Current lines of research:
Current lines of research:
Local slope, Eikonal equations in metric spaces.
State constrained dynamics, sweeping processes.
Metric properties of Wasserstein spaces.
Local slope, Eikonal equations in metric spaces.
State constrained dynamics, sweeping processes.
Metric properties of Wasserstein spaces.
Pointwise semi-Lipschitz functions and Banach-Stone theorems, E. Durand-Cartagena, J. A. Jaramillo, F. Venegas M. Studia math. (2025). https://doi.org/10.4064/sm240914-30-5
Absolutely minimal semi-Lipschitz extensions, A. Daniilidis, T. Minh Lê, F. Venegas M. Calc. Var. & PDE. 64, 301 (2025). https://doi.org/10.1007/s00526-025-03169-1
A Functional Characterization of Isometries Between Non-reversible Finsler Manifolds, F. Venegas M. J. Geom. Anal. 35, 56 (2025). https://doi.org/10.1007/s12220-024-01889-y
Asymmetric free spaces and canonical asymmetrizations,A. Daniilidis, J. M. Sepulre, F. Venegas M. Studia Mathematica 261 (2021), 55-102. https://old.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/all/261/1/113966/asymmetric-free-spaces-and-canonical-asymmetrizations
Smooth semi-Lipschitz functions and almost isometries between Finsler manifolds, A. Daniilidis, J. A. Jaramillo, F. Venegas M. J. Funct. Anal. 279(8), 108662 (2020) https://doi.org/10.1016/j.jfa.2020.108662
Functional analysis in asymmetric structures, PhD. Thesis (2023), Universidad Complutense de Madrid & Universidad de Chile. https://docta.ucm.es/rest/api/core/bitstreams/19c52253-9ca9-4a7e-a0e0-a7fca4ff3f8d/content
Un teorema tipo Banach-Stone para variedades de Finsler, Master's thesis (2018), Universidad de Chile. https://repositorio.uchile.cl/bitstream/handle/2250/152148/Un-teorema-tipo-Banach-Stone-para-variedades-de-Finsler.pdf?sequence=33
Structural properties of Wasserstein spaces and applications to optimization, Fondecyt de Postdoctorado 3250857, 2025-2028. Francisco Venegas (PI).
Slope-based Variational Analysis and Optimization, Fondecyt Regular 1251159, 2025-2029. David Salas (PI), Anton Svensson (SI), Francisco Venegas (SI).
SOGGA: Stochastic Optimization, Generalized Games and Applications, Math-Amsud project 23-MATH-13, 2024-2025. David Salas (PI), Anton Svensson (SI), Francisco Venegas (SI).
Unifying paradigms, models and structure in optimization, 2017–2020 FONDECYT Regular 1171854 (Thesis student).
Exploring structure in variational analysis: self-contractedness, permutation invariance and o-minimality, 2013–2016 FONDECYT Regular 1130176 (Thesis student).