The Topology & Geometry group at the University of Wisconsin-Milwaukee is one of the most active in the department. Ric Ancel, Craig Guilbault, Boris Okun and Chris Hruska are the regular faculty members in this area.
Regularly offered topology courses include a one semester undergraduate course in Elementary Topology , a yearlong graduate sequence titled Introductory Topology, and a yearlong graduate sequence in Algebraic Topology. For students specializing in topology ‘advanced topics’ courses are frequently offered. Topics recently covered in those courses include: differential topology, bundle theory, dimension theory, topological manifolds and polyhedra, surgery theory, PL Morse theory, relatively hyperbolic groups, and various other aspects of geometric group theory and geometric topology.
In addition to formal courses, the Topology Seminar meets twice weekly. There faculty and graduate students discuss and present current research. In addition, a Student Topology Seminar allows graduate students to learn material not covered in their regular coursework. Some recent student seminars have focused on: the geometry of surfaces and covering spaces, dimension theory, CAT(0) geometry, Gromov hyperbolic spaces and groups, piecewise linear topology, knot theory, geometry and topology of 3-manifolds, and Morse theory.
All members of the Topology & Geometry group have active research programs. Ancel and Guilbault have both been at UWM for a number of years and have written several papers jointly. Okun joined the UWM topology group in the fall of 2001; Hruska came to Milwaukee in 2006. Areas of interest include: manifold topology, CAT(0) geometry, and geometric group theory.
Interest in topology and geometric group theory amongst UWM graduate students is at an all-time high, with a record number of PhDs awarded during the 2014-15 academic year. Here is a list of alumni from the UWM PhD program in Topology & Geometry.
Hanspeter Fischer (Ph.D. 1998, ) Thesis: Visual Boundaries of Right Angled Coxeter Groups and Reflection Manifolds. Advisor: Ric Ancel. After a post-doc at Brigham Young University, Hanspeter joined the faculty at Ball State University, where he is now a full professor.
Julia Wilson (Ph.D. 1999) Thesis: Non-uniqueness of Boundaries of CAT(0) Groups. Advisor: Ric Ancel. Julia is now an associate professor of mathematics at SUNY-Fredonia.
David Radcliffe (Ph.D. 2001) Thesis: Unique Presentations of Coxeter Groups and Related Groups. Advisor: Ric Ancel.
Margaret May (Ph.D. 2007) Thesis: Finite-dimensional Z-compactifications. Advisor: Craig Guilbault. After several years as faculty and administrator at UW-Fond du Lac, Maggie switched jobs to join the mathematics faculty at Moraine Park Technical College.
Christopher Mooney (Ph.D. 2008) Thesis: On Boundaries of CAT(0) Groups. Advisor: Craig Guilbault. After a 3-year post-doc at the University of Michigan and several years as an assistant professor at Bradley University, Christopher left academics for private industry. He is now a software developer at Epic Systems near Madison, Wisconsin.
Timothy Schroeder (Ph.D. 2008) Thesis: L^2-Homology of Coxeter Groups. Advisor: Boris Okun. Tim is now an associate professor of mathematics at Murray State University.
Carrie Tirel (Ph.D. 2010) Thesis: Z-structures on product groups . Advisor: Craig Guilbault. Carrie is now an assistant professor of mathematics at the University of Wisconsin-Fox Valley.
Paul Fonstad (Ph.D. 2012) Thesis: A further classification of the boundaries of the Croke-Kleiner group. Advisor: Ric Ancel. Paul is now an assistant professor of mathematics at Franklim College in Indiana.
Jeremy Osborne (Ph.D. 2014) Thesis: Statistical Hyperbolicity of Relatively Hyperbolic Group . Advisor: Chris Hruska. Jeremy is now an lecturer at the University of Wisconsin-Parkside.
Peter Sparks (Ph.D. 2014) Thesis: Contractible n-Manifolds and the Double n-Space Property . Advisor: Craig Guilbault. Pete is currently a lecturer at the University of Wisconsin-Waukesha.
Jeffrey Rolland (Ph.D. 2015) Thesis: Some Results on Pseudo-Collar Structures on High-Dimensional Manifolds. Advisor: Craig Guilbault. Jeff is currently an adjunct professor at Marquette University.
Jason La Corte (Ph.D. 2015) Thesis: The Markov-Dubins problem with free terminal direction in a nonpositively curved cube complex. Advisor: Craig Guilbault. Beginning in the Fall of 2015, Jason will be an assistant professor at Berry College.
Molly Moran (Ph.D. 2015) Thesis: On the Dimension of Group Boundaries. Advisor: Craig Guilbault. Beginning in the Fall of 2015, Molly will be a visisting assistant professor at Colorado College.
Kevin Schreve (Ph.D. 2015) Thesis: The L^2 Cohomology of Discrete Groups . Advisor: Boris Okun. Beginning in the Fall of 2015, Kevin will be a post-doc at the University of Michigan.
Wiktor Mogilski (Ph.D. 2015) Thesis: The fattened Davis complex and the weighted L^2 -(co)homology of Coxeter groups. Advisor: Boris Okun.
Current Ph.D. students: Hung Tran, Matthew Haulmark, and Hoang Nguyen; all are all working on dissertations in Geometric Topology and/or Geometric Group Theory at UWM.
Students interested in studying geometric topology or geometric group theory at the University of Wisconsin-Milwaukee should feel free to contact Ancel, Guilbault, Okun or Hruska directly.