About me

I am currently working as a Profesora Titular de Universidad (Associate Professor) at the Algebra Department of the University of Seville, in Spain. Before coming back to Seville, I have been working in many different places!

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 at the University of Barcelona, where I worked with the group of Carles Casacuberta. Later I worked at the University of the Basque Country as a Juan de la Cierva - Formación researcher till July 2019, when I moved to the University of Huelva as Profesora Ayudante Doctora. I went back to Seville as a Juan de la Cierva - Incorporación postdoctoral researcher.

In 2019 I was awarded Vicent Caselles Prize, given by the Royal Spanish Mathematical Society and BBVA Foundation.

Link to journal.

Research interests

* Knot Theory.

* Braid groups.

* Link invariants and categorification.

* Khovanov homology.

* Combinatorial Knot Floer homology.

* Artin groups.

Publications

[19] "Quantum annular homology and bigger Burnside categories".
Mediterranean Journal of Mathematics. To appear.

With F. Cantero-Morán and S. García-Rodrigo.

[18] "Khovanov homology, wedges of spheres and complexity".
Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 118 (2024), 102.

With J. Przytycki.

[17] "Khovanov homology of positive links and of L-space knots".
Submitted.

With M. Kegel, N. Manikandan and L. Mousseau.

[16] "A Topological Theory for unoriented SL(4) Foams".
Mediterranean Journal of Mathematics, 21 (2024), 62.

With M. Khovanov, J. Przytycki and L. H. Robert.

[15] "Almost-extreme Khovanov spectra".
Selecta Mathematica, 27 (2021), 95, 45 pp.

With F. Cantero-Morán.

[14] "Khovanov homotopy type, periodic links and localizations".
Mathematische Annalen, 380 (2021), 1233-1309.

With M. Borodzik and W. Politarczyk.

[13] "On multiplying curves in the Kauffman bracket skein algebra of the thickened four-holed sphere".
Journal of Knot Theory and Its Ramifications, 30 (2021), 14, 2141001-29 pp.

With R. Bakshi, S. Mukherjee, J. H. Przytycki and X. Wang.

[12] "Extreme Khovanov Spectra".
Revista Matemática Iberoamericana, 36 (2020), 3, 661-670.

With F. Cantero-Morán.

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

With J. González-Meneses.

[10] "Geometric realization of the almost-extreme Khovanov homology of semiadequate links".
Geometriae Dedicata, 204 (2020), 1, 387-401.

With J. H. Przytycki.

[9] "The root extraction problem for generic braids".
Symmetry, 11 (2019), 1327.

With M. Cumplido and 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.



Preprints and ongoing projects


"On unknotting fibered positive knots and braids".
With M. Kegel, L. Lewark, N. Manikandan, F. Misev and L. Mousseau.

"On the destabilization problem".
With J. González-Meneses.

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.