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Wednesday, April 17, 2019 - 14:00 ,
Location: Skiles 006 ,
Sudipta Kolay ,
Georgia Tech ,
Organizer: Sudipta Kolay

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

Wednesday, April 10, 2019 - 14:00 ,
Location: Skiles 006 ,
Hongyi Zhou ,
Georgia Institute of Technology ,
hzhou@gatech.edu ,
Organizer: Surena Hozoori

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.

Wednesday, February 6, 2019 - 14:00 ,
Location: Skiles 006 ,
Surena Hozoori ,
Georgia Institute of Technology ,
shozoori3@gatech.edu ,
Organizer: Surena Hozoori

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.

Wednesday, January 30, 2019 - 14:00 ,
Location: Skiles 006 ,
Surena Hozoori ,
Georgia Institute of Technology ,
shozoori3@gatech.edu ,
Organizer: Surena Hozoori

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.

Wednesday, January 23, 2019 - 14:00 ,
Location: Skiles 006 ,
Surena Hozoori ,
Georgia Institute of Technology ,
shozoori3@gatech.edu ,
Organizer: Surena Hozoori
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.

Wednesday, January 16, 2019 - 14:00 ,
Location: Skiles 006 ,
Surena Hozoori ,
Georgia Institute of Technology ,
shozoori3@gatech.edu ,
Organizer: Surena Hozoori

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.

Wednesday, December 5, 2018 - 14:00 ,
Location: Skiles 006 ,
Agniva Roy ,
Georgia Tech ,
Organizer: Sudipta Kolay

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.

Wednesday, November 28, 2018 - 14:00 ,
Location: Skiles 006 ,
Sidhanth Raman ,
Georgia Tech ,
Organizer: Sudipta Kolay

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.

Wednesday, November 14, 2018 - 14:00 ,
Location: Skiles 006 ,
Hyunki Min ,
Georgia Tech ,
Organizer: Hyun Ki Min

Unlike

symplectic structures in 4-manioflds, contact structures are abundant in

3-dimension. Martinet showed that there exists a contact structure on any

closed oriented 3-manifold. After that Lutz showed that there exist a contact

structure in each homotopy class of plane fields. In this talk, we will review

the theorems of Lutz and Martinet.