Mathematics PhD Candidate at the University of Utah
Advised by Ken Bromberg
hoganson [at] math [dot] utah [dot] edu
Office: JWB 307
I'm interested in geometry, low dimensional topology, and geometric group theory. Specifically, I am studying the Lp metrics on Teichmüller space. I gave a short talk on my work at the Redbud Topology conference in Spring of 2021, the video of the talk is here. I am also working on questions about Big Mapping Class Groups ( arXiv ), and and an analog of Out(F_n) for infinite, locally finite graphs ( pdf ).My current coauthors and collaborators are Carolyn R. Abbot , George Domat, Sanghoon Kwak, Marissa Loving, Priyam Patel, and Rachel Skipper. In Fall 2020 I was supported on the NSF Research and Training Grant: Algebra, Geometry, and Topology at the University of Utah #1840190. While a master's student at Miami University I thought about Thompson's groups a lot, specifically the conjecture that Thompson's Group V is a universal coCF group. While advising a group of REU students as part of SUMSRI we proposed a potential counterexample to this conjecture: arXiv
I am teaching Math 1320, Engineering Calculus II in Spring 2022 as well as Math 13, a bridge course for students moving from Calculs I to Engineering Calculus II. We will be using Canvas for each.
In Spring 2021 I taught Math 2210-006, Calc III. We used standards based grading.
UpcomingAMS Sectional Meeting "Trends in Teichmüller Theory" at University of Virginia. March 2022. Joint Mathematics Meeting. Seattle, Washington. Januray 2022. Past Women in Groups, Geometry, and Dynamics. Glacier National Park, Montana. August 2021. (Pictured) Artin Groups, CAT(0) Geometry and related topics, A conference in honor of Ruth Charney. The Ohio State University, July 2021. Nearly Carbon Neutral Geometric Topology Conference I was a co-organizer of the Infinite-type surfaces and big mapping class groups session. Virtual, June 2021. Redbud Topology Workshop. Virtually at Oklahoma State University. March 2021 Topology Students Workshop. Virtually at Georgia Tech. July 2020 Young Geometric Group Theory IX. Saint-Jacut-de-la-mer, France. February 2020 Riemann Surfaces and their Moduli Spaces. University of Utah. February 2020 Wasatch Topology Conference. Midway, Utah. August 2019 Aspects of Geometric Group Theory. IHES summer school. July 2019 Young Geometric Group Theory VIII. Bilbao, Spain. June 2019 Visiting Graduate Student. Yale University. Fall Semester 2018. Wasatch Topology Conference. Midway, Utah. August 2018 Binghamton University Graduate Conference in Algebra and Topology. October 2014
I support this statement of inclusivity.
Some photos I've taken around home, the mountain west, and at conferences.