Seminars and Colloquia by Series

Unfoldings of 3D Polyhedra

Series
Geometry Topology Student Seminar
Time
Wednesday, September 11, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Nicholas Barvinok –

Cutting a polyhedron along some spanning tree of its edges will yield an isometric immersion of the polyhedron into the plane. If this immersion is also injective, we call it an unfolding. In this talk I will give some general results about unfoldings of polyhedra. There is also a notion of pseudo-edge unfolding, which involves cutting on a pseudo edge graph, as opposed to an edge graph. A pseudo edge graph is a 3-connected graph on the surface of the polyhedron, whose vertices coincide with the vertices of the polyhedron, and whose edges are geodesics. I will explain part of the paper "Pseudo-Edge Unfoldings of Convex Polyhedra," a joint work of mine with Professor Ghomi, which proves the existence of a convex polyhedron with a pseudo edge graph along which it is not unfoldable. Finally, I will discuss some connections between pseudo edge graphs and edge graphs. 

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.

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