(ptdc/mat-cal/4334/2014)

**Description:**

The purpose of this project is to combine analytic, geometric and computational techniques to study extremal values of different spectral quantities,
such as individual eigenvalues, functions of these eigenvalues and some global spectral quantities. More specifically, some of the objects under
consideration are the possible extremal sets of the first eigenvalue of the Laplacian with Robin boundary conditions, for which team members have recently
shown that the ball is no longer an optimiser for large negative values of the boundary parameter, thus providing a counter-example to a 1977 conjecture,
finite combinations of eigenvalues of the Laplace and Schrödinger operators, the functional determinant associated with these operators and the spectral
abscissa of the (non self-adjoint) operator associated with the damped wave equation. To handle these problems a wide range of methods is required, including those from geometric
analysis, functional analysis, control theory, numerical analysis, etc.

The host institution is the Group of Mathematical Physics of the University of Lisbon.

Time span: 15/05/2016-14/05/2019Funding institution:

**Research team:**

Davide Buoso (March 2017 - )

Pedro Freitas (PI)

Gianpaolo Piscitelli (December 2017 - )

Ophélie Rouby (January 2017 - June 2017)

Some previous publications by group members

(for other relevant publications see the respective homepages)Publications within the scope of this project

e-mail:psfreitas ( a@t )fc.ul.pt

Group of Mathematical Physics -
University of Lisbon

Department of Mathematics

Faculty of Sciences

Campo Grande, Edifício C6

P-1749-016 Lisboa, Portugal