A general formulation of reweighted least squares fitting [pdf], C. Giannelli, S. Imperatore, L. Kreusser, E. Loayza-Romero, F. Mohammadi, N. Villamizar, preprint 2024, arXiv:2404.03742.

An algebraic framework for geometrically continuous splines [pdf], A. Mantzaflaris, B. Mourrain, N. Villamizar, and B. Yuan, preprint 2023, arxiv:2305.09096.

Multivariate polynomial splines on generalized oranges [pdf], M. Sirvent, T. Sorokina, N. Villamizar, and B. Yuan, preprint 2023, arxiv:2307.09627.

A lower bound for the dimension of tetrahedral splines in large degree [pdf], M. DiPasquale and N. Villamizar, Constructive Approximation, 2023.  doi:10.1007/s00365-023-09625-5.

 Algebraic methods to study the dimension for supersmooth spline spaces [pdf], D. Toshniwal and N. Villamizar, Advances in Applied Mathematics, 142, 102412, 2023. doi:10.1016/j.aam.2022.102412.

 Completeness characterization of Type-I box splines [pdf], N. Villamizar, A. Mantzaflaris and B. Jüttler, In: Carla Manni and Hendrik Speleers (eds), Geometric Challenges in Isogeometric Analysis. Springer INdAM Series, 49: 279-304. Springer, Cham, 2022. doi:10.1007/978-3-030-92313-6_12.

Reflection groups and enumeration, A. Morales, V. Reiner, and N. Villamizar, to appear In: F.  Ardila, C. Benedetti, and A. Morales (eds), Algebraic and Geometric Combinatorics, Cambridge University Press, 2021.

 A lower bound for splines on tetrahedral vertex stars [pdf], M. DiPasquale and N. Villamizar, SIAM Journal on Applied Algebraic Geometry, 5(2), pp. 250-277, 2021. doi:10.1137/20M1341118.

 Dimension of polynomial splines of mixed smoothness on T-meshes [pdf], D. Toshniwal and N. Villamizar, Computer Aided Geometric Design, 80, pp. 101880, 2020. doi:10.1016/j.cagd.2020.101880.  

 Varieties of apolar subschemes of toric surfaces [pdf], M. Gallet, K. Ranestad and N. Villamizar, Arkiv för Matematik, 56 (1), pp. 73-99, 2018. doi:10.4310/ARKIV.2018.v56.n1.a6.

 Smooth splines on quad meshes with 4-split macro-patch elements [pdf], A. Blidia, B. Mourrain and N. Villamizar, Computer Aided Geometric Design, Volume 52-53, pp. 106-125, 2017, doi:10.1016/j.cagd.2017.03.003.

 Planar Linkages Following a Prescribed Motion [pdf], M. Gallet, C. Koutschan, Z. Li, G. Regensburger, J. Schicho and N. Villamizar, Mathematics of Computation, 86, 473-506, 2017. doi: 10.1090/mcom/3120 .

 Dimension and bases for geometrically continuous splines on surfaces of arbitrary topology [pdf], B. Mourrain, R. Vidunas and N. Villamizar, Computer Aided Geometric Design, 45, 108-133, 2016. doi:10.1016/j.cagd.2016.03.003.

 Characterization of hierarchical quartic box splines on a three directional grid [pdf], N. Villamizar, A. Mantzaflaris and B. Jüttler, Computer Aided Geometric Design, 41, 47-61, 2016. doi:10.1016/j.cagd.2015.11.004.

 Degenerations of Real Irrational Toric Varieties [pdf], E. Postinghel, F. Sottile and N. Villamizar, Journal of the London Mathematical Society Second Edition, 92 (2), 223-241, 2015. doi: 10.1112/jlms/jdv024.

 Bounds on the dimension of spline spaces on triangulations [pdf], N. Villamizar, Oberwolfach Reports, Multivariate Splines and Algebraic Geometry, 12 (2), 1191-1194, doi:10.4171/OWR/2015/21.

 Spline spaces on triangulations [book], N. Villamizar and B.Mourrain, In: T. Dokken, G. Muntingh (eds) SAGA– Advances in ShApes, Geometry, and Algebra, Geometry and Computing 10: 177-197, Springer, Cham, 2014. doi:10.1007/978-3-319-08635-4 10.

 Bounds on the dimension of spline spaces on tetrahedral partitions: a homological approach [pdf],  Mathematics in Computer Science, 8 (2): 157-174, 2014. doi:10.1007/s11786-014-0187-8.

 Ring structure of splines on triangulations [pdf], N. Villamizar, Proceedings Encuentro de Álgebra Computacional y Aplicaciones (EACA), Barcelona, June 2014: pp. 164-167.  http://www.ub.edu/eaca2014/2014_EACA_Conference_Proceedings.pdf.

 Homological techniques for the analysis of the dimension of triangular spline spaces [pdf], B. Mourrain and N. Villamizar, Journal of Symbolic Computation 50, 564-577, 2013. 564-577. doi:10.1016/j.jsc.2012.10.002.

 La conjetura abc [pdf], V. Albis and N. Villamizar, Lecturas Matemáticas, 34(1), 11-75, 2013. http://scm.org.co/archivos/revista/Articulos/1100.pdf.