Seminars and Colloquia by Series

Fillings of Contact 3 Manifolds and Relations in Mapping Class Groups of Surfaces

Series
Geometry Topology Student Seminar
Time
Wednesday, February 5, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Agniva RoyGeorgia Tech

A useful way of studying contact 3 manifolds is by looking at their open book decompositions. A result of Akbulut-Ozbagci, Ghiggini, and Loi-Piergallini showed that the manifold is filled by a Stein manifold if and only if the monodromy of an open book can be factorised as the product of positive Dehn twists. Then, the problem of classifying minimal fillings of contact 3 manifolds, or answering questions about which manifolds can be realised by Legendrian surgery, becomes questions about finding factorisations for a given mapping class. This talk will be expository and expand upon how these mapping classes come up, and also discuss known results, techniques, and future directions for research.

4-Dimensional Knot Surgery

Series
Geometry Topology Student Seminar
Time
Wednesday, January 29, 2020 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Anubhav MukherjeeGeorgia Tech

In the world of 4 manifolds, finding exotic structures on 4 manifolds is considered one of most interesting and difficult problems. I will give a brief history of this and explain a very interesting tool "knot surgery" defined by Fintushel and Stern. In this talk I will mostly focused on drawing pictures. If time permits, I will talk various interesting applications.

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.

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