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
Upcoming talks |
Videos |
Research |
Gallery |
Teaching |
Past talks |
Other worthwhile pursuits |
Contact
Pentagons and pentagon jewelry
Upcoming talks
March 1, University of Maryland - College Park
March 15, Boston College
April 21, AMS Eastern sectional meeting, Northeastern University
June 25, Grenoble, France
September 28, AMS sectional meeting, University of Delaware
November 5, Fields Medal Symposium in honor of Maryam Mirzakhani, Fields Institute (Toronto)
Spring 2019, LGBTQ+ Geometry, topology and dynamics conference, University of Michigan
Videos of past talks
Periodic trajectories on the regular pentagon, general-audience talk given to Swarthmore faculty, January 2018
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
Six examples of periodic pentagon trajectory families -- so beautiful!
My multivariable calculus lectures (new videos every Monday, Wednesday and Friday in 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)
Research
Papers:
- 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.
- Diana Davis, W. Patrick Hooper, Periodicity and ergodicity in the trihexagonal tiling, accepted pending revision in Commentarii Mathematici Helvetici.
- Diana Davis, Victor Dods, Cynthia Traub, Jed Yang, Geodesic trajectories on regular polyhedra, to appear in Discrete Mathematics.
- Diana Davis, Kelsey DiPietro, Jenny Rustad, Alexander St Laurent, Negative refraction and tiling billiards, to appear in Advances in Geometry.
- Keith Burns, Orit Davidovich, Diana Davis, Average pace and horizontal chords, The Mathematical Intelligencer, 39(4), 41-45 (2017).
- Diana Davis, Cutting sequences on translation surfaces, New York Journal of Mathematics, Volume 20 (2014) 399-429.
- Diana Davis, Cutting sequences, regular polygons, and the Veech group, Geometriae Dedicata, Volume 162, Issue 1 (2013), pages 231-261.
- Diana Davis, Dmitry Fuchs, Sergei Tabachnikov, Periodic trajectories in the regular pentagon, Moscow Mathematical Journal, vol. 3, 2011.
- 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.
- 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.
Pedagogy:
Book:
- Dynamics Done with your Bare Hands, European Mathematical Society, 2017. Buy the book or get the PDF. Lecture notes by Diana Davis, Bryce Weaver, Roland Roeder and Pablo Lessa.
Exposition: I wrote a survey article aimed at high school students, and it was translated into German and published in several places:
- Billiards and Flat Surfaces, A Snapshot of Modern Mathematics for Oberwolfach, 2014 (English).
- Billard und ebene Flächen, Volume 23, Issue 3, September 2015, 151-155 (German).
- Billard und ebene Flächen, Bulletin of the Verein Schweizerischer Mathematik-und Physiklehrkräfte, January 2016, 8-14 (German).
My Erdos number is 4.
Gallery: ooh, geometry and dynamics research, so pretty!
Contact me for larger sizes or more images. I have multitudes.
Teaching
Spring 2018 course web site for multivariable calculus, with links to videos of lectures, and handwritten lecture note handouts
Positions:
- Swarthmore College, Visiting Assistant Professor, 2017-2020
- Williams College, Visiting Assistant Professor, 2016-2017
- Northwestern University, Postdoctoral Lecturer, 2013-2016
Why yes, I do create my own problem-based textbook for each (recent) course:
Slides from the talk I gave explaining this curriculum and pedagogy at JMM 2018
Courses taught:
- The Magic of Numbers (Northwestern)
- Combinatorial Game Theory (Northwestern)
- Calculus 1 (Swarthmore)
- Calculus 2 (Brown)
- Multivariable calculus without linear algebra (Brown, Williams)
- Multivariable calculus with linear algebra (Northwestern, Swarthmore)
- Introduction to Proof (Northwestern)
- Linear algebra (Brown)
- Applied Real Analysis (Williams)
- Real Analysis (Swarthmore)
- Billiards, Surfaces and Geometry (Williams)
Undergraduate thesis students:
- Megumi Asada, Williams College 2017
- Paul Baird-Smith, Williams College 2017
- Dylanger Pittman, Williams College 2017
Past talks (title link is to video of talk)
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 and Germany.
I have given talks in CA, CO, 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)
- Running
- Spinning cards and other three-dimensional paper crafts
- Building stuff
- Recipes
Swarthmore College, Department of Mathematics and Statistics, 500 College Avenue, Swarthmore PA 19081
ddavis3(at)swarthmore.edu