Research

Research Interests

Singularity theory, more precisely equisingularity in complex algebraic and analytic geometry.

Publications 

1. Duarte D., Giles Flores A. On the Lipschitz saturation of toric singularities with smooth normalization, Journal of Commutative Algebra, Vol 1, pp 73-93 (2026) .                https://doi.org/10.1216/jca.2026.18.73 

2. Giles Flores A., da Silva O.N., J Snoussi. On the fifth Whitney cone of a complex analytic curve, Journal of Singularities, Vol 24, pp 96-118 (2022).                          http://dx.doi.org/10.5427/jsing.2022.24c                                                                               

3. Chávez-Martínez, E., Duarte, D. & Giles Flores, A. A higher-order tangent map and a conjecture on the higher Nash blowup of curves. Math. Z. 297, 1767–1791 (2021). https://doi.org/10.1007/s00209-020-02579-5

4. Giles Flores A., da Silva O.N., Teissier B. (2020) The biLipschitz Geometry of Complex Curves: An Algebraic Approach. In: Neumann W., Pichon A. (eds) Introduction to Lipschitz Geometry of Singularities. Lecture Notes in Mathematics, vol 2280. Springer, Cham. https://doi.org/10.1007/978-3-030-61807-0_8

5. Giles Flores A., O N Silva, J Snoussi, On Tangency in Equisingular Families of Curves and Surfaces, The Quarterly Journal of Mathematics, Volume 71, Issue 2, June 2020, Pages 485–505, https://doi.org/10.1093/qmathj/haz057

6. Giles Flores A. ; Bernard Teissier. Local polar varieties in the geometric study of singularities. Annales de la Faculté des sciences de Toulouse : Mathématiques, Serie 6, Volume 27 (2018) no. 4, pp. 679-775. doi : 10.5802/afst.1582. https://afst.centre-mersenne.org/articles/10.5802/afst.1582/

7. Giles Flores, A. Specialization to the tangent cone and Whitney equisingularity. Bulletin de la Société Mathématique de France, Tome 141 (2013) no. 2, pp. 299-342. doi : 10.24033/bsmf.2649. http://www.numdam.org/articles/10.24033/bsmf.2649/

Ph.D. Thesis 

 Specialization to the tangent cone and Whitney equisingularity. Mathematics [math]. Université Pierre et Marie Curie - Paris VI, 2011. English. tel-00631426.

Other publications

1. R. Esparza, L.J. ; Macías Ponce, J.C. ; Kú Carrillo, R. A. ; Delgadillo Alemán, S. ; Giles Flores, A. Ranking of the Academic Departments of the Autonomous University of Aguascalientes. Boletín de Estadística e Investigación Operativa,  Vol 37, No 1., Marzo 2021, pp 19-37. https://www.seio.es/beio/BEIOVol37Num1.pdf

2. Macías Ponce, J.C.; Giles Flores, A.; Delgadillo Alemán, S.; Kú Carrillo, R.A.; R. Esparza, L.J. A distribution rule for allocation problems with priority agents using the least squares method. Revista de Métodos Cuantitativos para la Economía y la Empresa, Vol 37, No1., Marzo 2024, pp 1-20. https://www.upo.es/revistas/index.php/RevMetCuant/article/view/7575 

3. Kú Carrillo, R.A. ; Delgadillo Alemán, S. ; R. Esparza, L.J. ; Macías Ponce, J.C. ; Giles Flores, A. ;  La beca al desempeño docente y el perfil de los profesores en la UAA. DOCERE, No. 30, Diciembre 2024, pp 21-26. https://doi.org/10.33064/2024docere306576