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Wednesday, February 13, 2019 - 14:00 ,
Location: Skiles 006 ,
Monica Flamann ,
Georgia Tech ,
Organizer: Sudipta Kolay

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

<p>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.</p>

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.

Wednesday, October 24, 2018 - 14:00 ,
Location: Skiles 006 ,
Surena Hozoori ,
Georgia Institute of Technology ,
shozoori3@gatech.edu ,
Organizer: Surena Hozoori

Boothby Wang fibrations are historically important examples of contact manifolds and it turns out that we can equip these contact manifolds with extra structures, namely K-contact structures. Based on the study of the relation of these examples and the regularity properties of the corresponding Reeb vector fields, works of Boothby, Wang, Thomas and Rukimbira gives a classification of K-contact structures.

Wednesday, October 10, 2018 - 14:00 ,
Location: Skiles 006 ,
Sudipta Kolay ,
Georgia Tech ,
Organizer: Sudipta Kolay

This talk will be an introduction to the homotopy principle
(h-principle). We will discuss several examples. No prior knowledge
about h-principle will be assumed.

Wednesday, October 3, 2018 - 14:00 ,
Location: Skiles 006 ,
Stephen Mckean ,
GaTech ,
Organizer: Anubhav Mukherjee

Many problems in algebraic geometry involve counting solutions to
geometric problems. The number of intersection points of two projective
planar curves and the number of lines on a cubic surface are two
classical problems in this enumerative
geometry. Using A1-homotopy theory, one can gain new insights to old
enumerative problems. We will outline some results in A1-enumerative
geometry, including the speaker’s current work on Bézout’s Theorem.

Wednesday, September 26, 2018 - 14:00 ,
Location: Skiles 006 ,
Agniva Roy ,
Georgia Tech ,
Organizer: Sudipta Kolay

The Schoenflies' conjecture proposes the following: An embedding of the n-sphere in the (n+1)-sphere bounds a standard (n+1)-ball. For n=1, this is the well known Jordan curve theorem. Depending on the type of embeddings, one has
smooth and topological versions of the conjecture. The topological version was settled in 1960 by Brown.
In the smooth setting, the answer is known to be yes for all
dimensions other than 4, where apart from one special case, nothing is
known. The talk will review the question and attempt to describe some of
the techniques that have been used in low dimensions,
especially in the special case, that was worked out by Scharlemann in
the 1980s. There are interesting connections to the smooth 4-dimensional
Poincare conjecture that will be mentioned, time permitting. The talk
is aimed to be expository and not technical.

Wednesday, September 19, 2018 - 14:00 ,
Location: Skiles 006 ,
Hyunki Min ,
Georgia Tech ,
Organizer: Hyun Ki Min

In 1957, Smale proved a striking result: we can turn a sphere inside out without any singularity. Gromov in his thesis, proved a generalized version of this theorem, which had been the starting point of the h-principle. In this talk, we will prove Gromov's theorem and see applications of it.