Craig R. Guilbault

Craig R. Guilbault is a Professor in the Department of Mathematical Sciences at the University of Wisconsin-Milwaukee (UWM), where he also serves as Department Chair. He is a leading researcher in geometric topology and geometric group theory, with a focus on the large-scale structure of spaces and groups. He is actively involved in the topology community through co-organizing the Annual Workshop in Geometric Topology and serving on editorial and steering committees.

• PhD, University of Tennessee, Knoxville (1988)
• BS, Northland College, Ashland, Wisconsin (1982)

His research centers on geometric topology and geometric group theory, particularly the study of ends of manifolds, group boundaries, Z-compactifications, and proper homotopy theory. He investigates how the topology at infinity influences global structure and develops tools like EZ-structures and coarse Z-boundaries to analyze noncompact spaces and groups. His work bridges algebraic, geometric, and topological methods to solve deep structural problems.

The recent publications highlight a sustained focus on boundaries of groups, compactifications of manifolds, and the interplay between large-scale geometry and homotopy theory. Themes include non-uniqueness phenomena, tameness at infinity, and the construction of topological invariants for noncompact spaces. His collaborations span multiple institutions and have advanced understanding in areas such as Baumslag-Solitar groups and Croke-Kleiner spaces.

He has received recognition through editorial roles and long-term leadership in conference organization, including:

• Co-organizer, UWM Topology Seminars
• Co-organizer, Annual Workshop in Geometric Topology (1991–Present)
• Editor, Topology Proceedings
• Member, Steering Committee, Spring Topology and Dynamics Conference

Guilbault has advised several graduate students, including Brendan Healy, Molly Moran, and Carrie Tirel, and has secured research support through NSF funding for workshops. He leads a vibrant research group in topology at UWM and continues to publish in top journals such as Algebraic & Geometric Topology, Fundamenta Mathematicae, and Geometry & Topology.

He is a key figure in the UWM Topology Research Group and contributes to national and international topology initiatives through editorial and organizational leadership. His work fosters collaboration and training in geometric and algebraic topology.