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Friday, September 24, 2010 - 14:00 ,
Location: Skiles 171 ,
Amey Kaloti ,
Ga Tech ,
Organizer: John Etnyre

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.

Friday, September 17, 2010 - 14:00 ,
Location: Skiles 171 ,
Dan Margalit ,
Georgia Tech ,
Organizer: Dan Margalit

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.

Thursday, September 9, 2010 - 11:00 ,
Location: Skiles 269 ,
Amey Kaloti ,
Georgia Tech. ,
ameyk@math.gatech.edu ,
Organizer:

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.

Friday, September 3, 2010 - 13:00 ,
Location: Skiles 114 ,
Dan Margalit ,
Georgia Tech ,
Organizer: Dan Margalit

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.

Friday, April 23, 2010 - 14:00 ,
Location: Skiles 269 ,
Thao Vuong ,
Georgia Tech ,
Organizer:

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.

Friday, April 16, 2010 - 14:00 ,
Location: Skiles 269 ,
Igor Belegradek ,
Georgia Tech ,
Organizer:

I will discuss moduli spaces of Riemannian metrics
with various curvature conditions, and then focus on the case
of nonnegative sectional curvature.

Friday, April 9, 2010 - 14:00 ,
Location: Skiles 269 ,
Igor Belegradek ,
School of Mathematics, Georgia Tech ,
Organizer:

I will review results on the structure of open nonnegatively curved manifolds due to
Cheeger-Gromoll, Perelman, and Wilking.

Friday, March 19, 2010 - 14:00 ,
Location: Skiles 269 ,
Alan Diaz ,
School of Mathematics, Georgia Tech ,
Organizer:

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.

Friday, March 12, 2010 - 14:00 ,
Location: Skiles 269 ,
Alan Diaz ,
Georgia Tech ,
Organizer:

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.

Friday, March 5, 2010 - 14:00 ,
Location: Skiles 269 ,
Anh Tran ,
Georgia Tech ,
Organizer:

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.