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Bio: I'm a tenured, research professor at the Instituto de Matemáticas UNAM (Investigador Titular B, SNI II) in the Universidad Nacional Autónoma de México, in Mexico City where I collaborate with the Applied Geometry Laboratory.
My curiosity is driven by problems where geometry, dynamics, and topology interact. In solving these, I use all the techniques I can understand, so I view mathematics as interconnected and organically woven together. Lately, I've been applying these theories to data science, network analysis, and machine learning problems.
I've been working here in UNAM since November 2009. During this time, I've carried out long research stays, on leave, at UPC in Barcelona, in the Max Planck Institute for Mathematics, in Bonn, in the Laboratoire Jean-Leray, in the University of Nantes sponsored by the CNRS, in UC Santa Barbara, and in IPAM UCLA (twice! for the Culture Analytics and the Geometry and Learning from Data in 3D and Beyond programmes).
Prior to all of that, I was a postdoc in the University of Munich LMU, in CIMAT, and a graduate student in DPMMS, in the University of Cambridge, where I completed my PhD in Geometry and Dynamics.
News:
[May 26th, 2025] Our EuLearn dataset is live and its companion paper too! Very excited to present these at the BIRS Casa Matemática Oaxaca this week (and here are the slides!).
previous news
previous news
[June 26th, 2024] Very excited to present my joint work with Haydee Contreras Peruyero on various aspects of smooth 4-manifolds at the Max Planck Institute's Topology Seminar next Monday July 1st, at 2pm. Check out the abstract here, see you there!
[June 17th, 2024] Thanks to the organizers of the Logik Oberseminar in the University of Bonn for inviting me to present my work on Turing complete flows. It was great to meet old and new friends :)
[May 16th, 2024] Looking forward to meeting the colleagues in Universidad del Rosario, in their SIAM chapter, to talk about Geometric Machine Learning today! Join us with the QR code below and practice your Spanish too :)
[April 25th, 2024] 🚨 I've updated my preprint on global manifold convolutions, you can get the new version here 📜.
[April 24th, 2024] Excited to present my work on Applied Geometry, at the international GEOTOP-A Seminar this Friday April 26th (10am in Mexico City).
Here's the abstract:
"Similarly to the growth of Applied Topology, the uses and applications of Geometry are now expanding into scientific, computational, and engineering domains. First, we'll review the recent history of this expanding Applied Geometry area.
I'll mention several collaborations. Developing and implementing algorithms inspired by the marked length spectrum that classifies complex networks (with Eliassi-Rad and Torres) and analyzing digital images using a variant of curve-shortening flow (with Velazquez Richards). As well as a definition I proposed of a global convolution on manifolds of arbitrary topology, relevant for deep learning on manifolds.
Furthermore, I'll present our joint work with Evangelista and Ruiz Pantaleón on computational Poisson geometry. This work includes a practical application in learning symbolic expressions of Hamiltonian systems. We've developed and released two Python packages that are instrumental in this process. These packages enable symbolic and numerical computations of objects in Poisson geometry, and they're compatible with the deep learning frameworks NumPy, TensorFlow, and PyTorch. We've utilized these packages to train neural networks, particularly hybrids with CNN and LSTM components, that learn symbolic expressions of Hamiltonian vector fields.
I'll present a tutorial on our computational Poisson Geometry modules if time allows."
For information to connect on Zoom in your local streaming time see:
[December, '22] Excited to share that our Applied Geometry Laboratory has been awarded a grant to use the HPC resources at the Miztli supercomputer.
[November, '22] Our paper Contour parametrization via anisotropic mean curvature flows, with Eduardo Velázquez Richards has been accepted in Applied Mathematics and Computation. Check out our parallelized code here!
[June, '22] I'll present our lab's work on a panel about social network analysis in the Seminario de Violencia y Paz at El Colegio de México on Wednesday June 29th . You can watch a video of my presentation here.
[March 8th, '22] Our paper Collapsing and group growth as obstructions to Einstein metrics on some smooth 4-manifolds with Haydeé Peruyero has been accepted in the New York Journal of Mathematics.
[Oct. 17th, '21] The schedule for our workshop Geometry & Learning from Data (21w5239) October 24-29, 2021, hosted at the Casa Matemática Oaxaca (CMO) is online!
[Oct. 5th, '21] My paper 'Turing approximations, toric isometric embeddings & manifold convolutions', where I explain how to use isometric embeddings into tori to define global convolutions on arbitrary smooth manifolds is available online.
[Aug. 2021] Our paper On computational Poisson geometry I: Symbolic foundations is now available in the Journal of Geometric Mechanics. Check out the code repo on github from our appliedgeometry lab, it works with NumPy, PyTorch, and TensorFlow.
[June 2021] Our paper Examples of Symbolic and Numerical Computation in Poisson Geometry has appeared in the proceedings of Geometric Science of information GSI 2021, (Lecture Notes in Computer Science , vol. 12829).
[Apr. 18th, '21] Our paper Maximal volume entropy rigidity for RCD*(-(N-1),N) spaces is now online at the Journal of the London Mathematical Society.
[Apr. 1st, '21] Our paper On Computational Poisson Geometry II: Numerical Methods has been accepted to appear in the Journal of Computational Dynamics. Thanks to the reviewers for their thorough and very useful feedback. Check out the code repo on github from our appliedgeometry lab.
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