(See past events)
Tyler Bongers, Washington University in Saint Louis
Friday, March 1 at 4:10pm in Ritter 202 with refreshments beforehand in the Ritter Hall Lobby.
Stretching and rotation properties of quasiconformal maps
Abstract: Quasiconformal maps in the plane are homeomorphisms that satisfy useful distortion inequalities: they map infinitesimal circles to ellipses. These maps arise naturally in complex dynamics and geometric function theory, as well as the study of elasticity and elliptic PDEs. In this talk, we will consider the local geometric properties of these maps and discuss the construction of extremizers for certain geometric regularity conditions related to stretching and rotation. This work will improve upon recent results of Astala-Iwaniec-Prause-Saksman and Hitruhin.
Louis H Kauffman, University of Illinois Chicago
Friday, March 22, at 4:10pm in Ritter 202 with refreshments beforehand in the Ritter Hall Lobby.
Introduction to Virtual Knot Theory
Abstract: Virtual knot theory studies the knot theory of embeddings of circles in thickened surfaces. By taking projections of the knot diagrams in surfaces to the plane one obtains a theory of diagrams that contain classical knot crossings and virtual crossings that are neither over nor under. The virtual crossings are an artifact of the projection of the knot to the plane but are very useful for the combinatorial topology. Virtual crossings also occur in planar projections of non-planar graphs, and there are many analogies between graph theory and knot theory in this domain. The talk will discuss invariants of virtual knots such as the Jones polynomial in Kauffman bracket form, the odd writhe,
the Manturov Parity Bracket, the Arrow polynomial and the Affine Index Polynomial. This theory has many interesting examples and many relations with classical knot theory
and with combinatorics and graph theory. The talk will be self-contained.
Departmental Awards Ceremony
Friday, April 26. Refreshments at 4:00pm. Case Lecture at 4:30pm, with awards to follow.
Spring 2019 Colloquium Schedule
Friday, February 15: Liberty Vittert, Washington University in Saint Louis
Friday, March 1: Tyler Bongers, Washington University in Saint Louis
Friday, March 22: Louis Kauffman, University of Illinois Chicago
April 2 or 4 (TBA): K. M. Rangaswamy, University of Colorado, Colorado Springs
Friday, April 12: Mihai Ciucu, Indiana University