Diana Davis

Diana Davis

Scholarship/Creative Work

Creative work: I made a video that explains my Ph.D. thesis result using dance and colors. Check it out:

Scholarship:

Diana Davis, W. Patrick Hooper, Periodicity and ergodicity in the trihexagonal tiling, 2016: arXiv.

Diana Davis, Victor Dods, Cynthia Traub, Jed Yang, Geodesic trajectories on regular polyhedra, to appear in Discrete Mathematics, 2016: arXiv, pdf.

Diana Davis, Kelsey DiPietro, Jenny Rustad, Alexander St Laurent, Negative refraction and tiling billiards, to appear in Advances in Geometry, 2016; arXiv, pdf.

Diana Davis, Irene Pasquinelli, Corinna Ulcigrai, Cutting sequences on Bouw-Möller surfaces: an S-adic characterization (submitted 2016): arXiv, pdf.

Diana Davis, Inquiry-based learning in a first-year honors course (submitted 2016): arXiv (pedagogy).

Keith Burns, Orit Davidovich, Diana Davis, Average pace and horizontal chords (submitted 2015): arXiv, pdf. Scientific American blog post about this paper.

Diana Davis, Cutting sequences on translation surfaces, New York Journal of Mathematics, Volume 20 (2014) 399-429: arXiv, pdf.

Diana Davis, Cutting sequences, regular polygons, and the Veech group, Geometriae Dedicata, Volume 162, Issue 1 (2013), pages 231-261: pdf.

Diana Davis, Dmitry Fuchs, Sergei Tabachnikov, Periodic trajectories in the regular pentagon, Moscow Mathematical Journal, vol. 3, 2011: arXiv, pdf.

Papers while a student at Williams College:

Elizabeth Adams, Ivan Corwin, Diana Davis, Michelle Lee, Regina Visocchi, Isoperimetric Regions in Gauss Sectors, Vol. 8, No. 1, 2007, Rose-Hulman Undergraduate Mathematics Journal: pdf.

Joseph Corneli, Ivan Corwin, Stephanie Hurder, Vojislav Sesum, Ya Xu, Elizabeth Adams, Diana Davis, Michelle Lee, Regina Visocchi, Neil Hoffman, Double Bubbles in Gauss Space and Spheres, Houston Journal of Mathematics, Vol. 34, No. 1, 2008: pdf.

Book:

Dynamics Done with your Bare Hands, European Mathematical Society, 2017. Buy the book or read the PDF. Lecture notes by Diana Davis, Bryce Weaver, Roland Roeder and Pablo Lessa.

Exposition: 

Diana Davis, Billiards and Flat Surfaces, a survey article aimed at high school students. Translated into German by Mitteilungen der DMV (Notices of the German Mathematical Society) and published in several places:

  • Billiards and Flat Surfaces, A Snapshot of Modern Mathematics for Oberwolfach (2014), online, pdf (English).
  • Billard und ebene Flächen, Volume 23, Issue 3, September 2015, 151-155: pdf (German).
  • Billard und ebene Flächen, Bulletin of the Verein Schweizerischer Mathematik-und Physiklehrkräfte, January 2016, 8-14, pdf (German).

Pedagogy: I teach problem-based, discussion-style math classes.

My report about this method, with data showing that it works: Inquiry-based learning in a first-year honors course

My problem-based curricula for:

  • a senior seminar on billiards, surfaces and geometry: Math 424
  • the last 2/3 of a multivariable calculus course at Northwestern: Math 290-3
  • multivariable calculus at Williams: Math 150

Videos of my students in class, showing the high quality of student interactions: my YouTube channel

Thesis students:

  • Megumi Asada ’17
  • Paul Baird-Smith ’17
  • Dylanger Pittman ’17 (co-advised with Frank Morgan)

Upcoming and recent talks:

  • City University of New York, dynamical systems seminar, April 2017
  • Swarthmore College, colloquium, February 2017
  • Siena College, February 2017
  • CIRM, Teichmüller space, polygonal billiards and interval exchanges (France), February 2017
  • University of Rhode Island, January 2017
  • Colby College, January 2017
  • Colorado College, January 2017
  • Joint Mathematics Meetings (Atlanta), January 2017
  • Lehigh University, Colloquium, November 2016
  • Williams College, science lunch, November 2016
  • Williams College, faculty seminar, November 2016
  • Smith College, Lunch talk series, September 2016
  • Smith College, Algebra/Geometry/Combinatorics seminar, September 2016
  • Williams College, SMALL Colloquium, July 2016
  • Williams College, FrankFest, February 2016
  • U.S. Naval Academy, January 2016
  • Colorado College, January 2016
  • Gonzaga University, January 2016
  • Joint Mathematics Meetings (Seattle), January 2016
  • Penn State University, Dynamical Systems Seminar, November 2015
  • CIRM, Dynamics and Geometry in the Teichmüller space (France), July 2015
  • Notre Dame, Summer school on boundaries and dynamics, May 2015; lecture notes (book).
  • University of Minnesota, Combinatorics Seminar, February 2015
  • Northwestern University, graduate student seminar, October 2014.
  • Bard College at Simons Rock, September 2014.
  • Northwestern University, Dynamical Systems Seminar: October 2013, January 2015.
  • Midwest Women in Mathematics Symposium, April 2014 and March 2015
  • University of Utah, Max Dehn Seminar, April 2014.
  • Northwestern Undergraduate Math Society, April 2014
  • University of Illinois at Urbana-Champaign, Ergodic Theory Seminar, April 2014.
  • Oberwolfach (Germany), Workshop on Flat Surfaces and Dynamics on Moduli Space, March 2014.
  • University of Chicago, Dynamics Seminar, March 2014.
  • ICERM, Brown University, workshop on Geometric Structures in Low-Dimensional Dynamics, November 2013; video of talk.
  • Simons Center for Geometry and Physics, Stony Brook, July 2013. Video of talk
  • Yale University, Geometry & Topology Seminar, April 2013.
  • University of Maryland College Park, Geometry & Topology Seminar, February 2013; slides.
  • Tufts University, Colloquium, February 2013; slides.
  • Harvard University, Geometry & Dynamics Seminar, February 2013; slides.
  • Indiana University, Geometry Seminar, January 2013; slides.
  • Southern Illinois University Edwardsville, January 2013.
  • Joint Mathematics Meetings (San Diego), January 2013; slides.
  • Oxford University (UK), graduate student seminar, December 2012.
  • Freie Universität Berlin (Germany), Discrete Geometry seminar, November 2012.
  • Summer @ ICERM REU, Brown University, July 2012. Handout from talk (pdf).
  • Colby College, Colloquium, March 2012.
  • University of Bristol (UK), Dynamics Seminar, February 2012.