(See past events)
Louis H Kauffman, University of Illinois Chicago
Friday, March 22, at 4:10pm in Ritter 231 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.
K. M. Rangaswamy, University of Colorado, Colorado Springs
Wednesday, April 3, at 4:10pm in Ritter 231 with refreshments beforehand in the Ritter Hall Lobby.
Title: Are Leavitt path algebras really commutative algebras in non-commutative clothing?
Abstract: Leavitt path algebras of directed graphs over a field are algebraic analogues of graph C*-algebras of operators on Hilbert spaces. This talk is a report on some of the recent investigations illustrating two essential features of these algebras. The first makes the Leavitt path algebras really useful tools in constructing examples of rings of various types. The second is about the ideal lattice of Leavitt path algebras, which seems to posess similarities with commutative rings. Various graphical constructions will illustrate these conclusions.
Doctoral Dissertation Defense
James Mixco, Saint Louis University
Thursday, April 11, at 10:00am.
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
Wednesday, April 3: K. M. Rangaswamy, University of Colorado, Colorado Springs
Friday, April 12: Mihai Ciucu, Indiana University