Dr Nelly Villamizar

Senior Lecturer, Mathematics

Telephone number

+44 (0) 1792 295852

Research Links

Available For Postgraduate Supervision


I am a Senior 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.

Website: https://sites.google.com/site/nvillami/

Areas Of Expertise

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

Career Highlights

Teaching Interests

MA-233 Projective Geometry: This module gives an introduction to various properties of projective geometry. It aims at strengthening the understanding of linear algebra by demonstrating its geometrical significance, while also pointing towards more advanced algebraic geometry.

MA-231 Advanced Geometry: This module covers conics sections, projective geometry as well as problems in non-euclidean geometry.

MA-312 Higher Algebra: This module approaches the theory of algebraic modules, exact sequences, and classification of abelian groups. It also introduces categories as a language and unifying force in modern mathematics.

MA-212 Groups and Rings:  This module approaches the theory of groups, rings and modules as abstract algebraic objects.


My primary area of research is Algebraic Spline Geometry, an emerging area at the interface between algebraic geometry and computer-aided geometric design and, centred around the interaction between algebra, geometry, combinatorics and algorithms. My research agenda is driven by the development of collaborations with colleagues both in pure and applied mathematics.

Award Highlights

Funded by the London Mathematical Society, the Edinburgh Mathematical Society, and the Glasgow Mathematical Journal Trust.

  • High order methods for computational engineering and data analysis, in
    collaboration with Dr. Angelos Mantzaflaris, Inria Sophia Antipolis–Méditerranée.

British Council & French Embassy in UK – Alliance Hubert Curien programme
Grant awarded to strengthen collaborations between UK and France.