Topology Seminar 2012--2013 Archive

Speaker: Dale Rolfsen

Title: Orderable groups and topology

Abstract: I will discuss how the concept of orderability of a group can be applied to problems in topology, particularly in the theory of 3-dimensional manifolds.

Date/Time: 3:30pm CLE A202 on April 2nd

Speaker: Dale Rolfsen

Title: A topological view of orderable groups

Abstract: Algebra and topology are old friends.  Many topological problems are solved by applying algebraic methods.  But sometimes the relationship can work the other way.  My talk will discuss how the topological viewpoint can be used to establish the basic facts regarding orderability of groups. These facts can be used, in turn, to show that certain groups of interest to topologists are orderable, for example knot groups and the group of PL homeomorphisms of a disk fixed on the boundary.

Date/Time: 3:30pm CLE A207 on April 3rd

Speaker: Ryan Budney

Title: Persistent homology applied to musical data

Abstract: This talk will describe various metric spaces that are useful for the analysis of musical data, such as spaces of chords and spaces of rhythms. Bill Sethares and I analyze readily-available musical data through the lens of "Persistent Homology". This talk will be a brief report on our results. Will take place in the U.Vic Stats Seminar.

Date/Time: 2:30pm, Friday March 1st, 2013. DSB C128.

Speaker: Jim McClure (Purdue)

Title: Poincare duality and sheaf theory

Abstract: The main theorem is that the Poincare duality isomorphism that is obtained from sheaf theory is the same as the classical isomorphism obtained from the cap product. This talk requires a minimal knowledge of sheaf theory (basically just a prior exposure to the definition of sheaf and to the derived category).

Date/Time: 1pm Thursday September 27th.

Location: HSD A264

Speaker: William Sethares (U. Wisconsin)

Title: Topology of Musical Data

Abstract: Techniques for discovering topological structures in large data sets are now becoming practical. This talk argues why the musical realm is a particularly promising arena in which to expect to find nontrivial topological features. The analysis is able to recover three important topological features in music: the circle of notes, the circle of fifths, and the rhythmic repetition of timelines, often pictured in the necklace notation.

Date/Time: March 8th, 3:30pm--4:30pm

Location: SSM A104

Speaker: Ryan Budney

Title: Some simple triangulations

Abstract: I'll describe the story of how Thurston observed some very simple triangulations of knot and link complements in the 3-sphere. This allowed for a relatively simple way to find hyperbolic structures on such manifolds, and was a key inspiration for the Geometrization Conjecture of 3-manifolds. Recently Ben Burton and I found an analogous triangulation for the complement of an embedded 2-sphere in the 4-sphere. While this does not lead to an amazing conjecture like Geometrization, it does lead to an interesting insight into things called Cappell-Shaneson knots, which are connected to the 4-dimensional Poincare conjecture. This is joint work with Ben Burton, and Jonathan Hillman.

Date/Time: September 28th, 3:30pm-4:30pm

Location: DSB C114