Research

My main interest is connecting geometry and number theory with ergodic theory. I am working on problems connecting the dynamics of certain classes of continued fractions to flows on modular surfaces. My advisor is Florin Boca.

Papers

(with Florin Boca) α -expansions with odd partial quotients. Journal of Number Theory, To Appear.

(with Florin Boca) Coding of geodesics on some modular surfaces and applications to odd and even continued fractions. Indagationes Mathematicae, October 2018. [Arxiv version ]

Continued fractions connecting number theory, dynamical systems, and hyperbolic geometry. Expository.

Invited Talks

Joint Math Meetings, Coding geodesic flows for various continued fractions, AMS Special Session: Geometry and Dynamics of Continued Fractions, January 18, 2019.

University of Virginia, Coding geodesic flows and various continued fractions, Geometry Seminar, December 4, 2018.

University of Maryland, Coding geodesic flows and various continued fractions, Student Dynamics Seminar, November 27, 2018.

University of Houston, Coding geodesic flows for even and odd continued fractions, Dynamics Seminar, November 19, 2018.

Queen’s University, α-odd continued fraction expansions,Dynamics, Geometry, and Groups Seminar, October 18, 2018.

University of Illinois at Urbana-Champaign Connecting the upper half plane, geodesic flows, and continued fractions, AWM Graduate Student Colloquium, October 3, 2018.

George Mason University, Increasing outreach activities in the Illinois Geometry Lab, Student Research Talks (StReeTs) at George Mason University, September 21, 2018.

Northwestern University, Coding geodesic flows and various continued fractions, Dynamical Systems Seminar, May 22, 2018.

Eastern Illinois University, Coding geodesic flows and various continued fractions, Math Colloquium, February 9, 2018.

Rose-Hulman Institute of Technology, From hyperbolic planes to continued fractions, Math Seminar, September 6, 2017.

Other Seminar and Conference Talks

University of Maryland, Cutting sequences of Lehner and Farey expansions, Workshop on Dynamical Systems and Related Topics, April 13, 2019.

George Mason University Increasing outreach activities in the Illinois Geometry Lab, Student Research Talks (StReeTs) at George Mason University, September 21, 2018

MAA Mathfest Using geodesics to generate continued fractions, Great Talks for a General Audience: Coached Presentations by Graduate Students, August 3, 2018

Summer Illinois Math Camp Unfolding Billiards Tables, SIM Camp Epsilon (rising 8th and 9th graders), June 29, 2018.

Agnes Scott College, Using modular surfaces to generate continued fractions, Carolina Dynamics Symposium, April 14, 2018.

University of Maryland, Coding continued fractions as cutting sequences, Workshop on Dynamical Systems and Related Topics, April 7, 2018.

George Mason University, Connecting outreach and continued fraction expansions through tessellations, Topology, Algebraic Geometry, and Dynamics Seminar, April 6, 2018.

MAA Trisectional Meeting, Using Geodesics to Generate Continued Fractions, March 23, 2018.

University of Illinois at Urbana-Champaign, Coding geodesic flows and various continued fractions, GEAR/Geometry, Groups, and Dynamics Seminar, February 15, 2018. Video

University of Illinois at Urbana-Champaign, Odd and grotesque continued fractions as geodesic flows, Graduate Student Geometry Topology Seminar, December 8, 2017.

Illinois Geometry Lab

I have served as a graduate mentor on four undergraduate research projects through the Illinois Geometry Lab.

Spring 2019, faculty mentor: Florin Boca, undergraduate students: TDB, Natural extension domains of α-odd continued fractions will look at the natural extension domain for various values of α.

Fall 2018, faculty mentor: Philipp Hieronymi, graduate student mentors: Simone Sisneros-Thiry and myself, undergraduate students: Yasir Badillo Acosta, Kelly Jezior, Alex Lehan, Kagen Quiballo, Iris Tong. Developing Exciting Outreach Material.

Spring 2016, faculty mentors: Jenya Sapir and Cary Malkiewich , graduate student mentors: Ruth Lou and myself, and undergraduate studets: Cameron Dart, Tyler Mulick, Zesheng Wang, Jessica Chen. Interactive Learning Tools for Linear Algebra. The game can be found at http://p415x.xyz/.

Fall 2014, faculty mentors: Jayadev Athreya and Francesco Cellarosi, and undergraduate students: Abigail Turner, Ananya Uppal, Peng Xu. Random Subsets of Discrete Sets looked at the gap distribution and pair correlation properties of random subsets of sequences, such as the Farey seqence.