Rocío Díaz Martín
I'm an Argentinian mathematician working as a Postdoctoral Scholar at Vanderbilt University, Nashville, TN, USA.
rocio.p.diaz.martin at Vanderbilt.edu
My interests in mathematics are broad, and I enjoy both research and teaching.
My research in mathematics is grounded in the field of Mathematical Analysis. My mathematical journey commenced with an in-depth study of Fourier Analysis, particularly Abstract Harmonic Analysis. Currently, I'm primarily focused on Frame and Sampling Theory, and Optimal Transport Theory applied to Machine Learning. For Frame and Sampling Theory, my emphasis lies on "Dynamical Sampling", and due to its connections with "Observability," I'm also interested in Control Theory.
Research
Publications
Y. Bai, R. Díaz Martín, I. Medri, R. M. S. Khan, and S. Kolouri, "Linear Optimal Partial Transport Embedding'', International Conference on Machine Learning (ICML) (2023) arXiv:2302.03232
R. Díaz Martín, I. Medri, and J. Osorio, "Error analysis on the Initial state reconstruction problem", Sampling Theory, Signal Processing, and Data Analysis, Springer, 21, article number: 18 (2023) arXiv:2105.02015, DOI:10.1007/s43670-023-00059-5
A. Aldroubi, R. Díaz Martín, I. Medri, G. K. Rohde, and S. Thareja. "The Signed Cumulative Distribution Transform for 1-D Signal Analysis and Classification", Foundations of Data Science, AIMS 4(1): 137-163 (2022). arXiv:2106.02146, DOI:10.3934/fods.2022001
R. Díaz Martín, I. Medri, and Ursula Molter, "Continuous and discrete dynamical sampling", Journal of Mathematical Analysis and Applications, 449(2): 125060 (2021). arXiv:2006.08046, DOI:10.1016/j.jmaa.2021.125060
R. Díaz Martín, I. Medri, and Ursula Molter, "Dynamical sampling: a view from control theory ", Applied and Numerical Harmonic Analysis, book series, Birkhauser, Boston. Excursions in Harmonic Analysis, Vol. 6, In Honor of John Benedetto's 80th Birthday, 269–295, Ch. 15 (2021). arXiv:2003.01488, DOI: 10.1007/978-3-030-69637-5 15
R. Díaz Martín, and L. Saal, "On commutative homogeneous vector bundles attached to nilmanifolds". Revista de la Unión Matemática Argentina, 62 (1): 141-151. (2021). arXiv:2002.07169 DOI:10.33044/revuma.1738
R. Díaz Martín, and I. Pacharoni, "Mehler–Heine formula: a generalization in the context of matrix spherical functions", Journal of Lie Theory, 30(1): 41-57 (2020). arXiv:1807.03904
R. Díaz Martín, and L. Saal, “Matrix Spherical Analysis on Nilmanifolds”, Transformation Groups, 24 (3), 887 -911 (2019). arXiv:1707.09390, DOI:10.1007/s00031-019-09518-7
R. Díaz Martín, and F. Levstein, “Spherical analysis on homogeneous vector bundles of the 3-dimensional euclidean motion group”, Monatshefte für Mathematik, 185(4), 621-649 (2018). arXiv:1704.07336, DOI:10.1007/s00605-017-1123-1
Pre-prints
A. Aldroubi, R. Díaz Martín, and I. Medri, "Dynamical Sampling for the Recovery of Spatially Constant Source Terms in Dynamical Systems". (2023) arXiv:2308.01462
P. De Napoli, and R. Díaz Martín, "Mean Value Inequalities and Characterizations of Sobolev spaces on graded groups". (2023) arXiv:2109.05064
R. Díaz Martín, Y. Bai, I. Medri, X. Liu, K. Yan, G. K. Rohde, and S. Kolouri, "LCOT: Linear circular optimal transport embedding". (2023) OpenReview
Other monographs
PhD Thesis
R. Díaz Martín. “Matrix spherical analysis on nilpotent groups”. Advisor: Linda Saal. (December 2018).
Undergraduate thesis to obtain the degree of Licenciada en Matemática (M.Sc. in Math. equivalent)
R. Díaz Martín. "Ejemplos de pares de Gelfand fuertes". Advisor: Linda Saal. (2014)
Math Education Articles
R. Díaz Martín, M. Moroni y F. Restrepo, “Un camino hacia la derivada: Secuencia de actividades para construir el concepto de velocidad instantánea empleando la velocidad media”, Revista de Educación Matemática (RevEM), Unión Matemática Argentina and FaMAF, UNC, 32 (2), 5-18 (2017).
Workshops
Y. Alen, J. Campos, R. Díaz Martín, A. Ladreyt, N. Murrone, I. Ojea, L. Stockdale, S. Ruiz Suárez, M. Vázquez and Q. Vivas, "Planificación y programación de tareas en una acería". Cursos y seminarios de matemática, Serie B, Fascículo 10, Universidad de Buenos Aires (UBA). Article from the Workshop "Taller de Matemática Inductrial - TAMI III''.
Teaching
2023: Multivariable Calculus. Vanderbilt University.
2023: Differential Equations with Linear Algebra. Vanderbilt University.
2022: Multivariable Calculus. Vanderbilt University.
2022: Differential Equations with Linear Algebra. Vanderbilt University.
2021: Single variable calculus. Vanderbilt University.
2021: Análisis Real / Medida y Probabilidad. FCEN - Universidad de Buenos Aires.
2021: Ecuaciones Diferenciales I (ODE). FaMAF - Universidad Nacional de Córdoba (UNC)-.
2020: Análisis Matemático II. FaMAF - UNC.
2018: Análisis Funcional I. FaMAF- UNC.
2018: Análisis Numérico I. FaMAF - UNC.
2018: Matemática I y II. FCA, Universidad Nacional de Córdoba.
2018: Curso de Nivelación. FaMAF - UNC.
2017: Geometría I. FaMAF-UNC.
2017: Análisis Matemático II. FaMAF - UNC.
2017: Curso de Nivelación. FaMAF - UNC.
2016: Álgebra / Álgebra II. FaMAF - UNC.
2016: Análisis Funcional II. FaMAF - UNC.
2015: Análisis Matemático II. FaMAF - UNC.
2015: Álgebra / Álgebra II. FaMAF - UNC.
Students
2019-2020: David A. Hulett. FaMAF-UNC.
Undergraduate thesis to obtain the degree of Licenciada en Matemática (M.Sc. in Math. equivalent): "De Fourier a Wavelets: un breve recorrido por el análisis tiempo-frecuencia"