**Institution**: UAM

**Position**: FPI

**Office**: 408 **Phone**:+34 912999 788

**E-mail**: david.fernandez()icmat.es

#### Biographical Review

I was born in 1987 in Valladolid, Spain. I did my undergraduate studies in Mathematics at Universidad Autónoma de Madrid where I acquired a solid knowledge of Partial Differential Equations.

I got the Master degree in Mathematics and Applications at Universidad Autónoma de Madrid (September, 2010) where I defended a master thesis (‘tesina’) entitled ‘Study on the genus in Theory of Algebraic Functions’ under the supervision of Dr. Orlando E. Villamayor.

I started my thesis on October, 2010 under the supervision of Dr. Luis Álvarez-Cónsul at Universidad Autónoma de Madrid and ICMAT. In this work, we try to extent some classical geometric structures in Symplectic and Poisson Geometry to a non-commutative framework. The guiding principle is the Kontsevich-Rosenberg Principle which states that meaningful concepts of non-commutative must correspond, under the representation functor, to their commutative counterparts. This exciting topic can be seen as a cross road between Algebraic Geometry, Symplectic and Poisson Geometry, Algebraic Geometry and Representation Theory. Also, non-commutative Geometry based on this principle has important connections and applications in some of the most promising physical theories since it plays an important role in the mathematical formalism of open string theory. Other research interests are Moduli Spaces or Generalized Complex Geometry.

Also, I am a member of the group of research ‘Moduli Spaces’ which is leading by Prof. Óscar García-Prada and a participant of the ‘Hitchin’s Laboratory’ which takes place at ICMAT. Moreover I have attended some schools and congress in Cambridge, Aarhus, Trieste or Barcelona.

Finally, I have given courses of Algebra at Universidad Autónoma de Madrid to undergraduate students in Mathematics and Physics Degrees and I am an active collaborator in dissemination activities.

#### Research Interest

Moduli spaces and the relationship between Algebraic Geometry, Differential Geometry and Physics.