I'm an Argentinian mathematician working as a Postdoctoral Researcher at Tufts University, MA, USA.
rocio.diaz_martin at Tufts.edu
My research in mathematics is grounded in the field of Harmonic Analysis. My mathematical journey commenced with an in-depth study of Fourier Analysis, particularly Abstract Harmonic Analysis. Later, I worked on Frame and Sampling Theory, and currently I added to my interests Applications of Optimal Transport Theory to Machine Learning.
X. Liu, Y. Bai, R. Díaz Martín, K. Shi, A. Shahbazi, B.A. Landman, C. Chang, and Soheil Kolouri, "Linear Spherical Sliced Optimal Transport: A Fast Metric for Comparing Spherical Data". ICLR 2025.
Y. Bai, R. Díaz Martín, A. Kothapalli, H. Du, X. Liu, and S. Kolouri, "Partial Gromov-Wasserstein Metric". ICLR 2025.
Y. Bai, A. Kothapalli, H. Du, R. Díaz Martín, and S. Kolouri, "Linear Partial Gromov-Wasserstein Embedding". ICLR 2025.
X. Liu, R. Díaz Martín, Y. Bai, A. Shahbazi, M. Thorpe, A. Aldroubi, and S. Kolouri, "Expected Sliced Transport Plans". ICLR, 2025.
A. Aldroubi, R. Díaz Martín, and I. Medri, "Dynamical sampling for the recovery of spatially constant source terms in dynamical systems". Journal of Linear Algebra and Applications, 696: 148-185, 2024.
H. Tran, Y. Bai, A. Kothapalli, A. Shahbazi, X. Liu, R. Díaz Martín, and S. Kolouri, "Stereographic Spherical Sliced Wasserstein Distances". ICML, 2024.
R. Díaz Martín, Y. Bai, I. Medri, X. Liu, K. Yan, G.K. Rohde, and S. Kolouri. "LCOT: Linear Circular Optimal Transport Embedding". ICLR 2024.
R. Díaz Martín, I. Medri, and G.K. Rohde. "Data representation with optimal transport". Accepted for publication in the ANHA volume in honor of Akram Aldroubi's 65th birthday.
J. Ashbrock, R. Díaz Martín, B. Johnson, I. Medri, and A. Powell, "Dynamical dual frames, annihilating polynomials, and spectral radius", Poincare Journal of Analysis and Applications, 10(2): 27-53, 2023.
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
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. “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)
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''.
2025: Statistics. Tufts University.
2024: Calculus II. Tufts University.
2024: Ordinary Differential Equations. Vanderbilt University.
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 (ODEs). 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.
2024-2025: Abihith Kothapalli. Department of Mathematics, Vanderbilt University, USA. (Co-mentor)
2024: Kaiwen Shi. Department of Mathematics, Vanderbilt University, USA. (Co-mentor)
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"
