Research

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My academic research is primarily focused in Metric Number Theory from a Diophantine approximations perspective. I am particularly interested in the connections and interplay between real and p-adic Diophantine approximation.

Publications

• Khintchine's Theorem with rationals coming from neighborhoods in different places, (submitted)
• (joint w. A. Calderon, S. Coles, D. Davis, and J. Lanier ) How to hear the shape of a billiard table, (preprint)

  • This work began at a research cluster on polygonal billiards, organized in summer 2017 by Moon Duchin.

• (joint w. H. Tyler ) Measurement and comparison of passing networks in collegiate soccer, Minnesota Journal of Undergraduate Mathematics, [S.l.], v. 1, n. 1, Dec. 2015.

  • This work began during the 2014 Jasper Summer Fellow’s program.

Talks

Invited

• Diophantine Approximations: From Pigeons to Continued Fractions, Undergraduate Colloquium, Manhattan College, Nov. 2020.

  • This talk was recorded and can be viewed here.

• Diophantine Approximations: What do pigeons have to do with it?, 403 Lecture, Southwestern University, Oct. 2020.

  • This talk was recorded and can be viewed here.

• A Dynamical View of Numbers, Undergraduate Colloquium, University of Hartford, Feb. 2019.

Contributed

• Khintchine's Theorem with rationals restricted to p-adic neighborhoods, Midwest Dynamical Systems Early Career Conference, Nov. 2020.

  • This was a short pre-recorded talk connected to a poster session. The recording can be viewed here.

• On Diophantine approximations across completions of Q, Graduate Student Seminar, Wesleyan University, Feb. 2020.
• How to hear the shape of a billiard table, Graduate Student Seminar, Wesleyan University, Sep. 2019.
• A connection between badly approximable numbers and continued fractions, Graduate Student Seminar, Wesleyan University, Oct. 2018.
• Continued Fractions and Geodesics on the Modular Surface, Strength in Numbers, Queen's University, Canada, May 2018.
• Dani's Correspondence and Schmidt Games, Topology et al. Seminar, Wesleyan University, Mar. 2018.
• Shedding light on Illumination, Graduate Student Seminar, Wesleyan University, Sep. 2017.
• A brief glance at Ergodic Theory, Graduate Student Seminar, Wesleyan University, Feb. 2017.
• A look at the $25,000,000,000 eigenvector, Graduate Student Seminar, Wesleyan University, Oct. 2016.
• Defensive Forwards and Offensive Backs: The 2013 Season of Manhattan College Women’s Soccer, Joint Mathematics Meetings, San Antonio, Jan. 2015.

  • Travel partially funded by an MAA grant.

Conferences Attended

• Midwest Dynamical Systems Early Career Conference, (virtual), Nov. 2020.
• Lattice Point Distribution and Homogeneous Dynamics, ICERM (virtual), Jun. 2020.
• Workshop on Dynamical Systems and Related Topics, Penn State, Sep. 2019.
• Midwest Dynamical Systems Early Career Conference, Ohio State University, May 2019.
• Beyond the Binary, University of Hartford, Apr. 2019.
• Workshop on Dynamical Systems and Related Topics, University of Maryland, Apr. 2019.
• Workshop on Dynamical Systems and Related Topics, Penn State, Sep. 2018.
• Houston Summer School on Dynamical Systems, University of Houston, May 2018.
• Strength in Numbers, Queen's University, Kingston, Canada, May 2018.
• Upstate New York Number Theory Conference, University of Buffalo, Apr. 2018.
• Workshop on Dynamical Systems and Related Topics, University of Maryland, Apr. 2018.
• Women in Mathematics in New England September, Smith College, Sep. 2017.
• Graduate Student Conference in Algebra, Geometry, and Topology, Temple University, Jun. 2017.
• Upstate New York Number Theory Conference, Binghamton University, May 2017.
• Joint Mathematics Meetings, Atlanta, GA, Jan. 2017.
• Joint Mathematics Meetings, San Antonio, TX, Jan. 2015.