Seminars and Colloquia by Series

Topology of knot complements

Series
Geometry Topology Student Seminar
Time
Wednesday, January 22, 2020 - 13:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hyun Ki MinGeorgia Tech

Please Note: Note the unusual time

Gordon and Luecke showed that the knot complements determine the isotopy classes of knots in S^3. In this talk, we will study the topology of various knot complements in S^3: torus knots, cable knots, satellite knots, etc. As an application, we will see some knot invariants using knot complements.

Involutive Heegaard Floer homology

Series
Geometry Topology Student Seminar
Time
Wednesday, December 11, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Sally CollinsGeorgia Tech

Introduced by Hendricks and Manolescu in 2015, Involutive Heegaard Floer homology is a variation of the 3-manifold invariant Heegaard Floer homology which makes use of the conjugation symmetry of the Heegaard Floer complexes. This theory can be used to obtain two new invariants of homology cobordism. This talk will involve a brief overview of general Heegaard Floer homology, followed by a discussion of the involutive theory and some computations of the homology cobordism invariants. 

Branched covers and contact 3 manifolds

Series
Geometry Topology Student Seminar
Time
Wednesday, December 4, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Agniva RoyGeorgia Tech

Branched covers are a generalization of covering spaces, and give rise to interesting questions in smooth as well as contact topology. All 3 manifolds arise as branched coverings of the 3-sphere. The talk will involve a discussion of the proof of this fact due to Montesinos, and will explore the work done towards understanding which contact 3 manifolds arise as the branched cover of the standard tight 3 sphere, and how the branch set can be regulated.

The Underlying Contact and Symplectic Topology of Anosov Flows in Dimension 3

Series
Geometry Topology Student Seminar
Time
Wednesday, November 27, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Surena HozooriGeorgia Institute of Technology

Anosov flows provide beautiful examples of interactions between dynamics, geometry and analysis. In dimension 3 in particular, they are known to have a subtle relation to topology as well. Motivated by a result of Mitsumatsu from 1995, I will discuss their relation to contact and symplectic structures and argue why contact topological methods are natural tools to study the related global phenomena.

Prime Decomposition of 3-Manifolds

Series
Geometry Topology Student Seminar
Time
Wednesday, November 20, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Thomas RodewaldGeorgia Tech

I will discuss the prime decomposition of three-manifolds. First I will define the connect sum operation, irreducible and prime 3-manifolds. Then using the connect sum operation as "multiplication," I will show any closed oriented three-manifold decomposes uniquely into prime factors using spheres. If time permits, I will show another way of decomposing using discs.

A Study of Knots & Links derived from Doubly Periodic Knitted Fabric Patterns

Series
Geometry Topology Student Seminar
Time
Wednesday, November 6, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Shashank MarkandeGeorgia Tech

The emergent shape of a knitted fabric is highly sensitive to the underlying stitch pattern. Here, by a stitch pattern we mean a periodic array of symbols encoding a set of rules or instructions performed to produce a swatch or a piece of fabric. So, it is crucial to understand what exactly these instructions mean in terms of mechanical moves performed using a yarn (a smooth piece of string) and a set of knitting needles (oriented sticks). Motivated by the fact that locally every knitting move results in a slip knot, we use tools from topology to model the set of all doubly periodic stitch patterns, knittable & non-knittable, as knots & links in a three manifold. Specifically, we define a map from the set of doubly-periodic stitch patterns to the set of links in S^3 and use link invariants such as the linking number, multivariable Alexander polynomial etc. to characterize them. We focus on such links derived from knitted stitch patterns in an attempt to tackle the question: whether or not a given stitch pattern can be realized through knitting.

Heegaard Floer obstruction to knot surgery

Series
Geometry Topology Student Seminar
Time
Wednesday, October 23, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Hongyi ZhouGeorgia Tech

Which manifold can be obtained from surgery on a knot? Many obstructions to this have been studied. We will discuss some of them, and use Heegaard Floer homology to give an infinite family of seifert fibered integer spheres that cannot be obtained by surgery on a knot in S^3. We will also discuss a recipe to compute HF+ of surgery on a knot (Short review on Heegaard Floer homology included).

Partial Torelli Groups

Series
Geometry Topology Student Seminar
Time
Wednesday, October 16, 2019 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Daniel MinahanGeorgia Tech

The Torelli group is the subgroup of the mapping class group acting trivially on homology.  We will discuss some basic properties of the Torelli group and explain how to define it for surfaces with boundary.  We will also give some Torelli analogues of the Birman exact sequence.

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