**Institution**: Consejo Superior de Investigaciones Científicas

**Position**: FPI

**Office**: 208 **Phone**:+34 912999 748

**E-mail**: pablo.portilla()icmat.es

#### Biographical Review

I am originally from Madrid. I studied my bachelor degree on Mathematics at Universidad Complutense de Madrid from 2007 to 2012. Soon, I started to grow an interest on geometry and topology and focused on subjects related to these topics. During this 5-year period I enjoyed spending time at “Lewis Carroll” student association and also working on a non-profit student mathematics magazine called Matgazine.

During academic year 2012-2013, I studied the “Master degree in Advanced Mathematics” at Universidad Complutense too. I really liked studying h-cobordism theorem (and all concepts involved in its proof like Morse theory and in general low-dimensional topology techniques); also, I was lucky to be introduced to knot theory by Jose Mª A. Montesinos. All this gave me some insight on topology beyond general topology and strengthened my likings for these subjects. I did my Master Thesis on Kähler 2-tori under the supervision of Vicente Muñoz. It consisted in studying the space GL(4,R)/GL(2,C) of complex structures of a 4-dimensional torus by fixing a complex structure on it and using its hyperkähler structure to get new complex structures (by means of hyperkähler rotation).

I started working at ICMAT around November 2013 when Javier Fernández de Bobadilla and María Pe offered me to start studying with them. A couple of months later this became official when I was given Severo Ochoa-FPI grant, and so I guess I will be here for, at least, 4 more years working on my PhD under their supervision.

Currently, I am studying singularity theory from both an algebraic and a differentiable point of view and, in particular, I am interested in understanding monodromy of singularities. Also I am interested in symplectic geometry techniques and other close fields mentioned in singularity theory such as contact topology or the theory of open books.