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"The mathematician's patterns, like the painter's or the poet's, must be beautiful; the ideas, like the colors or the words, must fit together in a harmonious way. Beauty is the first test: there is no permanent place in the world for ugly mathematics."
-Godfrey H. Hardy
Preprints
Preprints
Outer Contact Billiards, A. Chavez Caliz, C. Jackman. https://arxiv.org/abs/2608.19393
Symplectic billiards as Minkowski billiards, P. Albers, A. Chavez Caliz, S. Tabachnikov. https://arxiv.org/abs/2607.05986
To appear
To appear
Outer symplectic billiards, P. Albers, A. Chavez-Caliz, and S. Tabachnikov. (To appear in Journal of Symplectic Geometry) https://arxiv.org/pdf/2409.07990.
Papers
Papers
Outer symplectic billiard map at infinity, P. Albers, A. Chavez Caliz, and S. Tabachnikov. Journal of Modern Dynamics, vol. 22, 2026, pp. 321-343. https://www.aimsciences.org//article/doi/10.3934/jmd.2026008 (arXiv version here)
Projective self-dual polygons in higher dimensions, Chavez-Caliz, Ana. Advances in Geometry, vol. 23, no. 4, 2023, pp. 567-582. https://doi.org/10.1515/advgeom-2023-0024 (arXiv version here.)
Polígonos de Poncelet. Ana C Chavez-Caliz. Paskin Matemático (2022) no. 2, vol. 4, pag. 1-4 https://editorial.konradlorenz.edu.co/2022/05/paskin-matematico-vol-4-num-2.html?fbclid=IwAR3F4hV4Fh0R4QHewAfmPVtwaEMSPwWbeegz7BYuLkhq2ZYhXHVq1CsEnFE
More about areas and centers of Poncelet polygons. Ana C. Chavez-Caliz. Arnold Mathematical Journal, 7(1) (2021), 91-106 https://doi.org/10.1007/s40598-020-00154-8 (arXiv version here)
Talks
Talks
Outer contact billiards -------slides
Outer symplectic billiards at infinity ------ slides
De billares y otros vicios (Seminario de Matemáticas FISMAT Morelia) ------ slides
Projective Self-dual polygons (Copenhagen-Jerusalem Combinatorics Seminar) ----- recording ----- slides
Poncelet polygons and invariants ------- slides.
Editorial sample
Editorial sample
Proceedings from the workshop Billiards and quantitative symplectic geometry (coorganized with Lina Deschamps and Levin Maier): Open questions in billiards and quantitative symplectic geometry (arXiv, accepted for publication in Arnold Mathematical Journal)
Artwork
Artwork
Artwork of the book What is differentiable geometry? by Anton Petrunin and Sergio Zamora (paper version available on Amazon)
Cover of the article Moon in a puddle and the four-vertex theorem by Anton Petrunin and Sergio Zamora.
Design of the logo for the Topology Students Workshop 2020 hosted by the Georgia Institute of Technology.
I also helped with some of the drawings on the following website: https://mathfest.mathi.uni-heidelberg.de/poincare-conjecture/ , where the University of Heidelberg is announcing its celebration of the Poincaré conjecture, as part of the Millennium Problems MathFest.
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