Research Interests

My current work is in Geometric Group Theory. The basic idea of Geometric Group Theory is to think of a group as a geometric object or to study the geometry of spaces that the group acts “nicely” on.  Using tools from geometry and topology, we can study the space associated to the group, and gain some insight into algebraic properties of the group.

I am interested in CAT(0) spaces and their visual boundaries, Z-Structures (a generalization of CAT(0) and Hyperbolic group boundaries), and large scale geometry/ asymptotic geometry (in particular asymptotic dimension).

Publications

• C.Guilbault, M.Moran, C. Tirel. Z-Structures on Baumslag-Solitar Groups. Accepted Algebraic and Geometric Topology, 2019.
• C.Guilbault, M.Moran. Proper Homotopy Types and Z-Boundaries of Spaces Admitting Geometric Group Actions. Expositiones Mathematicae, 2018. 
• C. Guilbault and M.Moran. A Comparison of Large Scale Dimension of a Metic Space to the Dimension of its Boundary. Topology and its Applications, 199 :17-22, 2016.
•  M.Moran. Metrics on Visual Boundaries of CAT(0) Spaces. Geometriae Dedicata, 183 (1) :123-142, 2016.
• M.Moran. Finite-Dimensionality of Z-boundaries. Groups, Geometry, and Dynamics, 10 (2): 819-824, 2016.

Workshop in Geometric Topology

Each year (typically in June) the Workshop in Geometric Topology is held at one of several rotating locations. The three day workshop is a chance for Geometric Topologists (and Geometric Group Theorists) to share their research and collaborate.

In June 2016, I co-organized the workshop, along with Fred Tinsley, at Colorado College. For more information or to see videos of the principal lecture, click here for the conference website. The 2017 Workshop was held in Provo, Utah and the 2018 workshop was held in Grand Rapids, Michigan at Calvin College. Look out for the 2019 workshop at the University of Wisconsin-Milwaukee.

Selected Conferences and Workshops

• Workshop in Large Scale Geometry and Applications (May 2018) – The Fields Institute, Toronto, Canada
• AIM Boundaries of Groups Workshop (October 2016) – American Institute of Mathematics, San Jose, CA
• Workshop in Geometric Topology (June 2018, June 2017, June 2016, June 2014, June 2013, June 2012) – Calvin College, BYU, Colorado College, University of Wisconsin-Milwaukee, Calvin College, Oregon State

• Spring Topology and Dynamics Conference (March 2016, May 2015) – Baylor University, Bowling Green State University
• Topological Methods in Group Theory (June 2014) – The Ohio State University, Columbus, OH
• USTARS (April 2013) – Purdue University, West Lafayette, IN
• AMS Mathematical Research Community: Geometric Group Theory (June 2013) – Snowbird, UT
• Examples of Geometries Workshop ( June 2011) – The Ohio State University Columbus, OH
• EDGE: Enhancing Diversity in Graduate Education (June 2009) – Spelman College, Atlanta, GA
• Summer Program for Women in Mathematics (July 2008) – George Washington University, Washington, D.C.