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Academic Positions

Assistant Professor

University of Wisconsin Madison. Department of Statistics. 

August 2018 - Present.

Prager Assistant Professor

(Postdoctoral Position). Division of Applied Mathematics. Brown University.

July 2015 - June 2018


PhD, Mathematical Sciences

2010 - 2015

Carnegie Mellon University.

Thesis: “Variational Limits of Graph Cuts on Point Clouds.” Adviser: Dejan Slepcev.

MSc, Mathematical Sciences

2010 - 2012

Carnegie Mellon University.

BSc, Mathematics

2005 - 2010

Universidad de los Andes. Bogotá, Colombia. Cum Laude.


NSF CAREER: DMS-2236447 "Adversarial Robustness through the Lens of Mathematical Analysis and Geometry." 9/2023- 8/2028

NSF Grant: DMS-2005797 “Variational Methods for the Analysis of Unsupervised Learning Algorithms.” 9/2020- 8/2023

NSF Grant: DMS-1912802, Collaborative research: “Machine Learning and Inverse Problems in Discrete and Continuous Settings.” (PI together with Daniel Sanz-Alonso U. Chicago).  06/2019-8/2020


Aranda-Ordaz Award. Awarded through the Bernoulli Society. The award is “bestowed for one thesis in Probability and one thesis in Statistics written by students from Latin America, regardless of the country of the university offering the degree, or by students from other nationalities who received the degree from a Latin American university.” 2016.

Recent Talks

(Department seminars, thematic workshops, and conferences)

●Optimal Transport and Applications to Statistics mini-symposium at JSM, Toronto, Canada, August 2023.

●BIRS Workshop: Applied and Computational Differential Geometry and Geometric PDEs, August 2023.

●BIRS Workshop: New Trends in Fluids and Collective Dynamics, July 2023.

Mini Symposium on Data Geometry and Optimization at SampTA 23, New Haven, CT, USA, July 2023.

●BIRS-IMAG workshop: Nonlinear diffusion and nonlocal interaction models – entropies, complexity, and multi-scale structures; Granada, Spain, June 2023.

● Madison workshop in PDE 2023, UW-Madison, May 2023.

Workshop on optimal transport, mean field models, and machine learning, TUM, Munich, Germany, April 2023.

●UW-Madison Statistics Department seminar, April 2023.

●Kantorovich Initiative Seminar, February 2023.

Reunion workshop for the Geometric Methods in Optimization and Sampling program at the Simons Institute, Berkeley, California. January 2023.

●JMM, AMS Special Session on Mathematical Methods in Machine Learning and Optimization, Boston, USA, January 2023.

● Math Machine Learning Seminar MPI MIS + UCLA, December 2022.

Workshop on Scientific Machine Learning (WoSciML): Mathematics and Applications, Universidad Católica de Chile, November 2022.

● PSU-Purdue-UMD Joint Seminar on Mathematical Data Science, October 2022.

● PDE Seminar, UW Madison, October 2022.

● SIAM Conference on the Mathematics of Data Science minisymposium: "Optimal Control and PDE Insights into Deep Learning ", San Diego, September 2022.

● Mathematics of Machine Learning Seminar at UMass Amherst, September 2022.

● SIAM Annual meeting minisymposium:" Advances in Variational Methods and Applications to Materials and Machine Learning", Pittsburgh, July 2022.

● Hausdorff Center for Mathematics workshop: "Synergies between Data Science and PDE Analysis", Bonn, June 2022.

● Machine learning in Madrid  seminar, UAM-ICMAT, April 2022

● Statistic Seminar, Columbia University, April 2022

● Special session: Mathematical Foundation of Data Science in Scientific Computing for the AMS Spring Central Sectional Meeting, March 2022

● Special Session: Recent Developments of Variational Methods in Deterministic and Stochastic Systems for the AMS Spring Central Sectional Meeting, March 2022

● Mathematics Colloquium, University of Utah, March 2022

● Data Science Seminar, Department of Mathematics, University of Minnesota, March 2022

●Seminar at Chair for Dynamics, Control and Numerics, Department of Data Science, FAU Erlangen, February 2022

●Seminario de Estadística, Universidad Nacional de Colombia​​. December 2021.

● Statistics seminar at University of Washington. November 2021.

Workshop on Sampling Algorithms and Geometries on Probability Distributions at the Simons Institute, Berkeley, California. September 2021.

13th International Conference on Monte Carlo Methods and Applications. Special session on Wasserstein gradient flows and their applications. August 2021.

● 10th World Congress in Probability and Statistics. Session on Optimization in Statistical Learning. July 2021

● OSSUR-PDEs seminar series, GSSI L'Aquila. May 2021.

● One World Seminar Series on the Mathematics of Machine Learning. May 2021.

● Instituto de Ingeniería Matemática y Computacional, Universidad Católica de Chile. April 2021.

● TRIPODS workshop on Topics on Graph Algorithms and Their Applications, Tufts University. April 2021.

● HKBU Virtual Conference on Mathematics, Statistics and Data Science, Honk Kong Baptist University. April 2021.

● IFDS seminar, UW-Madison. March 2021.

● Special session on Graphs and Data Science, AMS Spring Southeastern Virtual Sectional Meeting. March 2021.

● Theory and Applications of Graph-based Learning minisymposium, SIAM CSE. March 2021.

● Optimal transport and mean field game seminar, UCLA- U. South Carolina, February 2021.

● Advances in Manifold Learning and Applications minisymposium, JMM meeting. January 2021.


● IMA workshop: Theory and Algorithms of Graph-based Learning. September 2020.

● One world seminar: Mathematical Methods for Arbitrary Data Sources", hosted by the University of Erlangen. June 2020.

● MSRI Workshop. Hot Topics: Optimal transport and applications to machine learning and statistics. May 2020.

● IPAM Program on High Dimensional Hamilton-Jacobi PDEs. Workshop II: PDE and Inverse Problem Methods in Machine Learning. April 2020.

●CASA Colloquium, TU Eindhoven. March 2020. 

● PDE and Applications Seminar, Delft University. Feb 2020.

● General Mathematics Colloquium, VU Amsterdam. Feb 2020.

● IMA Data Science Lab Seminar, University of Minnesota, Feb 2020.

● SIAM Conference on Analysis of Partial Differential Equations (PD19). December 2019, La Quinta, California. Minisymposium: “PDEs in Machine Learning”.

● SIAM Conference on Analysis of Partial Differential Equations (PD19). December 2019, La Quinta, California. Minisymposium: “Gradient Flows and Beyond: New Directions in Geometric Flows and Partial Differential Equations”.

● 9th International Congress on Industrial and Applied Mathematics, July 2019, Valencia, Spain. Minisymposium: “Geometry and Topology in Data Analysis”.

● Mathematics of Data seminar, Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany. May 2019.

● (ESI) Programme “Optimal Transport" at the Erwin Schrödinger International Institute for
Mathematics and Physics, Vienna, Austria. May 2019.

● Applied Math Seminar, Department of Mathematics, University of Wisconsin-Madison.
March 2019.

● Applied Math Seminar, Michigan State University. February 2019.

● SILO Seminar, University of Wisconsin-Madison. February 2019.

● CAM Colloquium, University of Chicago. February 2019.

● Applied analysis and PDE seminar, UC Santa Barbara. February 2019.

● Workshop on Optimal transportation and its applications, Centro de Giorgi, Scuola Normale Superiore, Pisa, Italy, November 2018.


● Ki-Net Young researchers workshop, University of Maryland, College Park, October 2018.


● Data Science Seminar, University of Minnesota, October 2018.


● Applied Probability and Risk Seminar, Columbia University, October 2018.


● Mathematics Colloquium, Universidad de Los Andes, August 2018.


● Primer congreso colombiano de matematicas aplicadas, Bogota, August 2018.


● Fractional PDEs: Theory, algorithms and applications workshop, ICERM, June 2018.


● Seminar on applied and computational analysis, DAMTP, University of Cambridge, June 2018.


● SIAM conference on mathematical imaging 2018, Nonlinear spectral theory and applications mini-symposium, June 2018.


● CERMICS seminar, Ecole des Ponts Paristech, May 2018


● SIAM UQ 2018, Data and UQ: Bayesian learning mini symposium, April 2018.


● Latmath 2018, Topology: new trends in applications and theory session, IPAM, March 2018.


● Computing and Mathematical Sciences, Caltech, February 2018.


● Department of Statistics, University of Wisconsin-Madison, January 2018.


● Oberwolfach workshop, Variational methods for evolution, November 2017.


● TGDA seminar, Ohio State University, November 2017.


● IDeAS seminar, Princeton University, October 2017.

● CNA seminar, Carnegie Mellon University , October 2017.


●SciCADE conference, Nonlocal partial differential equations and graph based techniques for imaging mini symposium, University of Bath, September 2017


● Computer science seminar, Purdue University, Aug 2017


●SIAM Conference on Applied Algebraic Geometry, Applied and Computational Topology mini symposium, Aug 2017


● SIAM Annual Meeting, Geometry and Computational Challenges in Data Science mini symposium, Pittsburgh, July 2017.


● IST Austria, June 2017.


● Universidad de Valladolid, June 2017.


● Saarland University, June 2017.


● Max Planck Institute for intelligent systems, June 2017.


● Georgia Tech, Working Group for Problems in Transport and Related Topics in Graphs, May 2017.


● Mathematics colloquium, Rensselaer Polytechnic Institute, April 2017.


● WINRS a meeting of math minds, Brown University, March 2017.


●SIAM conference on Computational Science and Engineering, Partial Differential Equation Techniques for Network Problems mini symposium, Feb. 2017.


● Latin-American congress of probability and mathematical statistics, CLAPEM, San Jos´e, Costa Rica, Dec 2016.


● WPI, PDE and analysis seminar, Nov. 2016.


●SIAM Conference on imaging science, Topology and Geometry across scales mini symposium, May 2016.


● UMASS Amherst, Applied Analysis and Computation Seminar, March 2016.


● Brown University, Pattern Theory Seminar, September 2015.


● Ki-Net -CNA Workshop: Groups and interactions in data, networks and biology, May 2015.


● AMS sectional meeting Michigan State University, March 2015.


● University of Maryland, Joint CSCAMM/KI-Net seminar, February 2015.


● ICERM research cluster: Geometric analysis methods for graph algorithms, February 2014.


● AMS sectional meeting University of California, Riverside, November 2013.


● UCLA applied mathematics seminar, October 2013.

Invited Longer Term Visits

● Simons Institute for the Theory of Computing  “Geometric Methods in Optimization and Sampling” program. August 30 to December 3, 2021.

● ​CCIMI (Cantab Capital Institute for the Mathematics of Information) within the Department of Applied Mathematics and Physics at the University of Cambridge. Duration: 1 month. June 2019. During my visit I taught a mini-course titled: “The use of geometry for learning, and the learning of geometry from data.”


● Max Planck Institute for Mathematics in the Sciences (Leipzig, Germany) Duration: 1 week in May 2019.


● (ESI) The Erwin Schrodinger International Institute for Mathematics and Physics (Vienna,Austria). Duration: 2 weeks in May 2019.

● ICERM “Network Science and Graph Algorithms” semester program. Duration: 1 month (February 2014).

Conferences/ Programs Organized

●Organizer of the “Third Graduate Student Conference: Geometry and Topology meet Data Analysis and Machine Learning (GTDAML2023).” June 8 - June 10 , 2023, Northeastern University, Boston, USA.

●Lead organizer of the AMS MRC program “Data Science at the Crossroads of Analysis, Geometry, and Topology.” 2022-2023.

●Organizer of the “Second Graduate Student Conference: Geometry and Topology meet Data Analysis and Machine Learning (GTDAML2021).” July 30 - August 1, 2021. More than a hundred graduate students from around the world participated in GTDAML 2021.

● Co-organizer of "Optimal Transport, Topological Data Analysis and Applications to Shape and Machine Learning" @ MBI OSU, July 27 - July 31, 2020.

● Co-founder and co-organizer of the series of graduate student conferences: “Geometry and topology meet Data Analysis and Machine learning.” The first edition took place in Ohio State University on June 1-2. More than 80 students participated in the conference from the midwest region and beyond. For more information visit: 

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