PhD student in theoretical cosmology at the Instituto de Física Teórica (IFT UAM-CSIC), Madrid.

I work on cosmic topology and tests of statistical isotropy, large-scale structure, the cosmic microwave background and higher-order statistics, on both the theory and the numerical side. I am a core member of the COMPACT Collaboration, and in the Euclid Collaboration I lead the team working on the cosmic-dipole measurement (Theory Working Group).

Website · INSPIRE-HEP · ORCID · mikel.martin@uam.es

CMB correlation matrices for a closed universe with the topology of the three-sphere or of a lens space. When space is multiply connected, statistical isotropy is broken: the harmonic-space covariance matrix is no longer diagonal and depends on where the observer sits. Python and Cython, with an example notebook and a script for computing many matrices on a cluster.

• Paper: Cosmic topology. Part IId. Eigenmodes and correlation matrices of lens spaces, Martin Barandiaran et al., COMPACT Collaboration (2026), arXiv:2610.12418.

Wigner d- and D-matrices for integer and half-integer spin at any angle, as a small Cython extension with optional OpenMP parallelisation. Half-integer spins are what you need for eigenmodes on the three-sphere, and common recursion-based libraries do not support them. Matrix elements are computed from Jacobi polynomials in log space to avoid overflow, with absolute errors of about 10⁻¹⁴ up to j = 2000 when checked against mpmath. The repository includes tests, an example notebook and benchmarks against spherical, wigner, SciPy and sympy.

Marked power spectra in which the density field is weighted by its local morphology: tidal shear, isotropy, filamentarity and a fractal-dimension estimator. Includes the tools to build the density field and the tidal-tensor eigenvalues, and an example notebook.

• Paper: Weighted Webs: Morphology-Informed Marked Fields, Martin Barandiaran, Cowell, Alonso, Carrón Duque & García-Bellido (2026), arXiv:2607.26021.

Minkowski functionals on local patches of the Planck CMB map, to test whether the hemispherical power asymmetry also shows up in the morphology of the fluctuations and not only in their variance. The functionals are computed with Pynkowski (designed for a cluster), and the analysis notebook reproduces the results of the paper.

• Paper: More Than Power: Revisiting the CMB Hemispherical Power Asymmetry with Morphological Descriptors, Carrón Duque, Martin Barandiaran & Martínez-Arrizabalaga (2026), arXiv:2603.22449.