Dr Nelly Villamizar

Athro Cyswllt, Mathematics

n.y.villamizar@abertawe.ac.uk

303
Trydydd Llawr
Y Ffowndri Gyfrifiadol
Campws y Bae

Ar gael ar gyfer Goruchwyliaeth Ôl-raddedig

Dolenni Ymchwil

Trosolwg

Rwy'n Uwch-ddarlithydd yn Adran Mathemateg Prifysgol Abertawe. Fy niddordebau ymchwil yw geometreg algebraidd gymhwysol, ac algebra cymudol, yn enwedig eu defnyddio i ddatrys problemau sy'n codi mewn modelu geometrig a Dylunio Geometrig drwy Gymorth Cyfrifiadur (CAGD). Cyn hynny, rhwng 2013 a 2017, roeddwn yn Ymchwilydd Ôl-ddoethurol gyda’r Group of Symbolic Computation yn RICAM, yn Linz, Awstria.

Meysydd Arbenigedd

Geometreg Algebraidd Gymhwysol
Algebra Cymudol
Brasamcan Sblein
Geometreg Sblein Algebraidd
Dylunio Geometrig drwy Gymorth Cyfrifiadur

Uchafbwyntiau Gyrfa

Diddordebau Addysgu

MA-231 Geometreg Uwch
Mae’r modiwl hwn yn cwmpasu trychiadau conig, geometreg dafluniol yn ogystal â phroblemau mewn geometreg di-Ewclid.
MA-312 Algebra Uwch
Mae’r cwrs hwn yn ymdrin â damcaniaeth grwpiau, cylchoedd a modiwlau fel gwrthrychau algebraidd haniaethol. Hefyd, mae’r cwrs yn cyflwyno categorïau fel iaith a grym unedig mewn mathemateg fodern.

Prif Wobrau Cydweithrediadau

Cyhoeddiadau

Uchafbwyntiau Ymchwil

Sirvent, M., Sorokina, T., Villamizar, N., & Yuan, B. (2024). Multivariate polynomial splines on generalized oranges. Journal of Approximation Theory, 299, 106016
https://doi.org/10.1016/j.jat.2024.106016, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa65585
DeepeshToshniwal, . & Villamizar, N. (2023). Algebraic methods to study the dimension of supersmooth spline spaces. Advances in Applied Mathematics, 142
https://doi.org/10.1016/j.aam.2022.102412, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa60699
DiPasquale, M. & Villamizar, N. (2023). A lower bound for the dimension of tetrahedral splines in large degree. Constructive Approximation
https://doi.org/10.1007/s00365-023-09625-5, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa63205
http://dx.doi.org/10.1007/s00365-023-09625-5
Villamizar, N., Morales, A., & Reiner, V. (n.d.) Reflection groups and enumeration. In Federico Ardila, Carolina Benedetti, Alejandro Morales (Ed.), Algebraic and Geometric Combinatorics Cambridge University Press
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56992
Villamizar, N., Mantzaflaris, A., & Jüttler, B. (2022). Completeness Characterization of Type-I Box Splines. In Geometric Challenges in Isogeometric Analysis. Springer INdAM Series (pp. 279-304). Springer International Publishing.
https://doi.org/10.1007/978-3-030-92313-6_12, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56991
DiPasquale, M. & Villamizar, N. (2021). A Lower Bound for Splines on Tetrahedral Vertex Stars. SIAM Journal on Applied Algebra and Geometry, 5(2), 250-277.
https://doi.org/10.1137/20m1341118, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56990
Toshniwal, D. & Villamizar, N. (2020). Dimension of polynomial splines of mixed smoothness on T-meshes. Computer Aided Geometric Design, 80, 101880
https://doi.org/10.1016/j.cagd.2020.101880, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa54305
Gallet, M., Ranestad, K., & Villamizar, N. (2018). Varieties of apolar subschemes of toric surfaces. Arkiv för Matematik, 56(1), 73-99.
https://doi.org/10.4310/ARKIV.2018.v56.n1.a6, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa34564
https://arxiv.org/abs/1601.00694
Mourrain, B. & Villamizar, N. (2013). Homological techniques for the analysis of the dimension of triangular spline spaces. Journal of Symbolic Computation, 50, 564-577.
https://doi.org/10.1016/j.jsc.2012.10.002, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa32879
Villamizar, N. & Mourrain, B. (2014). On the Dimension of Spline Spaces on Triangulations. In Tor Dokken and Georg Muntingh (Ed.), SAGA – Advances in ShApes, Geometry, and Algebra (pp. 177-197). Springer, Cham
https://doi.org/10.1007/978-3-319-08635-4_10, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa32880

Holl Ymchwil

Erthyglau Cylchgronau

Sirvent, M., Sorokina, T., Villamizar, N., & Yuan, B. (2024). Multivariate polynomial splines on generalized oranges. Journal of Approximation Theory, 299, 106016
https://doi.org/10.1016/j.jat.2024.106016, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa65585
DiPasquale, M. & Villamizar, N. (2023). A lower bound for the dimension of tetrahedral splines in large degree. Constructive Approximation
https://doi.org/10.1007/s00365-023-09625-5, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa63205
http://dx.doi.org/10.1007/s00365-023-09625-5
DeepeshToshniwal, . & Villamizar, N. (2023). Algebraic methods to study the dimension of supersmooth spline spaces. Advances in Applied Mathematics, 142
https://doi.org/10.1016/j.aam.2022.102412, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa60699
DiPasquale, M. & Villamizar, N. (2021). A Lower Bound for Splines on Tetrahedral Vertex Stars. SIAM Journal on Applied Algebra and Geometry, 5(2), 250-277.
https://doi.org/10.1137/20m1341118, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56990
Toshniwal, D. & Villamizar, N. (2020). Dimension of polynomial splines of mixed smoothness on T-meshes. Computer Aided Geometric Design, 80, 101880
https://doi.org/10.1016/j.cagd.2020.101880, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa54305
Gallet, M., Ranestad, K., & Villamizar, N. (2018). Varieties of apolar subschemes of toric surfaces. Arkiv för Matematik, 56(1), 73-99.
https://doi.org/10.4310/ARKIV.2018.v56.n1.a6, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa34564
https://arxiv.org/abs/1601.00694
Gallet, M., Koutschan, C., Li, Z., Regensburger, G., Schicho, J., & Villamizar, N. (2017). Planar linkages following a prescribed motion. Mathematics of Computation, 86(303), 473-506.
https://doi.org/10.1090/mcom/3120, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa32864
Blidia, A., Mourrain, B., & Villamizar, N. (2017). G 1 -smooth splines on quad meshes with 4-split macro-patch elements. Computer Aided Geometric Design, 52-53, 106-125.
https://doi.org/10.1016/j.cagd.2017.03.003, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa32862
Mourrain, B., Vidunas, R., & Villamizar, N. (2016). Dimension and bases for geometrically continuous splines on surfaces of arbitrary topology. Computer Aided Geometric Design, 45, 108-133.
https://doi.org/10.1016/j.cagd.2016.03.003, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa32863
http://www.sciencedirect.com/science/article/pii/S0167839616300309
Villamizar, N., Mantzaflaris, A., & Jüttler, B. (2016). Characterization of bivariate hierarchical quartic box splines on a three-directional grid. Computer Aided Geometric Design, 41, 47-61.
https://doi.org/10.1016/j.cagd.2015.11.004, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa32865
Postinghel, E., Sottile, F., Villamizar, N., & Villamizar, N. (2015). Degenerations of real irrational toric varieties. Journal of the London Mathematical Society, 92(2), 223-241.
https://doi.org/10.1112/jlms/jdv024, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa32867
Mourrain, B. & Villamizar, N. (2014). Bounds on the Dimension of Trivariate Spline Spaces: A Homological Approach. Mathematics in Computer Science, 8(2), 157-174.
https://doi.org/10.1007/s11786-014-0187-8, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa32869
Mourrain, B. & Villamizar, N. (2013). Homological techniques for the analysis of the dimension of triangular spline spaces. Journal of Symbolic Computation, 50, 564-577.
https://doi.org/10.1016/j.jsc.2012.10.002, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa32879

Penodau Llyfrau

Villamizar, N. & Mourrain, B. (2014). On the Dimension of Spline Spaces on Triangulations. In Tor Dokken and Georg Muntingh (Ed.), SAGA – Advances in ShApes, Geometry, and Algebra (pp. 177-197). Springer, Cham
https://doi.org/10.1007/978-3-319-08635-4_10, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa32880
Villamizar, N., Morales, A., & Reiner, V. (n.d.) Reflection groups and enumeration. In Federico Ardila, Carolina Benedetti, Alejandro Morales (Ed.), Algebraic and Geometric Combinatorics Cambridge University Press
SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56992

Cyfraniadau Cynadleddau

Villamizar, N., Mantzaflaris, A., & Jüttler, B. (2022). Completeness Characterization of Type-I Box Splines. In Geometric Challenges in Isogeometric Analysis. Springer INdAM Series (pp. 279-304). Springer International Publishing.
https://doi.org/10.1007/978-3-030-92313-6_12, SU Repository: https://cronfa.swan.ac.uk/Record/cronfa56991

Goruchwyliaeth

Ore extensions of trusses (cyfredol)

PhD

Goruchwyliwr arall: Prof Tomasz Brzezinski
Solving Polynomial Systems for Feedback Control (cyfredol)

PhD

Goruchwyliwr arall: Prof Chenggui Yuan
Higher rank tropicalisation (cyfredol)

PhD

Goruchwyliwr arall: Prof Jeffrey Giansiracusa

Goruchwyliwr arall: Prof Tomasz Brzezinski

Goruchwyliwr arall: Dr Edwin Beggs

Modiwlau a Addysgir

MA-233 Projective Geometry: theory and applications

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. The module starts by discussing affine transformations and isometries in Euclidean geometry. This is followed by the study of some properties of the projective plane, the connection of the subject to projections, and the idea of points at infinity where parallel lines meet. Subsequently, the focus will be in the axiomatic presentation of projective geometry, and the basic properties of projective spaces over arbitrary fields. In the last part of the module, the study of conics in projective space guides the introduction of homogeneous coordinates and the study of easy cases of Bézout's theorem, one of the fundamental results in both algebraic geometry and computer algebra. The module is developed via explicit examples and emphasizes those parts of projective geometry that are important in areas of applications such as Information Security, Statistics, Computer Graphics and Computer Vision.
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.
MA-M07 Further Mathematics for Data Science

The module develops mathematical foundations for data science and machine learning. The module covers basic problems of Vector Calculus, Linear Algebra and Optimization including concepts of partial derivatives, gradient and Hessian, eigenvalues and eigenvectors of matrices and their use in optimisation problems, method of gradient descent and its application in Machine Learning. It also highlights the use of Python in the numerical solution of these problems, as well as in symbolic computation.

Grantiau a Phrosiectau Allweddol

High order methods for computational engineering and data analysis - British Council a Llysgenhadaeth Ffrainc yn y DU – rhaglen Alliance Hubert Curien 2020 - 2022

Grant a ddyfarnwyd i gryfhau cysylltiadau rhwng Ffrainc a’r DU. Mewn cydweithrediad â’r Dr. Angelos Mantzaflaris, Inria Sophia Antipolis Méditerranée.

Swyddi Cysylltiedig

Gwyddonydd Ymchwil, RICAM

2013 - 2016

Dr Nelly Villamizar

Cyfeiriad ebost

Dolenni Ymchwil

Trosolwg

Meysydd Arbenigedd

Uchafbwyntiau Gyrfa

Uchafbwyntiau Ymchwil

Holl Ymchwil

Ore extensions of trusses (cyfredol)

Solving Polynomial Systems for Feedback Control (cyfredol)

Higher rank tropicalisation (cyfredol)

MA-233 Projective Geometry: theory and applications

MA-312 Higher Algebra

MA-M07 Further Mathematics for Data Science

High order methods for computational engineering and data analysis - British Council a Llysgenhadaeth Ffrainc yn y DU – rhaglen Alliance Hubert Curien 2020 - 2022

Gwyddonydd Ymchwil, RICAM