Seminar Geometry, Topology, Dynamical Systems
(Fall 2014, Spring 2015)

Except as otherwise noted, seminars are held in FO 2.702 on Mondays from 11 am to 12 pm.



Schedule

Date Speaker Affiliation Title Abstract
May 4 Ying Hu LSU Left-orderability and cyclic branched covers A group is called left-orderable if one can put a total order on the set of group elements so that inequalities are preserved by group multiplication on the left. The left-orderability of 3-manifold groups is closely related to the concepts of L-spaces and taut foliations, as conjectured by Boyer-Gordon-Watson. In this talk, we will discuss the left-orderability of fundamental groups of cyclic branched covers of the three sphere.
April 27th
Christopher Cornwell
Universite du Quebec a Montreal, CANADA
Knot theory through contact homology and the braid group
Legendrian contact homology (LCH) is a homology theory that, like the numerous Floer homology theories, uses a Gromov-type count of pseudo-holomorphic curves in its differential. In some settings the differential of LCH can be understood purely through topological and combinatorial data. In this talk I will focus on just such a setting. We will discuss how the combinatorial computation of LCH in this setting reveals a number of connections to knot theory. Central to the discussion will be a nice representation of the braid group. No previous knowledge of contact geometry will be assumed.
March 23rd
K. Peterson
Florida State University
Deformations of Hyperbolic 3-manifolds
A character variety of a 3-manifold M is the space X(M) of all hyperbolic structures on M. These algebraic varieties encode a lot of topological data about the 3-manifold. Culler and Shalen famously showed that X(M) detects many surfaces in M. I will talk about the connection between the geometry of X(M) and the topology of M, focusing on invariants like the genus of X(M) and the gonality of X(M).
Jan 16 (FRIDAY, 2pm in FO 1.202)
Maciek Mroczkowski
Gdansk University
Diagrams of links in Seifert manifolds and their application to skein modules
I will present diagrams of links in Seifert manifolds together with Reidemeister moves that connect any two diagrams of the same link. Then, I will show how these diagrams and moves can be used to compute some skein modules, such as Kauffman Bracket skein module and HOMFLYPT skein module.
Jan 16 (FRIDAY, 12pm in SLC 1.202)
Michal Jablonowski
Gdansk University
On a monoid associated to knotted surfaces
We describe a view to knotted surfaces in the four space as elements of a monoid with four types of generators: two classical braid generators and two of singular braid types. We present local and global relations on words that do not change a corresponding surface-knot type. Those new relations already appear to be useful: in a quest of a classification of twist-spun knots, and in a construction of classical diagrams having some minimal number of Reidemeister III moves required to connect them.
Dec 8
H. Poonawala
Laboratory for Autonomous Robotics and Systems, UTD
Applications of the Frobenius Theorem in Controls Engineering
Feedback Linearization and controllability of dynamical systems in R^n
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Nov 10
T. Ohsawa
Mathematical Sciences, UTD
How is quantum mechanics related to classical mechanics?, II
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Nov 3
T. Ohsawa
Mathematical Sciences, UTD
How is quantum mechanics related to classical mechanics?
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Oct 20
W. Krawcewicz
Mathematical Sciences, UTD
Pontriagin-Thom Theorem II
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Oct 13
Q. Hu
Mathematical Sciences, UTD
Introduction to differential equations with state-dependent delay
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Oct 6
W. Krawcewicz
Mathematical Sciences, UTD
Pontriagin-Thom Theorem
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Sep 22
A. Tran
Mathematical Sciences, UTD
Introduction to character varieties, III
An introduction to character varieties of finitely generated groups and their applications in topology will be given.
Sep 15
A. Tran
Mathematical Sciences, UTD
Introduction to character varieties, II
An introduction to character varieties of finitely generated groups and their applications in topology will be given.
Sep 8
A. Tran
Mathematical Sciences, UTD
Introduction to character varieties
An introduction to character varieties of finitely generated groups and their applications in topology will be given.
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