I am a Lecturer in the Department of Mathematics at Swansea University. My research interests are applied algebraic geometry, and commutative algebra, in particular, their applications for solving problems arising in geometric modeling and Computer Aided Geometric Design (CAGD). Previously, from 2013 to 2017, I was a Postdoctoral Researcher in the Group of Symbolic Computation at RICAM, in Linz, Austria. Please visit my homepage.


Areas of Expertise

  • Applied Algebraic Geometry
  • Commutative Algebra
  • Spline Approximation
  • Algebraic Spline Geometry
  • Computer Aided Geometric Design


  1. Villamizar, N. Varieties of apolar subschemes of toric surfaces Arkiv för Matematik 56 1 73 99
  2. Villamizar, N. Homological techniques for the analysis of the dimension of triangular spline spaces Journal of Symbolic Computation 50 564 577
  3. Villamizar, N. G 1 -smooth splines on quad meshes with 4-split macro-patch elements Computer Aided Geometric Design 52-53 106 125
  4. Villamizar, N. Dimension and bases for geometrically continuous splines on surfaces of arbitrary topology Computer Aided Geometric Design 45 108 133
  5. Villamizar, N. Planar linkages following a prescribed motion Mathematics of Computation 86 303 473 506

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  • MA-231 Advanced Geometry

    This module covers conics sections, projective geometry as well as problems in non-euclidean geometry.

  • MA-312 Higher Algebra

    This course approaches the theory of groups, rings and modules as abstract algebraic objects. The course also introduces categories as a language and unifying force in modern mathematics.


  • Topics in the theory of trusses. (current)

    Student name:
    Other supervisor: Prof Tomasz Brzezinski
  • Untitled (current)

    Student name:
    Other supervisor: Prof Jeffrey Giansiracusa