**Institution**: Consejo Superior de Investigaciones Científicas

**Position**: Contratado ERC

**Office**: 417 **Phone**:+34 912999 797

**E-mail**: miguel.vaquero()icmat.es

#### Biographical Review

I did my undergraduate studies at the University of Santiago de Compostela. After that I moved to the University of La Laguna where I was hired as a researcher to work with Juan Carlos Marrero and David Iglesias-Ponte for six months. Now I am getting my Ph. D. at ICMAT under the supervision of Manuel de León.

I am very interested in all topics related with Differential Geometry and Mathematical Physics. My research focuses on the Hamilton-Jacobi theory from the geometric point of view. Some issues that I am now developing, planning to develop or interested in are:

-Complete solutions of the Hamilton-Jacobi equation, connections with Lie groupoids and Lie algebroids.

-A Hamilton-Jacobi theory from the point of view of almost-Poisson manifolds. Connections with nonholonomic Mechanics.

-Develop a Hamilton-Jacobi theory for singular systems, in the Mechanics and Classical Field theory settings.

-Lagrangian submanifolds and applications to Mechanics and dynamical systems (periodic orbits, Hamilton-Jacobi).

-Geometric structures in Classical Field theories: mulstisymplectic, polysymplectic, k-symplectic...

-Exterior differential systems and applications to Mechanics, Control theory, reduction, Field theory...

#### Publications

## PAPERS:

-A Hamilton-Jacobi Theory for Singular Lagrangian Systems in the Skinner and Rusk Setting. Joint work with Manuel de León and David Martín de Diego. (International Journal of Geometric Methods in Modern Physics)

-On the Hamilton-Jacobi Theory for Singular Lagrangian Systems. Joint work with Manuel de León, Juan Carlos Marrero and David Martín de Diego. (Journal of Mathematical Physics)

-On poly-Poisson structures. Joint work with David Iglesias-Ponte and Juan Carlos Marrero. (to appear in Letters in Mathematical Physics)

## PREPRINTS:

-A universal Hamilton-Jacobi theory (submitted).

-Geneating functions, Hamilton-Jacobi theory and symplectic groupoids (in preparation)

-Hamilton-Jacobi theory, symmetries and coisotropic reduction (in preparation)

-A Hamilton-Jacobi theory in infinite dimensional phase spaces (in preparation)