**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 | Bio | Contact

Villanova Student Research Symposium, November 30 (plenary)

Trinity School, NYC, March 12, 2024 (assembly)

Dartmouth College, May 23, 2024 (geometry seminar & professional development seminar)

Anja S. Greer conference, June 26, 2024 (featured speaker)

I organized a seminar! You can see recordings here: Phillips Exeter Academy math seminar

It met in person six times in 2022-2023. The goal of the seminar is that everyone in the room understands the whole talk, an idea born at the Communicating Mathematics conference at Cornell in August 2022. To this end, we insist on lots of pictures, examples, interaction, and questions. Contact me if you would like to speak in a future seminar.

Illustrating mathematics

Gerrymandering and data science

Periodic trajectories on the regular pentagon: choose the version for non-mathematicians, high school students, math majors, and experts.

Interval exchange transformations from tiling billiards

Three flavors of billiards

Cutting sequences on Bouw-Möller surfaces (my Ph.D. thesis)

Public lecture about Dance your PhD (about my viral video)

**More videos** *my YouTube channel*

On learning and
On respect, speeches explaining my pedagogical and classroom philosophies

My discussion-based math classes: one group discusses under a tree, and five groups discuss at the blackboards

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)

Six examples of families of periodic paths on the pentagon -- so beautiful!

Curt McMullen’s Heidelberg Laureate lecture (he shows my video at 43:00)

Papers:

- Paul Baird-Smith, Diana Davis, Elijah Fromm, Sumun Iyer, Tiling billiards on triangle tilings, and interval exchange transformations, to appear in
*Journal of the London Mathematical Society*(2024). - Diana Davis and Serge Troubetzkoy, The horizontal chord set: to CIRM and back, to appear in
*American Mathematical Monthly*(2024). - Sara Asgari, Quinn Basewitz, Ethan Bergmann, Jackson Brogsol, Nathaniel Cox, Diana Davis, Martina Kampel, Becca Keating, Katie Knox, Angus Lam, Jorge Lopez-Nava, Jennifer Paige, Nathan Pitock, Victoria Song, Dylan Torrance, Assessing congressional districting in Maine and New Hampshire, preprint (2020).
- Harrison Bray, Diana Davis, Kathryn Lindsey and Chenxi Wu, The shape of Thurston's master teapot,
*Advances in Mathematics*, Volume 377 (2021). - Jon Chaika and Diana Davis, The typical measure preserving transformation is not an interval exchange transformation, resubmitted (2021).
- Diana Davis and Samuel Lelievre, Periodic paths on the pentagon, double pentagon and golden L, resubmitted (2023).
- Library of billiard trajectories
- Curt McMullen discussing this work (esp. 55:30-60:00)
- Talks I gave explaining this paper for non-mathematicians, high school students, math majors, and experts
- Scientific American article about this paper
- Coordinating jewelry
- The beautiful family (people's favorites)

- Aaron Calderon, Solly Coles, Diana Davis, Justin Lanier, Andre Oliveira, How to hear the shape of a billiard table, accepted pending revision in
*Annales de l'Institut Fourier*(2019). - Diana Davis, W. Patrick Hooper, Periodicity and ergodicity in the trihexagonal tiling,
*Commentarii Mathematici Helvetici*93(4), 661–707 (2018). - Diana Davis, Irene Pasquinelli, Corinna Ulcigrai, Cutting sequences on Bouw-Möller surfaces: an S-adic characterization,
*Annales scientifiques de l’Ecole normale superieure*, 52(4), 927-1023 (2021). - Diana Davis, Kelsey DiPietro, J.T. Rustad, Alexander St Laurent, Negative refraction and tiling billiards,
*Advances in Geometry*, 18(2), 133-159 (2018). - Keith Burns, Orit Davidovich, Diana Davis, Average pace and horizontal chords,
*The Mathematical Intelligencer*, 39(4), 41-45 (2017).- Scientific American article about this paper,
- Level Renner article about this paper,
- Full arXiv version with appendix.

- Diana Davis, Victor Dods, Cynthia Traub, Jed Yang, Geodesic trajectories on regular polyhedra,
*Discrete Mathematics*, 340(1), 3183-3196 (2017). - Diana Davis, Cutting sequences on translation surfaces,
*New York Journal of Mathematics*, Volume 20, 399-429 (2014). - Diana Davis, Cutting sequences, regular polygons, and the Veech group,
*Geometriae Dedicata*, 162(1), 231-261 (2013).- Video explaining this result using colors and dance

- 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*, 34(1) (2008). - Elizabeth Adams, Ivan Corwin, Diana Davis, Michelle Lee, Regina Visocchi, Isoperimetric Regions in Gauss Sectors,
*Rose-Hulman Undergraduate Mathematics Journal*, 8(1) (2007).

- Billiards, Surfaces and Geometry (for publication maybe soon I hope)
*Illustrating Mathematics*, American Mathematical Society, 2020 (editor). Buy the book or preview the PDF.-
*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.

Pedagogy:

- Diana Davis, Inquiry-based learning in a first-year honors course,
*PRIMUS*, 28(5), 387-408 (2018).

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, Mitteilungen der DMV, 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).

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

Click on a picture for the associated paper.

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

Positions:

- Phillips Exeter Academy, Instructor in Mathematics, 2020--
- Swarthmore College, Visiting Assistant Professor, 2017-2020
- Williams College, Visiting Assistant Professor, 2016-2017
- Northwestern University, Postdoctoral Lecturer, 2013-2016

**My how-to manual**on how to write a problem-based curriculum and teach a discussion-based course

- Billiards, Surfaces and Geometry (super duper version in preparation for publication)
- Real Analysis
- Previous version for Exeter
- Previous version for Swarthmore, with uniform convergence of sequences of functions and logic practice

- Introduction to Proofs (Northwestern)
- Multivariable calculus (Swarthmore)
- Previous version for Williams, with sequences and series, without vector calculus
- Previous version for Northwestern, last 2/3 of course only

- Discrete Mathematics (Swarthmore)
- Calculus 1 (Swarthmore)

Here are some slides from a short talk I gave about this pedagogical method.

Courses taught:

- The Magic of Numbers (Northwestern)
- Combinatorial Game Theory (Northwestern)
- Geometry, Precalculus, Trigonometry (Exeter)
- Calculus 1 (Swarthmore, Exeter)
- Calculus 2 (Brown, Exeter)
- Discrete mathematics (Swarthmore)
- Multivariable calculus without linear algebra (Brown, Williams, Exeter)
- Multivariable calculus with linear algebra (Northwestern, Swarthmore)
- Introduction to Proof (Northwestern)
- Linear algebra (Brown)
- Applied Real Analysis (Williams)
- Real Analysis (Swarthmore, Exeter)
- Billiards, Surfaces and Geometry (Williams, Exeter)

- Summer School on Boundaries and Dynamics, Notre Dame University
- Lines in positive genus: An introduction to flat surfaces, May 2015

- Anja S. Greer Conference on Mathematics and Technology, Phillips Exeter Academy
- Gerrymandering and Math: June 2023
- How to write a problem-based curriculum: June 2017, 2019, 2022, 2023
- How to teach a discussion-based course: June 2019, 2022
- Greatest hits of higher mathematics: June 2012, 2013
- Exeter Mathematics Program: June 2012, 2013, 2015

- Megumi Asada, Williams College 2017
- Paul Baird-Smith, Williams College 2017
- Dylanger Pittman, Williams College 2017

Illustrating Mathematics online seminar, October 13

Exeter math conference, June 2023 (three talks)

Université Grenoble Alpes, Topology seminar, March 2023 (

A Dynamical Weekend at Wesleyan, March 2023

JMM, Geometry and Dynamics in Moduli Spaces of Abelian Differentials, January 2023

Kansas State University, Art and Math Seminar, October 6, 2022

Communicating Mathematics, Cornell University, August 2022

Heidelberg University Fireside Chat, July 2022

Heidelberg University Community Seminar, July 2022

Aix-Marseille University, Rauzy Seminar, July 2022

Anja S. Greer Conference on Mathematics and Technology, Exeter, June 2022 (four talks)

AMS Spring Eastern Sectional Meeting, March 2022

IHES, informal seminar, March 2022

IST Austria, DynamIST seminar, March 2022

NCSSM Teaching Contemporary Mathematics conference, February 2022

Williams College AWM panel, February 2022

SUNY Stony Brook math club, February 2022

CIRM, Differential Geometry, Billiards, and Geometric Optics, October 2021

UNC Greensboro, teaching colloquium, September 2021

PROMYS, panel on women and LGBTQ+ in math, August 2021

Hampshire College Summer Studies in Mathematics, July 2021

Williams College Math Camp, July 2021

Bates College, guest lecture in Mathematics for Social Justice class, May 11 (with Quinn Basewitz, Martina Kampel, Corinne Mulvey and Madeleine Ward)

California State University - San Bernardino Colloquium, April 16 (with Quinn Basewitz, Katie Knox and Corinne Mulvey)

Trinity University Majors Seminar, March 2021

University of Nebraska Groups, Semigroups and Topology, February 2021

Math Encounters, MoMath, February 2021

Brown University AWM, December 2020

Yale and Boston University math club, November 2020

Gathering 4 Gardner Celebration of Mind 2020, October 2020

University of Glasgow, Maths Week Scotland, LMS popular lecture, September 2020

PROMYS colloquium, July 2020

Nearly Carbon Neutral Geometry & Topology Conference, Moduli Spaces of Surfaces mini-session, June 2020

Geometry, Topology and Dynamics Seminar, Université Paris-Saclay, Orsay (en français), May 2020

Screening and panel discussion of

Colloquium, St. Joseph's University, April 2020

Swarthmore peer teaching opportunity, March 2020

Ergodic theory seminar, Université Sorbonne (Jussieu), LPSM, Paris, March 2020

UMass Lowell, February 2020

University of Utah, Riemann surfaces and their moduli spaces RTG conference, February 2020

Episcopal Academy, Newtown Square, PA, February 2020

College of the Holy Cross, January 2020

Tufts University, dynamical systems seminar, December 2019

Providence College, Colloquium, December 2019

University of Oklahoma, plenary speaker, Math Day, November 2019

Bates College, Colloquium, November 2019

The College of New Jersey, Colloquium, October 2019

Brown University, Colloquium, October 2019

Duke University, Geometry/Topology seminar, September 2019

Yale University, SUMRY colloquium (with Nikki Kennedy and Beth Malmskog), July 2019

Redistricting teaching day, Tufts University, July 2019

Joint Meeting Brazil-France in Mathematics, IMPA (Brazil), July 2019

MathILy-Er Daily Gather, Bowdoin College, July 2019

Anja S. Greer conference on Mathematics and Technology, Phillips Exeter Academy (three talks), June 2019

University of Luxembourg (Luxembourg), June 2019

LG&TBQ Geometry, topology and dynamics conference, University of Michigan, June 2019 --

National IBLT Conference 2019, Denver (interactive session -- a talk would be ironic), June 2019

Appalachian State University (two talks), April 2019

Ohio State University (two talks), April 2019

Maryland Dynamics Conference, April 2019

Institut des Hautes Etudes Scientifiques (France), March 2019

Rutgers University, Topology seminar, March 2019

Boston University, Dynamical systems seminar, January 2019 slides

Joint Mathematics Meetings (Baltimore), AMS special session on continued fractions, January 2019

Joint Mathematics Meetings (Baltimore), MAA invited paper session on Beauty and Art in Research Mathematics (organizer), January 2019

Fields Medal Symposium in honor of Maryam Mirzakhani, Fields Institute (Toronto, Canada), November 2018

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), Research talk slides, January 2018

Joint Mathematics Meetings (San Diego), Teaching talk slides, January 2018

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

Anja S. Greer conference on Mathematics and Technology, Phillips Exeter Academy (two 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 (two talks)

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 (two talks) --

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

Anja S. Greer conference on Mathematics and Technology, Phillips Exeter Academy (two talks)

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

Anja S. Greer conference on Mathematics and Technology, Phillips Exeter Academy (two talks)

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

Anja S. Greer conference on Mathematics and Technology, Phillips Exeter Academy (two talks)

Colby College, Colloquium, March 2012

Brown University, Graduate student seminar, March 2012

University of Bristol (UK), Dynamics Seminar, February 2012

Brown University, Graduate student seminar, September 2011

Anja S. Greer conference on Mathematics and Technology, Phillips Exeter Academy (two talks)

Brown University, Graduate student seminar, April 2010

Williams College, thesis defense, May 2007

Williams College, student colloquium, September 2006

HRUMC, April 2006

Phillips Exeter Academy, talk for math club, November 2005

MathFest, student talk, August 2005

Bates College, AMS regional meeting, June 2005

HRUMC, Williams College, April 2005

I have given talks in USA, England, France, Germany, Israel, Ireland, Canada, Luxembourg, Brazil and Austria.

I have given talks in CA, CO, CT, DE, IL, IN, KS*, ME, MD, MA, MI, MN, NC, NE*, NH, NJ, NM, NY, OH, OK, PA, RI, TX*, UT, WA.

I am eager to give more talks. Invite me.

* these talks were on Zoom

Diana Davis completed her Ph.D. at Brown University in 2013 under the direction of Richard Schwartz. She was a postdoc at Northwestern University for three years, followed by visiting professorships at Williams College and Swarthmore College. While a graduate student, she won an international award for the video she created to explain her PhD thesis result using colors and dance, which "went viral" in the mathematical community. She has published over a dozen papers, mostly on aspects of mathematical billiards and dynamical systems, and has given over 100 talks in 25 states and 10 countries. Davis is also an educational innovator, creating and teaching problem-centered, discussion-based math courses of all levels, and studying their pedagogical effectiveness. Outside of research and teaching, she enjoys long-distance running, recreational sailing, traveling, and thinking about how to build community and create a sustainable world.

Phillips Exeter Academy, Mathematics Department, 20 Main Street, Exeter NH 03833

ddavis(at)exeter.edu