Publications, talks and more.

Research Interests: Computational Algebraic Geometry, Symbolic Computation, Curves and Surfaces, Mathematical Methods in CAGD.

Publications (inverse chronological order): 

54. Alcázar J.G., Bizzarri M., Lavicka M., Vrsek J. (2024), “Rotational symmetries of 3D point clouds using the covariance matrix and higher order tensors”, Applied Mathematical Letters, to appear.

53. Alcázar J.G., Hermoso C., Gözütok U., Çoban H.A. (2024), “Computation of symmetries of rational surfaces”, Electronic Research Archive (special issue on “Applications of Symbolic Computation”), to appear.

52. Alcázar J.G., Lavicka M., Vrsek J. (2024), “Symmetries of planar vector fields”, Computer Aided Geometric Design Vol. 111, 102290.

51. Alcázar J.G., Gözütok U., Çoban H.A. (2024), “Detecting affine equivalences between certain types of parametric curves, in any dimension”, AIMS Mathematics 9 (6), 13750-13769.

50. Alcázar J.G., Lavicka M., Vrsek J. (2023), “Computing symmetries of implicit algebraic surfaces”, Computer Aided Geometric Design Vol. 104, 102221.

49. Alcázar J.G., Díaz-Toca G.M. (2023), “Computing the topology of the image of a parametric planar curve under a birational transformation”, Computer Aided Geometric Design, Vol. 102, 102189.

48. Gözütok U., Çoban H. A., Sagiroglu Y., Alcázar J.G. (2023), “A new method to detect projective equivalences and symmetries of rational 3D curves”, Journal of Computational and Applied Mathematics, Vol. 419, 114782.

47. Alcázar J.G., Gözütok U., Çoban H.A., Hermoso C. (2022), “Detecting affine equivalences between implicit planar algebraic curves”, Acta Applicandae Mathematicae Vol. 182, No. 2.

46. Alcázar J.G., Hermoso C., Pérez-Díaz S., Shen Li-Yong (2022), “Using µ-bases to reduce the degree in the computation of projective equivalences between rational curves in n-space”, Journal of Computational and Applied Mathematics Vol. 416, 114571.

45. Alcázar J.G., Hermoso C. (2022), “Efficient reparametrization into standard form and algorithmic characterization of rational ruled surfaces”, Computer Aided Geometric Design Vol. 96, 102120.

44. Alcázar J.G., Muntingh G. (2022), “Affine equivalences of surfaces of translation and minimal surfaces, and applications to symmetry detection and design”, Journal of Computational and Applied Mathematics Vol. 411, 114206.

43. Alcázar J.G., Hermoso C. (2021), “Computing projective equivalences of planar curves birationally equivalent to elliptic and hyperelliptic curves”, Computer Aided Geometric Design Vol. 91, 102048.

42. Alcázar J.G., Quintero E. (2021), “Exact and approximate similarities of non-necessarily rational planar, parametrized curves, using centers of gravity and inertia tensors”, International Journal of Algebra and Computation Vol. 31, No 4, pp. 581-603.

41. Alcázar J.G., Pérez-Díaz S. (2021), “Computing the form of highest degree of the implicit equation of a rational surface ”, Advances in Applied Mathematics Vol. 123, pp. 102-128.

40. Alcázar J.G. (2020), “On the affine image of a rational surface of revolution”, Mathematics 8(11), 2061

39. Alcázar J.G., Quintero E. (2020), "Affine equivalences of trigonometric curves", Acta Applicandae Mathematicae Vol. 170, pp. 691-708

38. Knez M., Peternell M., Alcázar J.G. (2020), “Editorial: From Theoretical to Applied Geometry – Recent Developments”, Computer Aided Geometric Design, Special issue on the CGTA 2019 Congress, Vol. 81, 101192.

37. Alcázar J.G., Goldman R. (2020), “Recognizing algebraic affine rotation surfaces”, Computed Aided Geometric Design Vol. 81, 101905..

36. Alcázar J.G., Caravantes J., Díaz-Toca G., Tsigaridas E. (2020), “Computing the topology of a planar or space hyperelliptic curve”, Computer Aided Geometric Design Vol. 78, 101830.

35. Alcázar J.G., Quintero E. (2020), "Affine equivalences, isometries and symmetries of ruled rational surfaces", Journal of Computational and Applied Mathematics, Vol. 364.

34. Alcázar J.G., Goldman R. (2019), “Algebraic affine rotation surfaces of parabolic type”, Journal of Geometry Vol. 110 (3)

33. Nieto J.C., Alcázar J.G., Orden D., Marazuela S., Rodríguez G. (2019), "Estimation of spatio-temporal grouping properties using Delaunay triangulation and spline techniques", Ocean Engineering Vol. 187.

32. Alcázar J.G., Lavicka M., Vrsek J. (2019), "Symmetries and similarities of planar algebraic curves using harmonic polynomials", Journal of Computational and Applied Mathematics Vol. 357, pp. 302--318.

31. Alcázar J.G., Díaz Toca G.M., Hermoso C. (2019), "On the problem of detecting when two implicit plane algebraic curves are similar", International Journal of Algebra and Computation, Vol. 29, No. 5, pp. 775–793.

30. Alcázar J.G., Caravantes J., Díaz Toca G.M. (2018), "On the square-freeness of the offset equation to a rational plane curve", International Journal of Algebra and Computation, Vol. 28, No. 3, pp. 395–409

29. Alcázar J.G., Dahl H., Muntingh G. (2018), "Symmetries of canal surfaces and Dupin cyclides", Computer Aided Geometric Design Vol. 59, pp. 68-85. 

28. Alcázar J.G., Hermoso C., Muntingh G. (2018), "Similarity detection of rational space curves", Journal of Symbolic Computation 85, pp- 4-24.

27. Alcázar J.G., Goldman R. (2017), "Detecting when an implicit equation or a rational parametrization defines a conical or cylindrical surface, or a surface of revolution", IEEE Transactions on Visualization and Computer Graphics Vol. 23, Issue 12, pp. 2550-59.

26. Alcázar J.G., Goldman R., Hermoso C.,(2016), "Algebraic surfaces invariant under scissor shears", Graphical Models vol. 87, pp. 23-34.

25. Alcázar J.G., Hermoso C. (2016), "Recognizing projections of algebraic curves", Graphical Models vol. 87, pp. 1-10.

24. Alcázar J.G., Hermoso C., Muntingh G. (2016), "Detecting similarities of rational space curves", Proceedings ISSAC 2016 (Waterloo, Canadá, July 2016).

23. Alcázar J.G., Goldman R., (2016), "Finding the axis of revolution of a surface of revolution", IEEE Transactions on Visualization and Computer Graphics, Vol. 22 (9), pp. 2082--93.

22. Alcázar J.G., Hermoso C. (2016), "Involutions of Polynomially Parametrized Surfaces", Journal of Computational and Applied Mathematics Vol. 294, pp. 23-38.

21. Alcázar J.G., Caravantes J., Díaz Toca G.M. (2015), "A new method to compute the singularities of offsets to rational plane curves", Journal of Computational and Applied Mathematics, Vol. 290, pp. 385-402.

20. Alcázar J.G., Hermoso C., Muntingh G. (2015), "Symmetry detection of rational space curves from their curvature and torsion", Computer Aided Geometric Design Vol. 33, pp. 51-65.

19. Marvá M., Alcázar J.G., Bravo de la Parra R., Poggiale J.C. (2015), "A simple geometrical condition for the existence of periodic solutions of planar periodic systems. Application to some biological models", Journal of Mathematical Analysis and Applications, Vol. 423, Issue 2, pp. 1469-1479.  

18. Alcázar J.G., Hermoso C., Muntingh G. (2014), "Detecting similarity of Rational Plane Curves", Journal of Computational and Applied Mathematics vol. 269, pp. 1-13. 

17. Alcázar J.G., Hermoso C., Muntingh G. (2014), "Detecting Symmetries of Rational Plane and Space Curves", Computer Aided Geometric Design vol. 31, issues 3-4, pp. 109-209. 

16. Alcázar J.G. (2014), "Efficient detection of symmetries of polynomially parametrized curves", Journal of Computational and Applied Mathematics, vol. 255, pp. 715-724,

15. Alcázar J.G. (2013), "On the topology of algebraic curves continuously depending on parameters, and applications", International Journal of Algebra and Computation, Vol. 23, No. 7, pp- 1591-1610. 

14. Alcázar J.G., Díaz Toca G.M.(2012), "On the Shape of Curves Rational in Polar Coordinates", Computer Aided Geometric Design, vol. 29, pp. 665-675.

13. Alcázar J.G. (2012), "Computing the Shapes Arising in a Family of Space Rational Curves Depending on a Parameter", Computer Aided Geometric Design, vol. 29, issue 6, pp. 315-331.

12. Alcázar J.G. (2012), "Local Shape of Generalized Offsets to Algebraic Curves", Journal of Symbolic Computation, vol. 47 (3), pp. 327-341

11. Alcázar J.G. (2011), "Topology of Families of Implicit Algebraic Surfaces Depending on a Parameter", Proceedings CASC 2011, Lecture Notes in Computer Science.

10. Alcázar J.G. (2011), "The Shape of Conchoids to Algebraic Curves", Proceedings VII International Conference on Curves and Surfaces, Lecture Notes in Computer Science.

9.Alcázar J.G., Díaz Toca G.M. (2010), "Topology of 2D and 3D Rational Curves", Computer Aided Geometric Design 27 (7), 483-502.

8. Alcázar J.G. (2010), "Applications of Level Curves to Some Problems on Algebraic Surfaces", Contribuciones Científicas en Honor de Mirian Andrés, Universidad de La Rioja.

7. Alcázar J.G. (2009), "On the Shape of Rational Algebraic Curves Depending on One Parameter", Computer Aided Geometric Design, vol. 27, issue 2, pp. 162-17

6. Alcázar J.G. (2009) "Good Local Behavior of Offsets to Implicit Algebraic Curves", Mathematics in Computer Science,  vol. 2, nº 4, pp. 635-652.

5. Alcázar J.G. (2008) "Good Global Behavior of Offsets to Plane Algebraic Curves", Journal of Symbolic Computation, vol. 43, pp. 659-680. 

4. Alcázar J.G. (2008) "Good Local Behavior of Offsets to Regularly Parametrized Surfaces", Journal of Symbolic Computation vol. 43 (December), pp. 845-857.

3. Alcázar J.G., Sendra J.R. (2007) "Local Shape of Offsets to Rational Algebraic Curves", Journal of Symbolic Computation, vol. 41, pp. 338-351. An extended version was published as Technical Report SFB 2006-2 (RICAM, Austria).

2. Alcázar J.G., Schicho J., Sendra J.R.(2007) "A delineability-based method for Computing Critical Sets of Algebraic Surfaces", Journal of Symbolic Computation, vol 42 (June), pp. 678-691.

1. Alcázar J.G., Sendra J.R. (2005) "Computation of the Topology of Real Algebraic Space Curves", Journal of Symbolic Computation 39, pp. 719-744. A preliminary version was published as RISC-Linz Report Series Nº 04-02. 

Editorial Work:

“From Theoretical to Applied Geometry” (2020), Special issue of the Computer Aided Geometric Design (CAGD) on the congress CGTA 2019. Guest editors: Marjeta Knez, Martin Peternell, Juan G. Alcázar.

Talks, presentations, etc. (inverse chronological order):

• Alcázar J.G., Gozutok U., Çoban H-A. (2023), “Affine equivalences of rational and analytic parametric curves in arbitrary dimension”, CGTA (Conference on Geometry: Theory and Applications) 2023, June 2023, Kefermarkt (Austria).

• Alcázar J.G., Hermoso C., Pérez-Díaz S., Shen L-Y. (2022), “Projective equivalences and mu bases of rational curves in any dimension”, Curves and Surfaces, June 2022, Arcachon (France).

• Alcázar J.G., Hermoso C. (2019), "Projective equivalences of elliptic and hyperelliptic planar curves", International Conferences on Challenges in Mathematical Architecture, July 2019, Madrid (Spain).

• Alcázar J.G., Goldman R. (2019), "Recognizing algebraic affine rotation surfaces", CGTA (Conference on Geometry: Theory and Applications) 2019, Innsbrück (Austria).

• Alcázar J.G., Quintero E. (2018), "Computing symmetries of ruled rational surfaces", EACA 2018, Zaragoza (Spain). 

• Alcázar J.G., Quintero E. (2018), "Computing symmetries of ruled rational surfaces", Curves and Surfaces, June 2018, Arcachon (France). 

• Alcázar J.G., Caravantes J.. (2017), "On the computation of straight lines contained in rational surfaces",  Applications in Computer Algebra (ACA) 2017, Jerusalem (Israel).

• Alcázar J.G. (2017), "Symmetries of canal surfaces and Dupin cyclides", plenary talk CGTA 2017, Pilsen (Czech Republic).

• Alcázar J.G., Hermoso C., Muntingh G. (2016), "Detecting similarities of rational space curves",  ISSAC 2016 (Waterloo, Canadá, July 2016).

• Alcázar J.G., Hermoso C., Muntingh G., "Symmetry detection of rational space curves from their curvature and torsion", Applications in Computer Algebra (ACA) 2014, July 2014, New York (USA).

• Alcázar J.G., Hermoso C., Muntingh G., "Similarity Detection of Rational Curves", Applications in Computer Algebra (ACA) 2013, July 2013, Málaga (Spain).

• Alcázar J.G., Hermoso C., "Detecting Similarity of Plane Rational Curves", Geometry Seminar, Centre of Mathematics for Applications, June 2013, Oslo (Norway).

• Alcázar J.G., Hermoso C., "Detecting Simmetries of Rational Curves", VIII International Conference on Curves and Surfaces, July 2012, Oslo (Norway).

• Alcázar J.G., Díaz Toca G. "On the Shape of Curves which Are Rational in Polar Coordinates", Encuentros de Álgebra Computacional y Aplicaciones (EACA) 2012, June, Alcalá de Henares (Madrid).

• Alcázar J.G., "Detecting Features in the Shape of Rational Curves",  Geometry Seminar, Center of Mathematics for Applications (Oslo, Norway), May 2012.

• Alcázar J.G., Nieto J.C., Orden D. "Detección de grupos de oleaje", AICA 2011, Granada (Spain), Second Prize in the contest of industrial applications of Computer Algebra Perlas AICA, Red EACA.

• Alcázar J.G., "Topology of Families of Implicit Algebraic Surfaces Depending on a Parameter", CASC (Computer Algebra in Scientific Computation) 2011, Kassel (Germany), September 2011. Published in the Lecture Notes of Computer Science series. 

• Alcázar J.G., "Shapes in one-parameter families of algebraic objects", Seminar of the Algorithms and Complexity Department, Max Planck Institute fur Informatikk, Saarbrücken (Germany).

• Alcázar J.G., "Computing the shapes arising in one-parameter families of algebraic curves and surfaces", Geometry Seminar, Center of Mathematics for Applications, Oslo (Norway), September 2010.

• Alcázar J.G., "On the Shape of Conchoids to Algebraic Plane Curves", Seventh International Conference on Curves and Surfaces, Julio 2010, Avignon (France). Published in the Lecture Notes of Computer Science series. 

• Alcázar J.G., Díaz Toca G.M. "Topology of 2D and 3D Rational Curves", EACA 2010 (Santiago de Compostela, Spain), Julio 2010; short version published in Proceedings EACA 2010.

• Alcázar J.G., Marvá M., Orden D., "Realizar Encuestas Docentes es Fácil si Usted Sabe Cómo", VI Jornadas Internacionales de Innovación Universitaria, Universidad Europea de Madrid, September 2009.

• Alcázar J.G., Marvá M., “Tutorización Virtual de Asignaturas de Matemáticas mediante Moodle”, II Jornadas de Innovación Docente en Tecnologías de la Información y Telecomunicaciones (ID+TIC 2009), Escuela Superior Politécnica de la Universidad de Alcalá, April 2009.

• Alcázar J.G., “Estudio Algorítmico de las Propiedades Topológicas de Familias de Curvas”, Congreso de la Real Sociedad Matemática Española, Oviedo (Spain), February 2009.

• Alcázar J.G., "Local Shape of Generalized Offsets to Real Plane Algebraic Curves", EACA 2008 (Granada, Spain), September 2008, short version published in the Proceedings of EACA 2008.

• Alcázar J.G., "Local Shape of Classical and Generalized Offsets to Plane Algebraic Curves", Sixth Internacional Conference on Mathematical Methods for Curves and Surfaces, Tornsberg (Norway), July 2008.

•  Alcázar J.G., “Determinación algorítmica de los tipos topológicos presentes en una familia de curvas algebraicas planas, y aplicaciones”, Seminar of Algebraic Geometry, Faculty of Mathematics, Universidad Complutense de Madrid, May 2008.

• Alcázar J.G., "Local and Global Results on the Shape of Offsets", Workshop on Computer Algebra in Geometric Modeling and Industry, Castro Urdiales (Spain), December 2007.

• Alcázar J.G., Sendra J.R., “Computation of the Topology of a Family of Algebraic Curves depending on a parameter, applications, and an emphasis on offset curves”, RICAM (Johann Radon Institute for Computacional and Applied Mathematics, Linz, Austria). August 2007.

• Alcázar J.G., Schicho J., Sendra J.R., "Shape of Level Curves: Determination and Some Applications", EACA 2006 (Sevilla, Spain), September 2006. Short version published in Proceedings EACA 2006.

Advised Ph. D. Theses:

1. Emily Quintero, “Computation of affine equivalences, similarities and symmetries of certain types of curves and surfaces” (in the frame of a grant from the Carolina Foundation), defended June 23^rd, 2021.

Additional material for some publications:

• Maple sheet (here) for computing the projective equivalences between two elliptic cubic curves.

• Maple sheet (here) for computing the projective equivalences between two planar curves birational to elliptic curves (degree 4)

• Maple sheet (here) for computing the projective equivelences between two planar curves birational to hyperelliptic curves

• Maple sheet (here, see the pdf here) with the list of curves tested in the paper “Using mu-bases for reducing the degree in the computation of projective equivalences between curves in n-space”. An example for planar curves here, with the mu bases used here; and example for space curves here.