Contact information

Armando J. Cabrera Pacheco  Postdoctoral FellowUniversität Tübingen, Tübingen AI Center and Department of Computer Science Investigador SNI IEmail: a.cabrera at uni-tuebingen dot de

Research interests

Differential Geometry, Foundations of Machine Learning and Mathematical Relativity.

Education

Ph.D. in Mathematics, University of Miami, USA (2016). Advisor: Prof. Pengzi Miao.M.Sc. in Mathematics, University of Miami, USA (2012).Bachelor's degree in Mathematics, Universidad Autónoma de Yucatán, México (2009).

Publications


Foundations of Machine Learning


2. A. J. Cabrera Pacheco, R. Derr and R. C. Williamson, An axiomatic approach to loss aggregation and an adapted aggregating algorithm, 2024. [arXiv:2406.02292]

1. A. J. Cabrera Pacheco and R. C. Williamson, The geometry of mixability, TMLR, 2023. [arXiv:2302.11905]


Mathematical Relativity and Geometric Analysis


13. A. J. Cabrera Pacheco and M. Wolff, Families of non time-symmetric initial data sets and Penrose-like energy estimates, 2023. [arXiv:2310.13547]12. A. J. Cabrera Pacheco, M. Graf and R. Perales, Intrinsic flat stability of the positive mass theorem for asymptotically hyperbolic graphs, Gen. Relativity and Gravitation 55, 2023. [arXiv:2304.08443]11. A. J. Cabrera Pacheco, C. Cederbaum, P. Gehring, A. Peñuela Díaz, Constructing electrically charged Riemannian manifolds with minimal boundary, prescribed asymptotics, and controlled mass, J. Geom. Phys.  185, 2023. [arXiv:2106.14703]10. L. Aké Hau, A. J. Cabrera Pacheco and D. Solís, On the causal hierarchy of Lorentzian length spaces,  Class. and Quantum Grav. 37, 215013 (22 pp), 2020. [arXiv:2003.03451]9. A. Alaee, A. J. Cabrera Pacheco and S. McCormick, Stability of a quasi-local positive mass theorem for graphical hypersurfaces of Euclidean space, Trans. Amer. Math. Soc. 374, no. 5, 3535–3555, 2021. [arXiv:1911.12343]8. A. J. Cabrera Pacheco and C. Cederbaum, A survey on extensions of Riemannian manifolds and Bartnik mass estimates, Mexican mathematicians in the world—trends and recent contributions, 1–30, Contemp. Math. 775, Amer. Math. Soc., 2021. [arXiv:1904.05830]7. A. Alaee, A. J. Cabrera Pacheco and C. Cederbaum, Asymptotically flat extensions with charge, Adv. Theor. Math. Phys. 23(8), 1951-1980, 2019. [arXiv:1903.09014]6. A. J. Cabrera Pacheco, C. Ketterer and R. Perales, Stability of graphical tori with almost nonnegative scalar curvature, Calc. Var. 59, 134, 2019. [arXiv:1902.03458]5. A. J. Cabrera Pacheco, On the stability of the positive mass theorem for asymptotically hyperbolic graphs. Ann. Glob. Anal. Geom. 56, 443-463, 2019. [arXiv:1803.01899]4. A. J. Cabrera Pacheco, C. Cederbaum and S. McCormick, Asymptotically hyperbolic extensions and an analogue of the Bartnik mass, J. Geom. Phys. 132, 338-357, 2018. [arXiv:1802.0331]3. A. J. Cabrera Pacheco, C. Cederbaum, S. McCormick and P. Miao, Asymptotically flat extensions of CMC Bartnik data, Class. Quantum Grav. 34, 105001 (15 pp), 2017. [arXiv:1612.05241] 2. A. J. Cabrera Pacheco and P. Miao, Higher dimensional black hole initial data with prescribed boundary metric, Math. Res. Lett. 25(3), 937-956, 2018. [arXiv:1505.01800] 1. A. J. Cabrera Pacheco and P. Miao, Isometric embeddings of 2-spheres into Schwarzschild manifolds, Manuscripta Math. 149, 459-469, 2016.

As an undergraduate student
1. A. J. Cabrera Pacheco and D. A. Solis Gamboa, Espacio conforme y compactificación en espacio-tiempos de curvatura constante (Undergraduate thesis), Eureka (Mexico) 24, 29-48, 2009. [Journal]

Outreach

1. A. J. Cabrera Pacheco and S. Jahns, Un enfoque riemanniano de la relatividad general: el teorema de la masa positiva y la unicidad de agujeros negros estáticos, Abs. & Appl. 24, 2019. [Journal]


Conference organization

- "Avances recientes en Geometría de Lorentz" (co-organized with D. Solís and A. Sánchez-Valenzuela). [poster]   Location: CIMAT-Mérida, México.    Dates: 30/aug/18-1/sep/18. - "Mathematical Relativity: A Riemannian Approach" (co-organized with L. Hernández Lamoneda). [webpage]   Location: CIMAT-Guanajuato, México.   Dates: 27/may/19-29/may/19.- "Encuentro iberoamericano de geometría diferencial en Granada" (co-organized with J. L. Flores and M. Sánchez).  [webpage]   Location: IEMath-GR, Granada, Spain.   Dates: 10/jun/19-12/jun/19.

Teaching


Past:

-Mathematics for Machine Learning. Master level. University of Tübingen. Winter 2023-2024.

-Mathematics for Machine Learning. Master level. University of Tübingen. Winter 2022-2023. [Teaching award]

- Riemannian Geometry. Master and advanced undergraduate level. University of Tübingen. Summer 2020.- Seminar: Selected topics on mathematical relativity and geometric analysis. Master in Mathematical Physics. University of Tübingen. Winter 2019.- Geometry of initial data sets. Master in Mathematical Physics. University of Tübingen. Winter 2018.- Honors Calculus II. Undergraduate course. University of Connecticut. Spring 2017.- Honors Calculus II. Undergraduate course. University of Connecticut. Fall 2016.- Calculus II. Undergraduate course. University of Miami. Fall 2015.- Calculus II. Undergraduate course. University of Miami. Spring 2015.- Calculus II. Undergraduate course. University of Miami. Fall 2014.- Calculus I. Undergraduate course. University of Miami. Fall 2013.

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