Geometry and Topology Seminar 2019-2020

The Geometry and Topology seminar meets in room 901 of Van Vleck Hall on Fridays from 1:20pm - 2:10pm.
For more information, contact Richard Kent.

Fall 2012

date	speaker	title	host(s)
September 7
September 14
September 21	Owen Sizemore (Wisconsin)	Operator Algebra Techniques in Measureable Group Theory	local
September 28	Mireille Boutin (Purdue)	The Pascal Triangle of a discrete Image: definition, properties, and application to object segmentation	Mari Beffa
October 5	Ben Schmidt (Michigan State)	Three manifolds of constant vector curvature	Dymarz
October 12	Ian Biringer (Boston College)	TBA	Dymarz
October 19
October 26	Jo Nelson (Wisconsin)	Cylindrical contact homology as a well-defined homology theory? Part I	local
November 2	Jennifer Taback (Bowdoin)	TBA	Dymarz
November 9
November 16	Jonah Gaster (UIC)	TBA	Kent
Thanksgiving Recess
November 30	Shinpei Baba (Caltech)	TBA	Kent
December 7	Kathryn Mann (Chicago)	TBA	Kent
December 14

Fall Abstracts

Owen Sizemore (Wisconsin)

Operator Algebra Techniques in Measureable Group Theory

Measurable group theory is the study of groups via their actions on measure spaces. While the classification for amenable groups was essentially complete by the early 1980's, progress for nonamenable groups has been slow to emerge. The last 15 years has seen a surge in the classification of ergodic actions of nonamenable groups, with methods coming from diverse areas. We will survey these new results, as well as, give an introduction to the operator algebra techniques that have been used.

Mireille Boutin (Purdue)

The Pascal Triangle of a discrete Image: definition, properties, and application to object segmentation

We define the Pascal Triangle of a discrete (gray scale) image as a pyramidal ar- rangement of complex-valued moments and we explore its geometric significance. In particular, we show that the entries of row k of this triangle correspond to the Fourier series coefficients of the moment of order k of the Radon transform of the image. Group actions on the plane can be naturally prolonged onto the entries of the Pascal Triangle. We study the induced action of some common group actions, such as translation, rotations, and reflections, and we propose simple tests for equivalence and self- equivalence for these group actions. The motivating application of this work is the problem of recognizing ”shapes” on images, for example characters, digits or simple graphics. Application to the MERGE project, in which we developed a fast method for segmenting hazardous material signs on a cellular phone, will be also discussed.

This is joint work with my graduate students Shanshan Huang and Andrew Haddad.

Ben Schmidt (Michigan State)

Three manifolds of constant vector curvature.

A Riemannian manifold M is said to have extremal curvature K if all sectional curvatures are bounded above by K or if all sectional curvatures are bounded below by K. A manifold with extremal curvature K has constant vector curvature K if every tangent vector to M belongs to a tangent plane of curvature K. For surfaces, having constant vector curvature is equivalent to having constant curvature. In dimension three, the eight Thurston geometries all have constant vector curvature. In this talk, I will discuss the classification of closed three manifolds with constant vector curvature. Based on joint work with Jon Wolfson.

Ian Biringer (Boston College)

TBA

Jo Nelson (Wisconsin)

Cylindrical contact homology as a well-defined homology theory? Part I

In this talk I will define all the concepts in the title, starting with what a contact manifold is. I will also explain how the heuristic arguments sketched in the literature since 1999 fail to define a homology theory and provide a foundation for a well-defined cylindrical contact homology, while still providing an invariant of the contact structure. A later talk will provide us with a large class of examples under which one can compute a well-defined version of cylindrical contact homology via a new approach the speaker developed for her thesis that is distinct and completely independent of previous specialized attempts.

Jennifer Taback (Bowdoin)

TBA

Jonah Gaster (UIC)

TBA

Shinpei Baba (Caltech)

TBA

Kathryn Mann (Chicago)

TBA

Spring 2013

date	speaker	title	host(s)
January 25
February 1
February 8
February 15
February 22
March 1
March 8
March 15
March 22	Michelle Lee (Michigan)	TBA	Kent
Spring Break
April 5
April 12
April 19
April 26
May 3
May 10

Spring Abstracts

Michelle Lee (Michigan)

TBA

Archive of past Geometry seminars

2011-2012: Geometry_and_Topology_Seminar_2011-2012

2010: Fall-2010-Geometry-Topology