Seminars and Colloquia by Series

Grid Homology

Series
Geometry Topology Student Seminar
Time
Wednesday, November 18, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
online
Speaker
Sally Collins

Grid homology is a purely combinatorial description of knot Floer homology in which the counting of psuedo-holomorphic disks is replaced with a counting of polygons in grid diagrams. This talk will provide an introduction to this theory, and is aimed at an audience with little to no experience with Heegaard Floer homology. 

Symplectic Geometry of Anosov Flows in Dimension 3 and Bi-Contact Topology

Series
Geometry Topology Student Seminar
Time
Wednesday, November 4, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
online: https://bluejeans.com/872588027
Speaker
Surena HozooriGeorgia Tech

We give a purely contact and symplectic geometric characterization of Anosov flows in dimension 3 and set up a framework to use tools from contact and symplectic geometry and topology in the study of questions about Anosov dynamics. If time permits, we will discuss some uniqueness results for the underlying (bi-) contact structure for an Anosov flow, and/or a characterization of Anosovity based on Reeb flows.

Topology of cable knots

Series
Geometry Topology Student Seminar
Time
Wednesday, October 7, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Hyunki MinGeorgia Tech

Cabling is one of important knot operations. We study various properties of cable knots and how to characterize the cable knots by its complement.

Exotic behavior of manifolds

Series
Geometry Topology Student Seminar
Time
Wednesday, September 30, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Anubhav MukherjeeGeorgia Tech

Poincare Conjecture, undoubtedly, is the most influential and challenging problem in the world of Geometry and Topology. Over a century, it has left it’s mark on developing the rich theory around it. In this talk I will give a brief history of the development of Topology and then I will focus on the Exotic behavior of manifolds. In the last part of the talk, I will concentrate more on the theory of 4-manifolds.

The skein algebra as a quantized character variety

Series
Geometry Topology Student Seminar
Time
Wednesday, September 23, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Tao YuGeorgia Tech

In 1925, Heisenberg introduced non-commutativity of coordinates, now known as quantization, to explain the spectral lines of atoms. In topology, finding quantizations of (symplectic or more generally Poisson) spaces can reveal more intricate structures on them. In this talk, we will introduce the main ingredients of quantization. As a concrete example, we will discuss the SL2-character variety, which is closely related to the Teichmüller space, and the skein algebra as its quantization.

Knot Concordance

Series
Geometry Topology Student Seminar
Time
Wednesday, September 9, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Hugo ZhouGeorgia Tech

Two knots are concordant to each other if they cobound an annulus in the product of S^3. We will discuss a few basic facts about knot concordance and look at J. Levine’s classical result on the knot concordance group.

Symplectic Fillings of Contact Structures

Series
Geometry Topology Student Seminar
Time
Wednesday, September 2, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Speaker
Agniva RoyGeorgia Tech

Finding fillings of contact structures is a question that has been studied extensively over the last few decades. In this talk I will discuss some motivations for studying this question, and then visit a few ideas involved in the earliest results, due to Eliashberg and McDuff, that paved the way for a lot of current research in this direction.

The Alexander method and recognizing maps

Series
Geometry Topology Student Seminar
Time
Wednesday, August 26, 2020 - 14:30 for 30 minutes
Location
Online
Speaker
Roberta ShapiroGeorgia Tech

 How can we recognize a map given certain combinatorial data? The Alexander method gives us the answer for self-homeomorphisms of finite-type surfaces. We can determine a homeomorphism of a surface (up to isotopy) based on how it acts on a finite number of curves. However, is there a way to apply this concept to recognize maps on other spaces? The answer is yes for a special class of maps, post-critically finite quadratic polynomials on the complex plane (Belk-Lanier-Margalit-Winarski). 

            In this talk, we will discuss Belk-Lanier-Margalit-Winarski’s methods, as well zome difficulties we face when trying to extend their methods to other settings.

Using and Understanding Torsion in Big Mapping Class Groups

Series
Geometry Topology Student Seminar
Time
Wednesday, August 26, 2020 - 14:00 for 30 minutes
Location
Speaker
Santana AftonGeorgia Tech

An infinite-type surface is a surface whose fundamental group is not finitely generated. These surfaces are “big,” having either infinite genus or infinitely many punctures. Recently, it was shown that mapping class groups of these infinite-type surfaces have a wealth of subgroups; for example, there are infinitely many surfaces whose mapping class group contains every countable group as a subgroup. By extending a theorem for finite-type surfaces to the infinite-type case — the Nielsen realization problem — we give topological obstructions to continuous embeddings of topological groups, with a few interesting examples.

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