Seminars and Colloquia by Series

Geodesics in the complex of curves with small intersection

Series
Geometry Topology Seminar
Time
Monday, May 5, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Dan Margalit – Georgia Institute of Technology
In joint work with Joan Birman and Bill Menasco, we describe a new finite set of geodesics connecting two given vertices of the curve complex. As an application, we give an effective algorithm for distance in the curve complex.

L-space knots and Heegaard Floer theory

Series
Geometry Topology Seminar
Time
Monday, April 21, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Faramarz Vafaee – MSU
Heegaard Floer theory consists of a set of invariants of three-and four-dimensional manifolds. Three-manifolds with the simplest HeegaardFloer invariants are called L-spaces and the name stems from the fact thatlens spaces are L-spaces. The primary focus of this talk will be on thequestion of which knots in the three-sphere admit L-space surgeries. Wewill also discuss about possible characterizations of L-spaces that do notreference Heegaard Floer homology.

Monoids in the braid and mapping class groups from contact topology

Series
Geometry Topology Seminar
Time
Wednesday, April 16, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Jeremy Van Horn-Morris – University of Arkansas
A monoidal subset of a group is any set which is closed under the product (and contains the identity). The standard example is Dehn^+, the set of maps whcih can be written as a product of right-handed Dehn twists. Using open book decompositions, many properties of contact 3-manifolds are encoded as monoidal subsets of the mapping class group. By a related construction, contact topology also produces a several monoidal subsets of the braid group. These generalize the notion of positive braids and Rudolphs ideas of quasipositive and strongly quasipositive. We'll discuss the construction of these monoids and some of the many open questions.

The reduced knot Floer complex

Series
Geometry Topology Seminar
Time
Monday, April 14, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
David Krcatovich – MSU
The set of knots up to a four-dimensional equivalence relation can be given the structure of a group, called the (smooth) knot concordance group. We will discuss how to compute concordance invariants using Heegaard Floer homology. We will then introduce the idea of a "reduced" knot Floer complex, see how it can be used to simplify computations, and give examples of how it can be helpful in distinguishing knots which are not concordant.

Ptolemy coordinates and the A-polynomial

Series
Geometry Topology Seminar
Time
Friday, April 11, 2014 - 13:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Christian Zickert – University of Maryland –
The Ptolemy coordinates are efficient coordinates for computingboundary-unipotent representations of a 3-manifold group in SL(2,C). Wedefine a slightly modified version which allows you to computerepresentations that are not necessarily boundary-unipotent. This givesrise to a new algorithm for computing the A-polynomial.

Detection of torus knots

Series
Geometry Topology Seminar
Time
Monday, April 7, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Xingru Zhang – SUNY Buffalo
We show that each (p,q)-torus knot in the 3-sphere is determined by its A-polynomial and its knot Floer homology. This is joint work with Yi Ni.

Cohomology of arithmetic groups over function fields

Series
Geometry Topology Seminar
Time
Monday, March 31, 2014 - 14:05 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Kevin Wortman – University of Utah
Suppose that F is a field with p elements, and let G be the finite-index congruence subgroup of SL(n, F[t]) obtained as the kernel of the homomorphism that reduces entries in SL(n, F[t]) modulo the ideal (t). Then H^(n-1)(G;F) is infinitely generated. I'll explain the ideas behind the proof of the above result, which is a special case of a result that applies to any noncocompact arithmetic group defined over function fields.

Non-looseness of non-loose knots

Series
Geometry Topology Seminar
Time
Monday, March 3, 2014 - 14:00 for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ken Baker – University of Miami
A contact structure on a 3-manifold is called overtwisted ifthere is a certain kind of embedded disk called an overtwisted disk; it istight if no such disk exists. A Legendrian knot in an overtwisted contact3-manifold is loose if its complement is overtwisted and non-loose if itscomplement is tight. We define and compare two geometric invariants, depthand tension, that measure how far from loose is a non-loose knot. This isjoint work with Sinem Onaran.

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