November 3rd 2023. 16:00-18:00: Fabricio Macià (UPM)
An introduction to the geometry of the Laplacian
Overview on the major themes in spectral geometry
and presentation of some results by Zeldtich on inverse spectral theory:
specifically, how to obtain global properties of the geodesic flow, such
as periodicity, from the multiplicites of the eigenvalues of the
Laplacian).
November 15rd 2023. 17:30-20:00: Santiago Verdasco (UPM)
Hörmander's sharp Weyl Law I
Hörmander's sharp Weyl law for the counting
function of eigenvalues of elliptic operators and some refinements due
to Sogge and Zelditch. (This is a key step in proving some of the
results presented in the first session and has a number of interesting
applications).
Hörmander, Lars. The spectral function of an elliptic operator. Acta
Math. 121 (1968), 193–218 (MR0609014).
Sogge, Christopher D.; Zelditch, Steve. Riemannian manifolds with
maximal eigenfunction growth. Duke Math. J. 114 (2002), no. 3, 387–437
(MR1924569).
November 29rd 2023. 17:30-20:00: Santiago Verdasco (UPM)
Hörmander's sharp Weyl Law II
Hörmander's sharp Weyl law for the counting
function of eigenvalues of elliptic operators and some refinements due
to Sogge and Zelditch. (This is a key step in proving some of the
results presented in the first session and has a number of interesting
applications).
Hörmander, Lars. The spectral function of an elliptic operator. Acta
Math. 121 (1968), 193–218 (MR0609014).
Sogge, Christopher D.; Zelditch, Steve. Riemannian manifolds with
maximal eigenfunction growth. Duke Math. J. 114 (2002), no. 3, 387–437
(MR1924569).
December 13th 2023. 17:30-20:00: Santiago Verdasco (UPM)
Hörmander's sharp Weyl Law III
Hörmander's sharp Weyl law for the counting
function of eigenvalues of elliptic operators and some refinements due
to Sogge and Zelditch. (This is a key step in proving some of the
results presented in the first session and has a number of interesting
applications).
Hörmander, Lars. The spectral function of an elliptic operator. Acta
Math. 121 (1968), 193–218 (MR0609014).
Sogge, Christopher D.; Zelditch, Steve. Riemannian manifolds with
maximal eigenfunction growth. Duke Math. J. 114 (2002), no. 3, 387–437
(MR1924569).
February 21st 2024. 11:00-13:00: Fabricio Macià (UPM)
Maximally Degenerate Laplacians and Yau's conjecture
PID2021-124195NB-C3