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Rodrigo Davila Figueroa
- Assistant Professor
- Ext: 2137
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My primary research area is complex Kleinian groups, with a particular focus on representation variety of surface groups in SL(3,C). I am currently working on knot theory and classical Kleinian groups, studying the Hausdorff dimension of dynamically generated wild knots. I have also collaborated in convex geometry and topological data analysis. My broader interests include classical hyperbolic geometry, Teichmüller theory, and differential geometry, both in its theoretical and applied aspects. Publication List: 1. Exceptional Algebraic Curves for Infinite Subgroups of PGL(n+1,C). Angel Cano, Luis Loeza, and Rodrigo Davila Figueroa. International Journal of Mathematics. August 2026. DOI: 10.1142/S0129167X26500692 2. On the Geometry of Strictly Convex Surfaces Parameterized by Their Support Function and Ellipsoids in R^(n+1). Daniel Ballesteros-Chávez & Rodrigo Dávila-Figueroa. Symmetry 17 (8): 1309 (2025). DOI: 10.3390/sym17081309 3. Topological Data Analysis and Convolutional Neural Networks for Gravitational Wave Detection. Arredondo, Felipe De Jesús Felix, Sandoval, Sofia Alvarez, Matamoros Alvarado, David Alejandro,... Ucan-Puc, Alejandro, Figueroa, Rodrigo Dávila. Lecture Notes in Computer ScienceOpen source preview, 2026, 16222 LNAI, pp. 143–164. 4. Fenchel–Nielsen coordinates for SL(3,ℂ) representations Rodrigo Dávila Figueroa and John R. Parker. Geometriae Dedicata, Vol. 219, Article 63 (2025). 5. Ribbon graphs and the fundamental group of surfaces Rodrigo Dávila Figueroa. Workshop on Kleinian Groups and Related Topics 2019-11-01 | Conference paper (https://cathi.uacj.mx/bitstream/handle/20.500.11961/9377/main.pdf?sequence=1&isAllowed=y)
Education
- Doctorate, Universidad Nacional Autonoma de Mexico, Mexico, 2024
Doctorate, Universidad Nacional Autonoma de Mexico, Mexico, 2024
Experience
- Full Time Lecturer, Math & Science, Education Pathways, UAE, 2 years
- Lecturer, Applied Math Department, Universidad Autonoma de la Ciudad de Mexico, Mexico, 5 years
- Lecturer, Math & Science, Prepa Tec de Monterrey, Mexico, 2 years
- Part-time lecturer, Math Department, Escuela Superior de Ingenieria Mecanica y Electrica, Mexico, 1.5 years
- Part-time Assistant Lecturer, Mathematics Department, Universidad Nacional Autonoma de Mexico, Mexico, 2 years
Full Time Lecturer, Math & Science, Education Pathways, UAE, 2 years
Lecturer, Applied Math Department, Universidad Autonoma de la Ciudad de Mexico, Mexico, 5 years
Lecturer, Math & Science, Prepa Tec de Monterrey, Mexico, 2 years
Part-time lecturer, Math Department, Escuela Superior de Ingenieria Mecanica y Electrica, Mexico, 1.5 years
Part-time Assistant Lecturer, Mathematics Department, Universidad Nacional Autonoma de Mexico, Mexico, 2 years
Teaching Area
- Mathematics
Mathematics
Research
- Complex Kleinian
- Complex Dynamics
- Differential Geometry
- Complex Analysis
Complex Kleinian
Complex Dynamics
Differential Geometry
Complex Analysis
Publications
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JournalRodrigo Davila Figueroa John R. Parker, Fenchel-Nielsen Coordinates for SL(3,C) Representations, Geometriae Dedicata, Jun 2025, doi: https://doi.org/10.1007/s10711-025-01021-6
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JournalDaniel Ballesteros Chavez Rodrigo Davila Figueroa, On the Geometry of Strictly Convex Surfaces Parameterized by Their Support Function and Ellipsoids in Rn+1, Symmetry, Aug 2025, doi: https://doi.org/10.3390/sym17081309
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JournalRodrigo Davila Figueroa, Ribbon Graphs and the Fundamental Group of Surfaces, AVANZA, IX, pp.43 - 72, Jun 2020
Rodrigo Davila Figueroa John R. Parker, Fenchel-Nielsen Coordinates for SL(3,C) Representations, Geometriae Dedicata, Jun 2025, doi: https://doi.org/10.1007/s10711-025-01021-6
We define Fenchel-Nielsen coordinates for representations of surface groups to SL(3, C). We also show how these coordinates relate to the classical Fenchel-Nielsen coordinates and to their generalisations by Kourouniotis, Tan, Goldman, Zhang and Parker-Platis
About the journal
Daniel Ballesteros Chavez Rodrigo Davila Figueroa, On the Geometry of Strictly Convex Surfaces Parameterized by Their Support Function and Ellipsoids in Rn+1, Symmetry, Aug 2025, doi: https://doi.org/10.3390/sym17081309
We investigate strictly convex hypersurfaces in Euclidean space that are parameterized by their support function. We obtain a differential equation for the support function restricted to curves on the sphere, and we give explicit parameterizations of ellipsoids in Rn+1 as the inverse of their Gauss map, where symmetry plays an important role.
About the journal
Rodrigo Davila Figueroa, Ribbon Graphs and the Fundamental Group of Surfaces, AVANZA, IX, pp.43 - 72, Jun 2020
In the present work we are going to give a formal exposition of the ribbon graphs topic based on notes of Labourie, since is difficult to find as such in the literature. As an application we are going to compute the fundamental group of surfaces using ribbon graphs as a combinatorial version of it.