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

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 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. |