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.
2005 - 2010
Universidad de los Andes. Bogota, Colombia. Cum Laude.
● NSF Grant: Collaborative research: “Machine Learning and Inverse Problems in Discrete and Continuous Settings.” (PI together with Daniel Sanz-Alonso U. Chicago). Duration: 12 Months. Start date: 06/2019.
● 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.
(Department seminars, thematic workshops, and conferences)
● 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.
● 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
● 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
● 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: https://tgda.osu.edu/gtdaml2019/
The second edition of the conferences is scheduled to take place at UW Madison during the summer of 2020. More details will be released as they become available.
N. Garcia Trillos, Z. Kaplan, T. Samakhoana and D. Sanz-Alonso "On the consistency of graph-based Bayesian learning and the scalability of sampling algorithms." To appear in the Journal of Machine Learning Research (JMLR). 2020. Preprint available in ArXiv: https://arxiv.org/abs/1710.07702
N. Garcia Trillos, “Gromov-Hausdorff convergence of Wasserstein spaces on point clouds.” To appear in Calculus of Variations and Partial Differential Equations. 2020. Preprint available in ArXiv: https://arxiv.org/abs/1702.03464
N. Garcia Trillos, M. Gerlach, M. Hein, D. Slepcev "Error estimates for spectral convergence of the graph Laplacian on random geometric graphs towards the Laplace--Beltrami operator." Foundations of Computational Mathematics (FOCM) (2019). https://link.springer.com/article/10.1007/s10208-019-09436-w
N. Garcia Trillos. “Variational limits of k-nn graph-based functionals on data clouds.” SIMODS, 1(1):93-120, 2019.
N. Garcia Trillos, D. Sanz-Alonso, R. Yang, “Local Regularization of Noisy Point Clouds: Improved Global Geometric Estimates and Data Analysis” Journal of Machine Learning Research 20 (2019) 1-37 9; http://jmlr.org/papers/v20/19-261.html
N. Garcia Trillos, Z. Kaplan, D. Sanz-Alonso “Variational Characterizations of Local Entropy and Heat Regularization in Deep Learning” Entropy 2019, 21(5), 511; https://doi.org/10.3390/e21050511.
N. Garcia Trillos and D. Sanz-Alonso. “Continuum limits of posteriors in graph bayesian inverse problems.” SIAM Journal on Mathematical Analysis, 50(4):4020-4040, 2018.
N. Garcia Trillos and D. Slepcev. “A variational approach to the consistency of spectral clustering.” Applied and Computational Harmonic Analysis, 45(2):239-281, 2018.
N. Garcia Trillos and R. Murray. “A new analytical approach to consistency and overtting in regularized empirical risk minimization.” European Journal of Applied Mathematics, 28(6):886-921, 2017.
A. Ramdas, N. Garcia Trillos, M. Cuturi. On Wasserstein Two-Sample Testing and Related Families of Nonparametric Tests. Entropy 2017, 19(2), 47; https://doi.org/10.3390/e19020047
N. Garcia Trillos, D. Slepcev, J. Von Brecht, T. Laurent, and X. Bresson. “Consistency of Cheeger and ratio graph cuts.” The Journal of Machine Learning Research, 17(1):6268-6313, 2016.
N. Garcia Trillos and D. Slepcev. “Continuum limit of total variation on point clouds.” Archive for rational mechanics and analysis, 220(1):193-241, 2016.
J. Calder, N. Garcia Trillos, "Improved spectral convergence rates for graph Laplacians on epsilon-graphs and k-NN graphs." Preprint available in ArXiv: https://arxiv.org/abs/1910.13476
N. Garcia Trillos, F. Hoffmann, B. Hosseini, "Geometric structure of graph Laplacian embeddings." Preprint available in ArXiv: https://arxiv.org/abs/1901.10651
N. Garcia Trillos, R. Murray, “A maximum principle argument for the uniform convergence of graph Laplacian regressors.” Preprint available in ArXiv: https://arxiv.org/abs/1901.10089
N. Garcia Trillos , R. Murray, and D. Sanz-Alonso. “Spatial extreme values via variational techniques.” Preprint available in ArXiv: