Catherine Pfaff's Webpage

Research | Teaching | Organizational Work | Talks | Outreach | Notes

I am the Ky Fan Visiting Assistant Professor at the University of California, Santa Barbara (UCSB).

Starting July 2018 I will be a Tenure-Track Assistant Professor at Queen's University at Kingston.

Catherine Pfaff
UCSB Math Dept.
South Hall, Room 6607
Santa Barbara, CA 93106

Office: South Hall RM. 6702
Office Hours: Tues, Thurs 9:30-10:40am
(or by appointment)
Fax: (805) 893-2385
Email: cpfaff "at"


Welcome to my site!

My name is Catherine Pfaff. I'm an American from a small town (primarily established by my grandfather) in the beautiful Pacific Northwest. My love for mathematics sprung out of my college years at the University of Chicago, where my studies primarily focused on abstract algebra, geometry, and topology. I specifically grew from the Directed Reading Program at the University of Chicago, which I thus established a duplicate of at Rutgers University. I earned my PhD from Rutgers University (New Brunswick) under the advisement of Lee Mosher. During these years my primary focus shifted. My oral qualifying exam topics were manifolds, algebraic geometry, and coarse geometry. Through my study of coarse geometry, I became interested in geometric group theory. Working with Lee Mosher, this interest in geometric group theory focused into the rich subjects of mapping class groups and outer automorphisms of free groups (the Out(F_r)).

My Out(F_r) interests are primarily focused on understanding conjugacy invariants and the conjugacy problem, classifying elements of Out(F_r), determining properties held by generic elements of Out(F_r), and understanding the dynamics of the action of Out(F_r) on Culler-Vogtmann Outer Space. I am also heavily involved in looking at automorphisms of right-angled Artin groups and the space of convex real projective structures on a surface.

I spent three years living in Europe (Barcelona, Spain; Marseille, France; and Bielefeld, Germany). During these years I developed interests in new subjects such as dynamical systems and ergodic theory, symbolic dynamics and substitution systems, tiling theory, CAT(0) cube complexes, mapping class groups, Teichmuller theory, right-angled Artin groups, hyperbolic geometry, and Bass-Serre theory.

In Spring 2018 I am teaching Math 108A (Advanced Linear Algebra I) at UCSB. My passion for research is heavily rivaled by my passion for teaching. My students are one of the greatest joys in my life.

Research | Teaching | Organizational Work | Outreach | Notes