Corey Bregman Ph.D.
- Ph.D. Rice University 2017
- B.A. Columbia University 2010
Corey Bregman grew up in Westchester, New York. For his undergraduate education, he attended Columbia University where he studied Mathematics, Philosophy and Classical Greek, graduating summa cum laude in 2010. From 2011 to 2017, Corey obtained a Ph.D. in Mathematics from Rice University, under the supervision of Dr. Andrew Putman. In Fall 2016, he was a member at MSRI for the semester-long program on Geometric group theory. Before joining USM's faculty, Corey held a three-year postdoctoral position at Brandeis University.
My research lies in the field of geometric group theory, which studies the interplay between algebraic properties of infinite groups and the geometric spaces on which they act. I am particularly interested in restrictions imposed by certain geometric structures on group actions, for example, restrictions on the fundamental groups of compact Kaehler manifolds. I am also interested automorphism groups of free groups, surface groups and right-angled Artin groups. Usually the study of automorphisms leads to moduli spaces of particular metric structures such as Outer space and Teichmueller space. My work blends techniques from geometric group theory, low-dimensional topology and algebraic geometry.
Rational growth and almost convexity of higher-dimensional torus bundles, Int. Math. Res. Notices (2019), no. 13, 4004-4046.
Hyperelliptic graphs and the period mapping on outer space (w/ N. Fullarton), J. Topol. 11 (2018), no. 1, 221-256.
Awards and Recognition
NSF Grant DMS-1906269, 2019-2022
Simons Travel Grant 2018-2021