Diana Davis

"Mathematics is an art of human understanding. ... Mathematical concepts are abstract, so it ends up that there are many different ways they can sit in our brains. A given mathematical concept might be primarily a symbolic equation, a picture, a rhythmic pattern, a short movie -- or best of all, an integrated combination of several different representations." - William Thurston

Curriculum Vitae | Research statement | Teaching statement
Upcoming talks | Videos | Research | Gallery | Teaching | Past talks | Other worthwhile pursuits | Contact

Pentagons and pentagon jewelry

Upcoming talks
November 5, Fields Medal Symposium in honor of Maryam Mirzakhani, Fields Institute (Toronto, Canada)
January 18, JMM, Baltimore, AMS special session
June 2019, LG&TBQ Geometry, topology and dynamics conference, University of Michigan

Videos of past talks
Periodic trajectories on the regular pentagon: versions for non-mathematicians, high school students, math majors, and experts.
Interval exchange transformations from tiling billiards, CIRM, February 2017
Cutting sequences on Bouw-Moeller surfaces, ICERM, November 2013
Public lecture about Dance your PhD, Simons Center, July 2013

More videos
On learning, a speech explaining my pedagogical philosophy
Six examples of families of periodic paths on the pentagon -- so beautiful!
My multivariable calculus lectures (40 classes from spring 2018)
How to make sure your bartender is fair
Linear Algebra Done Wrong (I am the bear)
Video of one of my discussion-based math classes
Curt McMullen’s Heidelberg Laureate lecture (he shows my video at 43:00)



  1. Diana Davis and Samuel Lelievre, Periodic paths on the pentagon, double pentagon and golden L, preprint (2018).
  2. Paul Baird-Smith, Diana Davis, Elijah Fromm, Sumun Iyer, Tiling billiards on triangle tilings, and interval exchange transformations, submitted (2018).
  3. Aaron Calderon, Solly Coles, Diana Davis, Justin Lanier, Andre Oliveira, How to hear the shape of a billiard table, submitted (2018).
  4. Diana Davis, W. Patrick Hooper, Periodicity and ergodicity in the trihexagonal tiling, to appear in Commentarii Mathematici Helvetici (2018).
  5. Diana Davis, Irene Pasquinelli, Corinna Ulcigrai, Cutting sequences on Bouw-Möller surfaces: an S-adic characterization, to appear in Annales scientifiques de l’Ecole normale superieure (2018).
  6. Diana Davis, Kelsey DiPietro, Jenny Rustad, Alexander St Laurent, Negative refraction and tiling billiards, Advances in Geometry, 18(2), 133-159 (2018).
  7. Keith Burns, Orit Davidovich, Diana Davis, Average pace and horizontal chords, The Mathematical Intelligencer, 39(4), 41-45 (2017).
  8. Diana Davis, Victor Dods, Cynthia Traub, Jed Yang, Geodesic trajectories on regular polyhedra, Discrete Mathematics, 340(1), 3183-3196 (2017).
  9. Diana Davis, Cutting sequences on translation surfaces, New York Journal of Mathematics, Volume 20, 399-429 (2014).
  10. Diana Davis, Cutting sequences, regular polygons, and the Veech group, Geometriae Dedicata, 162(1), 231-261 (2013).
  11. Diana Davis, Dmitry Fuchs, Sergei Tabachnikov, Periodic trajectories in the regular pentagon, Moscow Mathematical Journal, vol. 3 (2011).
  12. 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, 34(1) (2008).
  13. Elizabeth Adams, Ivan Corwin, Diana Davis, Michelle Lee, Regina Visocchi, Isoperimetric Regions in Gauss Sectors, Rose-Hulman Undergraduate Mathematics Journal, 8(1) (2007).
Pedagogy: Book: Exposition: I wrote a survey article aimed at high school students, and it was translated into German and published in several places: My Erdos number is 4.

I have published articles in journals based in USA, Russia, Germany, France and Switzerland.

Gallery: ooh, geometry and dynamics research, so pretty!

“a “a “a “cutting “a “a

Contact me for larger sizes or more images. I have multitudes.


Spring 2018 course web site for multivariable calculus, with links to videos of lectures, and handwritten lecture note handouts


Why yes, I do create my own problem-based textbook for each (recent) course: I gave a slide talk and a pep talk lecture explaining this curriculum and pedagogy.

Courses taught:

Undergraduate thesis students:
Past talks (title link is to video of talk)

Lunch talk on active learning pedagogy, October 2018 slides
AMS sectional meeting, University of Delaware, September 2018 slides
Swarthmore College, Colloquium, September 2018
William Rowan Hamilton Geometry & Topology Workshop, Trinity College Dublin (Ireland)
Aix-Marseille Université (France), July 2018
Teichmüller dynamics, mapping class groups, and applications, Institut Fourier (France), June 2018 slides
Drexel University, Colloquium, April 2018
AMS Eastern sectional meeting, Northeastern University, April 2018 slides
Boston College, Dynamics seminar, March 2018
University of Maryland - College Park, Dynamics seminar, March 2018
Swarthmore College, Faculty Lunch, January 2018
Joint Mathematics Meetings (San Diego), January 2018 Research talk slides, Teaching talk slides
Tel Aviv University, January 2018 slides

University of Michigan, November 2017
Brown University, November 2017
Villanova University, colloquium, September 2017
Yale University, SUMRY colloquium, July 2017
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 are this book.
Midwest Women in Mathematics Symposium, March 2015
University of Minnesota, Combinatorics Seminar, February 2015
Northwestern University, Dynamical Systems Seminar, January 2015

Northwestern University, graduate student seminar, October 2014
Bard College at Simons Rock, September 2014
Midwest Women in Mathematics Symposium, April 2014
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.
Simons Center for Geometry and Physics, Stony Brook, July 2013
Northwestern University, Dynamical Systems Seminar, October 2013
Yale University, Geometry & Topology Seminar, April 2013
University of Maryland College Park, Geometry & Topology Seminar, February 2013
Tufts University, Colloquium, February 2013
Harvard University, Geometry & Dynamics Seminar, February 2013
Indiana University, Geometry Seminar, January 2013
Southern Illinois University Edwardsville, January 2013
Joint Mathematics Meetings (San Diego), January 2013

Oxford University (UK), graduate student seminar, December 2012
Freie Universität Berlin (Germany), Discrete Geometry seminar, November 2012
Summer @ ICERM REU, Brown University, July 2012
Colby College, Colloquium, March 2012
University of Bristol (UK), Dynamics Seminar, February 2012

I have given talks in USA, England, France, Germany, Israel and Ireland.
I have given talks in CA, CO, DE, IL, IN, ME, MD, MA, MI, NH, NY, PA, RI, UT, WA.
I am eager to give more talks. Invite me.
Other worthwhile pursuits (section under construction)

Swarthmore College, Department of Mathematics and Statistics, 500 College Avenue, Swarthmore PA 19081