Geometric Topology at UW-Milwaukee

The Geometric Topology 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.

Ancel, Guilbault, Okun and Hruska all 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, differential and CAT(0) geometry, and geometric group theory.

Interest in geometric topology and geometric group theory amongst UWM graduate students is at an all-time high. Currently there are nine students working on dissertations and a few others who have begun their studies in those areas. Recent UWM Ph.D. graduates in geometric topology and geometric group theory include:

**Hanspeter Fischer** (Ph.D.
1998, ) Thesis: *Visual Boundaries of Right Angled Coxeter Groups and
Reflection Manifolds*. Advisor: Ric Ancel. After completing his degree, Hanspeter spent
two years as a post-doc at Brigham Young University. Since then he has worked his way up to the rank of full professor of mathematics at Ball State University.

**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. David is currently on the faculty at Century College in Minnesota.

**Margaret May** (Ph.D. 2007) Thesis: *Finite-dimensional Z-compactifications.* Advisor: Craig Guilbault. Maggie is currently an assistant professor of mathematics at the University of Wisconsin-Fond du Lac.

**Christopher Mooney** (Ph.D. 2008) Thesis: *On Boundaries of CAT(0) Groups*. Advisor: Craig Guilbault. After completing a three-year post-doc at the University of Michigan in Ann Arbor, Christopher became an assistant professor of mathematics at Bradley University.

**Timothy Schroeder** (Ph.D. 2008) Thesis: *L2-Homology of Coxeter Groups*. Advisor: Boris Okun. Tim is now an assistant 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.

**Current Ph.D. students:** Jeffrey Rolland, Pete Sparks, Wiktor Mogilski, Hung Tran, Jeremy Osborne, Molly Moran, Kevin Schreve and Jason LaCorte; 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.

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