson invariant is defined for the class of oriented integral homology 3-spheres. It satisfies certain properties, and reduce to Rohlin invariant after mod 2. We will define Casson invariant as half of the algebraic intersection number of irreducible representation spaces (space consists of representations of fundamental group to SU(2)), and then prove this definition satisfies the expected properties.

Dynamics and Topology of Contact 3-Manifolds with negative $\alpha$-sectional curvature: Lecture 4

Series
Geometry Topology Student Seminar
Time
Wednesday, February 6, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Surena Hozoori – Georgia Institute of Technology –
In this series of (3-5) lectures, I will talk about different aspects of a class of contact 3-manifolds for which geometry, dynamics and topology interact subtly and beautifully. The talks are intended to include short surveys on "compatibility", "Anosovity" and "Conley-Zehnder indices". The goal is to use the theory of Contact Dynamics to show that conformally Anosov contact 3-manifolds (in particular, contact 3-manifolds with negative α-sectional curvature) are universally tight, irreducible and do not admit a Liouville cobordism to the tight 3-sphere.

Dynamics and Topology of Contact 3-Manifolds with negative $\alpha$-Sectional Curvature: Lecture 3

Series
Geometry Topology Student Seminar
Time
Wednesday, January 30, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Surena Hozoori – Georgia Institute of Technology –
In this series of (3-5) lectures, I will talk about different aspects of a class of contact 3-manifolds for which geometry, dynamics and topology interact subtly and beautifully. The talks are intended to include short surveys on "compatibility", "Anosovity" and "Conley-Zehnder indices". The goal is to use the theory of Contact Dynamics to show that conformally Anosov contact 3-manifolds (in particular, contact 3-manifolds with negative α-sectional curvature) are universally tight, irrducible and do not admit a Liouville cobordism to tight 3-sphere.

Dynamics and Topology of Contact 3-Manifolds with negative $\alpha$-Sectional Curvature: Lecture 2

Series
Geometry Topology Student Seminar
Time
Wednesday, January 23, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Surena Hozoori – Georgia Institute of Technology –
In this series of (3-5) lectures, I will talk about different aspects of a class of contact 3-manifolds for which geometry, dynamics and topology interact subtly and beautifully. The talks are intended to include short surveys on "compatibility", "Anosovity" and "Conley-Zehnder indices". The goal is to use the theory of Contact Dynamics to show that conformally Anosov contact 3-manifolds (in particular, contact 3-manifolds with negative α-sectional curvature) are universally tight, irrducible and do not admit a Liouville cobordism to tight 3-sphere.

Dynamics and Topology of Contact 3-Manifolds with negative $\alpha$-Sectional Curvature: Lecture 1

Series
Geometry Topology Student Seminar
Time
Wednesday, January 16, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Surena Hozoori – Georgia Institute of Technology –
In this series of (3-5) lectures, I will talk about different aspects of a class of contact 3-manifolds for which geometry, dynamics and topology interact subtly and beautifully. The talks are intended to include short surveys on "compatibility", "Anosovity" and "Conley-Zehnder indices". The goal is to use the theory of Contact Dynamics to show that conformally Anosov contact 3-manifolds (in particular, contact 3-manifolds with negative $\alpha$-sectional curvature) are universally tight, irrducible and do not admit a Liouville cobordism to tight 3-sphere.

Some well disguised ribbon knots

Series
Geometry Topology Student Seminar
Time
Wednesday, December 5, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Agniva Roy – Georgia Tech

The talk will discuss a paper by Gompf and Miyazaki of the same name. This paper introduces the notion of dualisable patterns, a technique which is widely used in knot theory to produce knots with similar properties. The primary objective of the paper is to first find a knot which is not obviously ribbon, and then show that it is. It then goes on to construct a related knot which is not ribbon. The talk will be aimed at trying to unwrap the basic definitions and techniques used in this paper, without going too much into the heavy technical details.

The Converse Of The Archimedean Property of the Sphere and Related Results in Convex Geometry and Measure Theory

Series
Geometry Topology Student Seminar
Time
Wednesday, November 28, 2018 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sidhanth Raman – Georgia Tech
The Archimedes Hatbox Theorem is a wonderful little theorem about the sphere and a circumscribed cylinder having the same surface area, but the sphere can potentially still be characterized by inverting the statement. There shall be a discussion of approaches to prove the claim so far, and a review of a weaker inversion of the Hatbox Theorem by Herbert Knothe and discussion of a related problem in measure theory that would imply the spheres uniqueness in this property.

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