SupervisoryTeam

Supervisor Photo

Enrique Artal Bartolo

Supervisor Details

Email: artal@unizar.es

Organization Type: University

Organization Name: Universidad de Zaragoza

Short Biography: Teaching Assistant (University of Geneva), Beca de Reincorporación in Zaragoza, post-doc in Bordeaux. Full Professor in UCM (1993-94) and Zaragoza (1994-2005), Catedrático in Zaragoza (2005-). Member of the Mathematics Institute IUMA. Deputy Dean of the FSc, Head of the MathDpt, Coordinator of the Mathematics Master and Bachelor at UNIZAR. Member of the Real Academia de Ciencias de Zaragoza. Adviser for 8 PhD thesis, 13 Bachelor thesis and 3 Master thesis. I have participated in 21 competitive R&D competitive national programs 4 of which as a PI. 89 research papers, 13 of which in Q1 and 1564 citations, h-index 22. More than 60 participations in International Conferences or Seminars as invitated speaker. Organizer of 8 Conferences, funded by I-Math and R&D competitive programs. 3 international research stays. Scientific evaluator for the Spanish National R&D, international agencies and international journals. Areas of interest: Topology of Quasi-projective Varieties, Algebraic and Arithmetic Aspects of Singularity Theory, Zariski Pairs, Intersection of Quadrics, Artin groups and Quasi-projective groups, Normal Surface Singularities, computer algebra (Sagemath).

Co-Supervisor Photo

Javier FERNANDEZ DE BOBADILLA

Co-Supervisor Details

Email: jbobadilla@bcamath.org

Organization Type: University or other type of organization

Organization Name: Basque Center for Applied Mathematics

Short Biography: Ikerbasque Research Professor at BCAM. Ph.D. 2001, University of Nijmegen. 1.- Negative answers to Zariski's question B, dating from 1970, and a 1985 question of D. Massey. (Invent. Math.) 2.- Proof of Nash Conjecture together with M. Pe Pereira Annals of Math). 3.- Proof, with I. Pallares, of the Brasselet-Schurmann-Yokura conjecture on L-classes for singular varieties. Subsequent stronger proof with I. Pallares and M. Saito (JEMS). 4.- Proof with T. Pelka of the 1970 Zariski multiplicity conjecture for families of isolated singularities (under review). 5.- More than 35 peer reviewed publications. 6.- Member of the Institute for Advanced Studies in Princeton for 1 year, Jean Morlet Chair holder to lead a semester in Singularity Theory at CIRM in 2021. Co-organizer of Renyi Semester “Singularities and low dimensional topology” 2023. 7.- I completed 6 Ph.D. directions, 6 current students. More than 16 postdocs. 8.- 1 ERC Starting and 1 ERC Consolidator Grants. PI of National Projects. Guarantor of 3 Severo Ochoa projects. 9.- Managing editor of “Journal of Singularities”; editor of Bulletin and Journal of the London Math. Soc.

Added Value: The Basque Center for Applied Mathematics (BCAM) is a world-class interdisciplinary Research Center in the field of Applied Mathematics that was founded in 2008 as a Basque Excellence Research Center (BERC), with a focus on interdisciplinary research in Mathematics, as well as training and attracting talented scientists, and promoting scientific and technological advances worldwide. The center has been awarded (2013, 2018) twice with the Severo Ochoa distinction that consolidates BCAM as one of the most relevant institutions of the field in Europe. As a distinguished member of BCAM, Prof. Javier Fernández de Bobadilla, can add a strong academic value to the project, given his extended curriculum. Also, BCAM is an excellent platform for many different future projects and job opportunities. Finally, the international connections provided by BCAM will be a great asset for the future.

Other Co-Supervisor Photo

María Teresa Lozano Imízcoz

Other Co-Supervisor

Email: tlozano@unizar.es

Organization Type: University

Organization Name: Universidad de Zaragoza

Short Biography: PhD in 1974. Postdoctoral stay as Honorary Fellow in Wisconsin University (1976-1978) (Madison, U.S.A). Full Professor (1978-1990), Catedrática of Geometry and Topology (U.Z.) (1990-2016) and Emeritus Professor (2016-). Permanent member of the Real Academia de Ciencias Exactas, Físicas, Químicas y Naturales de Zaragoza from 1996. Corresponding member of the Real Academia de Ciencias Exactas, Físicas y Naturales de España from 2006. 30 participations in International Conferences or Seminars as an invitated speaker. 80 research papers, 618 citations. Areas of interest: Invariants of knots and links. Universal groups and knots. Geometric structures on 3-dimensional manifolds and orbifolds. Topological invariants from geometry. Geometric Aspects of Singularity Theory. Regular collaborations with J.M. Montesinos- Amilibia, and H. Hilden.

ResearchGroup

Description: Our research group has been growing since the 1990’s, where it started at U. Complutense de Madrid around the transversal topic of singularity theory with a group of 2 professors (Prof. Ignacio Luengo-Velasco and Prof. Enrique Artal) and 2 students (A. Melle-Hernández and J.I. Cogolludo). Nowadays, this group has become a coordinated link of groups in Madrid, Zaragoza, and Bilbao, with a total of 18 professors and 14 PhD students. Grupo Singular https://blogs.mat.ucm.es/singular/ Our active connections with international researchers include Université de Bordeaux, Moscow University, Université de Lille, Cimat, Renyi Mathematical Institute, University of Leuven, Louisiana State University, University of Illinois at Chicago, University of Michigan-Ann Arbor, Martin-Luther-Universität Halle-Wittenberg, Rwth Aachen University, Babes-Bolyai University, Cluj-Napoca, Université de Pau et de Pays de Ladour, UNAM, Tokushima University, Tokyo Metropolitan University, National Institute of Technology of Ibaraki. Grupo Singular has a long and solid research and training tradition, centered around the theory of singularities from several points of view: algebraic, geometric, analytical, topological and combinatorial, and its applications in areas such as cryptography, discrete geometry, computing, biology, and the physics of space.

ResearchLine

Description: Title: Invariants of Surface Singularities The current PhD project revolves around singularity theory and its applications. The purpose focused on solving one of the problems around surface singularities that involves the MacKay correspondence that connects the geometrical and algebraic understanding of minimal curves and their invariants with the minimal resolution of the surface singularity.

CareerDevelopment

Objectives

  • Future postdoc employment at the University
  • Increased employability in the non-academic sector
  • International mobility
  • Building collaborative networks
  • Trainings to enhance career opportunities
  • Application of postdoctoral grants (MSCA, Juan de la Cierva, etc.)
  • Application for projects and funding (Horizon Europe, national plans, etc.)
  • Involvement in teaching, supervision, or mentoring

Expected Outputs

  • PhD defense
  • Application of grants (MSCA, Juan de la Cierva, etc.)
  • Publication of articles
  • Attendance to international conferences

Other Outputs: Possible contribution to development of software

Training Skills

  • Project Management
  • Time Management
  • Open Science
  • Gender and diversity dimension of research
  • Supervision
  • Advanced Digital Skills
  • Responsible use of Artificial Intelligence
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