Fernando Alcalde CuestaFoto Andaina 15-5-2006

Professor

Department of Mathematics

Rúa Lope Gómez de Marzoa s/n

15782 Santiago de Compostela (Spain)

 

Research team: https://geodynapp.wordpress.com

Personal blog (spanish): http://fernandoalcalde.wordpress.com/

Personal blog (galician):   http://fernandoalcalde.blogspot.com/

E-mail: fernando.alcalde (at) usc.es, fernando.alcaldecuesta (at) gmail.com

españolgalego


TEACHING

 

Academic Year 2017-18

Topology of Euclidean Spaces - Undergraduate Course

Graph Theory - Graduate Course

Mathematics and Statistics II - Undergraduate Course

Students' evaluation of teaching in the academic year 2016-17

Topology of Euclidean Spaces - 4.26/5

Graph Theory - 4.44/5

 


RESEARCH 

 

I am interested in problems which are substantial in nature and related to geometry, dynamical systems and their interactions. They are usually situated on the frontiers of traditional areas and call for the application of a diverse range of techniques. Recently, in collaboration with other researchers, we have initiated the study of the evolutionary dynamics of complex networks and its applications in the areas of systems biology and innovation processes in economy.

I am responsible for the GeoDynApp team (Spanish Excellence Grant MTM2016-77642-C2-2-P) which is part of the ECSING research group and the USC group of Foliations and Dynamical Systems.

I currently work in collaboration with Françoise Dal'Bo (Rennes), Gilbert Hector (Lyon), Matilde Martínez (Montevideo), Ana Rechtman (Strasbourg), Paul Schweitzer S.J. (Rio de Janeiro) e Alberto Verjovsky (Cuernava).

 

Recent works (selected)

F. Alcalde Cuesta, F. Dal'Bo, M. Martínez, A. Verjovsky. On the construction of minimal foliations by hyperbolic surfaces on 3-manifolds. Submitted to publication.

F. Alcalde Cuesta, P. González Sequeiros, Á. Lozano Rojo, A method for validating Rent's rule for technological and biological networks. Scientific Reports, 7 (2017), 5378.

F. Alcalde Cuesta, P. González Sequeiros, Á. Lozano Rojo, Suppressors of selection. PLOS ONE, 12 (07) (2017), 1-11.

F. Alcalde Cuesta, P. González Sequeiros, Á. Lozano Rojo, R. Vigara Benito. An accurate database of the fixation probabilities of all undirected graphs of order 10 or less, in Bioinformatics and Biomedical Engineering IWBBIO 2017. Lecture Notes in Computer Science, 10209 (2017), 209-220.

F. Alcalde Cuesta, P. González Sequeiros, Á. Lozano Rojo, R. Vigara Benito. An accurate database of the fixation probabilities of all undirected graphs of order 10 or less, Mendeley Data, v2, 2017.

F. Alcalde Cuesta, Á. Lozano Rojo, A.C. Vázquez Martínez, Insertion-tolerance and repetitiveness for random graphs. Stochastic and Dynamics, 17 (2017), 1750023. ArXiv 1604.05541.

F. Alcalde Cuesta, F. Dal'Bo, M. Martínez, A. Verjovsky,  Minimality of the horocycle flow on foliations by hyperbolic surfaces with non-trivial topology. Discrete and Continuous Dynamical SystemsSeries A, 36 (9) (2016), 4619 – 4635. CorrigendumDiscrete and Continuous Dynamical SystemsSeries A, 37 (8) (2017), 4585 - 458.

F. Alcalde Cuesta, P. González Sequeiros, Á. Lozano Rojo, Exploring the topological sources of robustness against invasion of biological and technological networks. Scientific Reports, 6 (2016), 20666.

F. Alcalde Cuesta, F. Dal'Bo, Remarks on the dynamics of the horocyclic flow for homogeneous foliations by hyperbolic surfaces Expositiones Mathematicae, 33 (2015), 431-451.

F. Alcalde Cuesta, P. González Sequeiros, Á. Lozano Rojo, Fast and asymptotic computation of the fixation probability for Moran processes on graphs. Biosystems, 129 (2015), 25-35. 

F. Alcalde Cuesta, P. González Sequeiros, Á. Lozano Rojo, A geometric proof of the Affability Theorem for planar tilings. ArXiv 1112.2125v3

F. Alcalde Cuesta, Reti. MaddMaths! - Società Italiana di Matematica Applicata e Industriale, 2012.

F. Alcalde Cuesta, A. Rechtman, Averaging sequences. Pacific Journal of Mathematics, 255 (2012), 1–23.

F. Alcalde Cuesta, A. Rechtman, Minimal Følner foliations are amenable. Discrete and Continuous Dynamical Systems – Series A, 31 (2011), 685-707.

F. Alcalde Cuesta, M. P. Fernández de Córdoba, Nombre de branchement d’un pseudogroupe. Monatshefte für Mathematik, 163 (2011), 389-414.

F. Alcalde Cuesta, Á. Lozano Rojo, M. Macho Stadler, Transversely Cantor laminations as inverse limits. Proceedings of the American Mathematical Society, 139 (2011), 2615-2630.

F. Alcalde Cuesta, A. Lozano Rojo, M. Macho Stadler, Dynamique transverse de la lamination de Ghys-Kenyon. Astérisque, 323 (2009), 1-16. pdf

 

Highlights and recognition

Member of the Scientific Committe of the Spanish Topology Network

The Journal of the Spanish Physics Society echoes the publication of the paper A method for validating Rent's rule for technological and biological networks in Vol 31 No 3 (2017).

Research in Paris 2017: The project "Dynamics of the horocycle flow for hyperbolic surface laminations" (Fernando Alcalde Cuesta, Françoise Dal'Bo, Matilde Martínez, Alberto Verjovsky) has been granted by the Henri Poincaré Institut.

Institut Henri Poincaré

The Journal of the Spanish Physics Society echoes the publication of the paper Exploring the topological sources of robustness against invasion of biological and technological networks in Vol 30 No 2 (2016).

 

Work in progress

F. Alcalde Cuesta, G. Hector, P. Schweitzer S.J., A generalization of Novikov's theorem on the existence of  Reeb component in codimension one foliations.

F. Alcalde Cuesta, Á. Lozano Rojo, A.C. Vázquez Martínez. Universal graphed relations.

F. Alcalde Cuesta, Á. Lozano Rojo, R. Vigara Benito. Foliations without holonomy on compact 3-manifolds.

Á. Lozano Rojo, P. González Sequeiros, J. Piñeiro Abal, R. Vigara Benito, F. Alcalde Cuesta, Fixation properties of small order graphs.

 

Recent invited talks at international conferences

Minimal foliations of hyperbolic 3-manifolds. Geometry of Singularities and Differential Equations, Celebrating the contributions of Felipe Cano to the Theory of Singularities, Santander (Spain), 26-30 June 2017.

Joint work with Françoise Dal'Bo, Matilde Martínez, and Alberto Verjovsky.

Minimal foliations by hyperbolic surfaces on compact 3-manifolds. Congreso Bienal de la RMSE, Sesión especial Topología geométrica en honor a María Teresa Lozano, Zaragoza, 30 January-3 February de 2017.

Joint work with Françoise Dal'Bo, Matilde Martínez, and Alberto Verjovsky.

Dynamics of the horocycle flow for homogeneous and non-homogeneous foliations by hyperbolic surfaces, Geometry and Dynamics of Foliations (Foliations 2014), ICMAT Madrid, 1-5 September 2014.

Joint work with Françoise Dal'Bo, Matilde Martínez, and Alberto Verjovsky.

Foliations2014-ICMAT

 

Insertion-Tolerance and Local Isomorphism Property for Random Graphs, Random walks on groups (Geowalks 2014), IHP Paris, 27-31 January 2014.

Joint work with Á. Lozano Rojo and A.C. Vázquez Martínez.

 

Seminars and Graduate Courses (selected)

Dinámica evolutiva sobre grafos: nuevos resultados. 100 Seminario Iberoamericano de Matemáticas, Tordesillas (Spain), 17-18 January 2018.

Foliaciones sin holonomía de 3-variedades compactas. Seminario de Sistemas Dinámicos IMERL, Montevideo (Uruguay), 11 June 2016.

Moran model on graphs. Graphs and Groups in Galicia, La Coruña (Spain), 17 March 2016.

Dynamique du flot horocyclique sur les surfaces et les variétés feuilletées. CIMPA Research School "Structures géométriques et théorie du contrôle", Dakar (Senegal), 7-18 May 2012.

Laminaciones, grafos y medidas. IV Escuela Doctoral ECSING (PUC del Perú, Universidade Federal de Minas Gerais, UNAM Cuernava, UNAM México DF, Universidad de Valladolid), Valladolid (Spain), 13-24 June 2011.

 

Research Expertise and Interest

  • Dynamics of groups, foliations and dynamical systems
  • Dynamics in negative curvature
  • Random graphs and networks
  • Evolutionary dynamics on graphs and complex networks and applications in systems biology

Hirsch foliation