Page 380 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 380
SPECTRAL THEORY AND INTEGRABLE SYSTEMS (MS-57)
[2] P.-G. Lemarié, Multipliers and Morrey spaces, Potential Analysis, 38(2013), 741-752.
[3] V. Maz’ya, Sobolev spaces, Springer, Berlin, 1984.
On the Lax operator of the Benjamin-Ono equation and Tao’s gauge
transform
Thomas Kappeler, tk@math.uzh.ch
University of Zurich, Switzerland
Coauthors: Patrick Gérard, Petar Topalov
I will report on recent results on the spectral theory of the Lax operator of the Benjamin-Ono
equation, discuss applications to the analysis of this equation, and explain the role of Tao’s
gauge transform in all this.
Eigenfunctions on random hyperbolic surfaces of large genus
Etienne Le Masson, etienne.le-masson@u-cergy.fr
CY Cergy Paris University, France
High frequency eigenfunctions in chaotic systems such as hyperbolic surfaces are known to
exhibit some universal behaviour of delocalisation and randomness. We will introduce to some
results on the behaviour of eigenfunctions on random compact hyperbolic surfaces, in the limit
where the genus (or equivalently the volume) tends to infinity, and the frequency is in a fixed
window. These results suggest that in the large scale limit we can expect a similar univer-
sal behaviour. We will focus on the Weil-Petersson model of random surfaces introduced by
Mirzakhani. One advantage of this point of view is the analogy with eigenvectors of random
regular graphs, about which there has been very strong developments in the recent years. Based
on joint works with Tuomas Sahlsten and Joe Thomas.
A scalar Riemann–Hilbert problem on the torus
Mateusz Piorkowski, mateusz.piorkowski@univie.ac.at
University of Vienna, Austria
Coauthor: Gerald Teschl
In this talk we will present a case study of a scalar Riemann–Hilbert problem on the torus.
This work has been motivated by the analysis of the KdV equation with steplike initial data via
the nonlinear steepest descent method. It turns out that the model problem for the transition
region can be naturally formulated as a scalar Riemann–Hilbert problem on the torus. This
approach does not only lead to the explicit Riemann–Hilbert solutions given in terms of Jacobi
theta functions, but also illuminates the uniqueness and ill-posedness issues raised in an earlier
paper.
378
[2] P.-G. Lemarié, Multipliers and Morrey spaces, Potential Analysis, 38(2013), 741-752.
[3] V. Maz’ya, Sobolev spaces, Springer, Berlin, 1984.
On the Lax operator of the Benjamin-Ono equation and Tao’s gauge
transform
Thomas Kappeler, tk@math.uzh.ch
University of Zurich, Switzerland
Coauthors: Patrick Gérard, Petar Topalov
I will report on recent results on the spectral theory of the Lax operator of the Benjamin-Ono
equation, discuss applications to the analysis of this equation, and explain the role of Tao’s
gauge transform in all this.
Eigenfunctions on random hyperbolic surfaces of large genus
Etienne Le Masson, etienne.le-masson@u-cergy.fr
CY Cergy Paris University, France
High frequency eigenfunctions in chaotic systems such as hyperbolic surfaces are known to
exhibit some universal behaviour of delocalisation and randomness. We will introduce to some
results on the behaviour of eigenfunctions on random compact hyperbolic surfaces, in the limit
where the genus (or equivalently the volume) tends to infinity, and the frequency is in a fixed
window. These results suggest that in the large scale limit we can expect a similar univer-
sal behaviour. We will focus on the Weil-Petersson model of random surfaces introduced by
Mirzakhani. One advantage of this point of view is the analogy with eigenvectors of random
regular graphs, about which there has been very strong developments in the recent years. Based
on joint works with Tuomas Sahlsten and Joe Thomas.
A scalar Riemann–Hilbert problem on the torus
Mateusz Piorkowski, mateusz.piorkowski@univie.ac.at
University of Vienna, Austria
Coauthor: Gerald Teschl
In this talk we will present a case study of a scalar Riemann–Hilbert problem on the torus.
This work has been motivated by the analysis of the KdV equation with steplike initial data via
the nonlinear steepest descent method. It turns out that the model problem for the transition
region can be naturally formulated as a scalar Riemann–Hilbert problem on the torus. This
approach does not only lead to the explicit Riemann–Hilbert solutions given in terms of Jacobi
theta functions, but also illuminates the uniqueness and ill-posedness issues raised in an earlier
paper.
378
