Research

Research Interests

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

Publications 

1. 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                                                                               

2. 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

3. 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

4. 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

5. 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/

6. 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