Seminars and Colloquia by Series

Introduction to (some versions of) Heegaard-Floer Homology

Series
Geometry Topology Working Seminar
Time
Friday, September 24, 2010 - 14:00 for 2 hours
Location
Skiles 171
Speaker
Amey Kaloti – Ga Tech
This will be an introduction to the basic aspects of Heegaard-Floer homology and knot Heegaard-Floer homology. After this talk (talks) we will be organizing a working group to go through various computations and results in knot Heegaard-Floer theory and invariants of Legendrian knots.

Curve complexes and mapping class groups II

Series
Geometry Topology Working Seminar
Time
Friday, September 17, 2010 - 14:00 for 2 hours
Location
Skiles 171
Speaker
Dan Margalit – Georgia Tech
We will prove that the mapping class group is finitely presented, using its action on the arc complex. We will also use the curve complex to show that the abstract commensurator of the mapping class group is the extended mapping class group. If time allows, we will introduce the complex of minimizing cycles for a surface, and use it to compute the cohomological dimension of the Torelli subgroup of the mapping class group. This is a followup to the previous talk, but will be logically independent.

Non-loose torus knots.

Series
Geometry Topology Working Seminar
Time
Thursday, September 9, 2010 - 11:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Amey Kaloti – Georgia Tech. –

Please Note: This talk is part of the oral exam for the speaker. Please note the special time, place. Also the talk itself will be 45 min long.

Non-loose knots is a special class of knots studied in contact geometry. Last couple of years have shown some applications of these kinds of knots. Even though defined for a long time, not much is known about their classification except for the case of unknot. In this talk we will summarize what is known and tell about the recent work in which we are trying to give classification in the case of trefoil.

Curve complexes and mapping class groups

Series
Geometry Topology Working Seminar
Time
Friday, September 3, 2010 - 13:00 for 2 hours
Location
Skiles 114
Speaker
Dan Margalit – Georgia Tech
The mapping class group is the group of symmetries of a surface (modulo homotopy). One way to study the mapping class group of a surface S is to understand its action on the set of simple closed curves in S (up to homotopy). The set of homotopy classes of simple closed curves can be organized into a simplicial complex called the complex of curves. This complex has some amazing features, and we will use it to prove a variety of theorems about the mapping class group. We will also state some open questions. This talk will be accessible to second year graduate students.

Incompressible Surfaces via Branched Surfaces

Series
Geometry Topology Working Seminar
Time
Friday, April 23, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Thao Vuong – Georgia Tech
We will give definitions and then review a result by Floyd and Oertel that in a Haken 3-manifold M, there are a finite number of branched surfaces whose fibered neighborhoods contain all the incompressible, boundary-incompressible surfaces in M, up to isotopy. A corollary of this is that the set of boundary slopes of a knot K in S^3 is finite.

Introduction to Khovanov Homology, Part 2

Series
Geometry Topology Working Seminar
Time
Friday, March 19, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Alan Diaz – School of Mathematics, Georgia Tech
Last week we motivated and defined Khovanov homology, an invariant of oriented links whose graded Euler characteristic is the Jones polynomial. We'll discuss the proof of Reidemeister invariance, then survey some important applications and extensions, including Lee theory and Rasmussen's s-invariant, the connection to knot Floer homology, and how the latter was used by Hedden and Watson to show unknot detection for a large class of knots.

Introduction to Khovanov Homology

Series
Geometry Topology Working Seminar
Time
Friday, March 12, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Alan Diaz – Georgia Tech
Khovanov homology is an invariant of oriented links, that is defined as the cohomology of a chain complex built from the cube of resolutions of a link diagram. Discovered in the late 90s, it is the first of, and inspiration for, a series of "categorifications" of knot invariants. In this first of two one-hour talks, I'll give some background on categorification and the Jones polynomial, defineKhovanov homology, work through some examples, and give a portion of the proof of Reidemeister invariance.

Introduction to the AJ Conjecture, Part II

Series
Geometry Topology Working Seminar
Time
Friday, March 5, 2010 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 269
Speaker
Anh Tran – Georgia Tech
I will explain another approach to the conjecture and in particular, study it for 2-bridge knots. I will give the proof of the conjecture for a very large class of 2-bridge knots which includes twist knots and many more (due to Le). Finally, I will mention a little bit about the weak version of the conjecture as well as some relating problems.

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