About me

I am currently working as a Juan de la Cierva postdoctoral researcher at the Department of Mathematics of the University of the Basque Country, in collaboration with the groups of Ilya Kazachkov and Javier Gutiérrez. I am member of the research group "Groups, Topology and Applications".

I obtained my PhD Degree from the University of Seville in March 2016, supervised by Juan González-Meneses (University of Seville) and Pedro M. G. Manchón (Polytechnic University of Madrid).

I received a Degree in Mathematics (July 2011) and a Degree in Statistics (July 2012), from the University of Seville. In July 2012 I got a Master’s Degree in Advanced Mathematics.

I have been a visiting predoctoral researcher at The George Washington University (February – May 2013), University of Illonis at Chicago (September – December 2014) and Indiana University at Bloomington (February – May 2015), under the supervision of Józef H. Przytycki, Louis H. Kauffman and Charles Livingston, respectively.

As a postdoctoral researcher, I have been working at the Institute of Mathematics and Its Applications of the University of Zaragoza (April – May 2016), the Institute of Mathematics of the University of Barcelona (June - July 2016) and the University of Seville (July 2016 – January 2017).

I spent one year (January 2017 - January 2018) working as an Assistant Professor at the Institute of Mathematics of the Polish Academy of Sciences (IMPAN), in Warsaw, in collaboration with the group of Maciej Borodzik.

In January 2018 I enrolled the Barcelona Graduate School of Mathematics as a BGSMath-María de Maeztu Junior postdoctoral researcher in the University of Barcelona, where I worked with the group of Carles Casacuberta.

Since August 2018 I am working in the University of the Basque Country (first, as a postdoctoral researcher funded by the University, and currently under the Juan de la Cierva Formación program).

Research interests

* Knot Theory.

* Braid groups.

* Link invariants and categorification.

* Khovanov homology.

* Combinatorial Knot Floer homology.

* Artin groups.

Publications

[11] "Geometric realization of the almost-extreme Khovanov homology of semiadequate links".
Geometriae Dedicata. To appear.

With J. H. Przytycki.

[10] "Extreme Khovanov Spectra".
Revista Matemática Iberoamericana. To appear.

With F. Cantero-Morán.

[9] "Polynomial braid combing".
Mathematics of Computation, 88 (2019), 318, 2027-2045.

With J. González-Meneses.

[8] "Search for torsion in Khovanov homology".
Experimental Mathematics, 27 (2018), 4, 488-497.

With S. Mukherjee, J. H. Przytycki, X. Wang and S. Y. Yang.

[7] "Homotopy type of circle graph complexes motivated by extreme Khovanov homology".
Journal of Algebraic Combinatorics, 48 (2018), 119-156.

With J. H. Przytycki.

[6] "A geometric description of the extreme Khovanov homology".
Proceedings of The Royal Society of Edinburgh: Section A, 148 (2018), 3, 541-557.

With J. González-Meneses and P. M. G. Manchón.

[5] "Strongly quasipositive links with braid index 3 have positive Conway polynomial".
Journal of Knot Theory and Its Ramifications, 25 (2016), 12, 1642015 - 14pp.
[4] "Alexander-Conway polynomial state model and Link homology".
Journal of Knot Theory and Its Ramifications, 25 (2016), 3, 1640005 - 8 pp.

With L. H. Kauffman.

[3] "On a conjecture by Kauffman on alternative and pseudoalternating links".
Topology and its Applications, 188 (2015), 82-90.
[2] "A particular type of non-associative algebras and graph theory".
Proceedings of the 2011 international conference on Applied and Computational Mathematics, (2011), 72-77. ISBN: 978-1-61804-002-2.

With J. Núñez and M. T. Villar.

[1] "Mathematical tools for the future: Graph Theory and graphicable algebras".
Applied Mathematics and Computation, 219 (2013), 6113-6125.

With J. Núñez and M. T. Villar.



Teaching

Teoría de Números y Criptografía.

Degree in Mathematics. Universidad de Sevilla. Second semester, 2013/2014.

Álgebra Lineal.

Degree in Statistics. Universidad de Sevilla. Second semester, 2014/2015.

Álgebra Lineal y Geometría.

Degree in Physics and Double Degree in Physics and Materials Engineering. Universidad de Sevilla. First semester, 2015/2016.

Álgebra Lineal.

Degree in Statistics. Universidad de Sevilla. First semester, 2016/2017.

Topología.

Degree in Mathematics. Universidad de Barcelona. Second semester, 2017/2018.

Introducción al Cálculo Integral.

Degree in Mathematics. Universidad de Barcelona. Second semester, 2017/2018.

Matemáticas I

Degrees in Chemistry and Biology. Universidad del País Vasco. First semester, 2018/2019.

Global Geometry of Curves and Surfaces.

Degree in Mathematics. Universidad del País Vasco. Second semester, 2018/2019.


Publications (on Teaching)


[2] "Cómo surgen los teoremas: una innovación docente en la asignatura de Álgebra Lineal y Geometría".
Actas de las III Jornadas de docencia universitaria de la Universidad de Sevilla. Publicado por el Servicio de Formación y Evaluación de la Universidad de Sevilla. ISBN: 978-84-86849-76-4.
[1] "Enheduanna, Teano y Aglaonike, precursoras de Hipatia".
Boletín Sociedad Puig Adam de Profesores de Matemáticas, 85 (2010), 45-57.

With J. Núñez, A. Olivares, and E. Rodríguez.