Mathematical Sciences

School of Natural Sciences & Mathematics

Geometry, Topology, Dynamical Systems Seminar, AY 14-15




DateSpeakerAffiliationTitleAbstract
May 4Ying HuLSULeft-orderability and cyclic branched coversA 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 skeinmodules 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.</TD
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
Nov 10 T. Ohsawa Mathematical Sciences, UTD How is quantum mechanics related to classical mechanics?, II
Nov 3 T. Ohsawa Mathematical Sciences, UTD How is quantum mechanics related to classical mechanics?
Oct 20 W. Krawcewicz Mathematical Sciences, UTD Pontriagin-Thom Theorem II
Oct 13 Q. Hu Mathematical Sciences, UTD Introduction to differential equations with state-dependent delay

Oct 6 W. Krawcewicz Mathematical Sciences, UTD Pontriagin-Thom Theorem

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.