Research

Research Summary

I completed my Ph. D at Howard University under the direction of Professor Todd Drumm. My dissertation was an investigation of the discreteness problem for non-elementary rank 3 free subgroups of PSL(2, R). My research interests primarily fall within the (enveloping) theory of geometric structures on manifolds, the conceptual framework of which wonderfully exhibits rich intersections of geometry & topology, algebra, analysis, dynamics, and number theory. I count myself a happy geometer in that these interrelationships are profoundly rich, have broad application, and offer glimpses of the unity and harmony of mathematics as a whole.

Publications

– “A discreteness algorithm for 4-punctured sphere groups.” AMS Contemporary Mathematics Series, 2020; Volume 759. [arXiv:1703.08241].

– w/ Jean-Philippe Burelle, Sean Lawton: “Rank 1 character varieties of finitely presented groups.” Geometriae Dedicata, 192(1), 1-19. 2018. [arXiv:1910.10055].

Past Invited Talks & Presentations

• Invited Talk: CMS Smmmer Meeting, University of Saskatchewan, "Geometry and Representation Theory," June 2024.

• Invited Lectures:  Pundit "Practicum for Undergraduates in Number Theory."  IPAM, October 2021.

• Invited Colloquia: Geometry & Topology Seminar, Boston College, March 2021. 

• Invited Talk: AMS Sectional Meeting at UV Charlottesville. “Trends in Teichmüller Theory,” March 13-15, 2020. (Meeting cancelled due to Covid-19)

• Invited Talk: AMS Sectional Meeting at UC Riverside. “Interactions Between Geometric Group Theory & Teichmüller Theory,” Nov 9-10 2019.

• Invited Talk: AMS Special Session, JMM Baltimore “The Mathematics of Historically Black Colleges and Universities in the Mid-Atlantic, Emerging Mathematicians,” 2019.

• Invited Colloquia: Topology, Algebraic Geometry, & Dynamics Seminar, George Mason University, 2018.

• Invited Colloquia: Geometry, Topology and Dynamics Seminar, University of Illinois Chicago, 2017.

• Invited Talk: NAM Granville-Brown-Haynes Session, Recent Doctoral Recipients, Seattle, 2016.

• Invited Talk: MSRI Postdoctoral Member MSRI: “Dynamics on Moduli Spaces of Geometric Structures,” PostDoc Seminar, 2015.

• Invited Talk: AMS Special Session, JMM Baltimore “Deformations Spaces of Geometric Structures on Low-Dimensional Manifolds,” 2014.

• Invited Talk: GEAR Focused Workshop: Character Varieties and Geometric Structures, Howard University, 2013.