## – Europe/Lisbon

Room P3.10, Mathematics Building — Online

Evans Harrell, Georgia Institute of Technology

What does the average eigenvalue know?

The average of the first *k* eigenvalues of a self-adjoint operator, as a function of *k*, has implications for inverse problems. What information does it contain about the shape of a domain or the structure of a graph on which the operator is defined? I'll describe some recently developed tools for approaching inverse problems through averages of operators, with selected applications to the spectra of operators on domains and graphs.

Financiado por fundos nacionais através da FCT

UID/MAT/00208/2013, UID/MAT/00208/2019, UIDB/00208/2020 e UIDP/00208/2020.

DOI: 10.54499/UIDB/00208/2020, 10.54499/UIDP/00208/2020