Page 396 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 396
ANALYSIS ON GRAPHS (MS-48)
Subordinacy theory on star-like graphs
Netanel Levi, netanel.levi@mail.huji.ac.il
Hebrew University of Jerusalem, Israel
The notion of subordinacy was introduced by Gilbert and Pearson, and it enables one to separate
the singular and absolutely continuous parts of the spectrum of Schroedinger operators on the
line via asymptotic properties of solutions to the eigenvalue equation. Informally speaking, a
solution is called subordinate if it decays faster than any other linearly independent solution. We
present a generalization of the Gilbert-Pearson subordinacy theory to Schroedinger operators
on star-like graphs, which are graphs that consist of a compact component C, to which a finite
number of half-lines are attached. We use our result to draw conclusions on the multiplicity of
the singular spectrum of such operators.
Asymptotics of Green functions: Riemann surfaces and Graphs
Noema Nicolussi, noema.nicolussi@univie.ac.at
École Polytechnique (CMLS), France
Analysis on graphs and Riemann surfaces admits many interesting parallels. Both settings admit
a canonical measure (the Arakelov–Bergman and Zhang measures) and an associated canonical
Green function reflecting crucial geometric information.
Motivated by the question of describing the limit of the Green function on degenerating
families of Riemann surfaces, we introduce new higher rank versions of metric graphs and
their Laplace operators. We discuss how these limit objects describe the asymptotic of the
Green function on metric graphs and Riemann surfaces close to the boundary of their respective
moduli spaces.
Based on joint work with Omid Amini (École Polytechnique).
Solitons for the KdV equation on metric graphs
Christian Seifert, christian.seifert@tuhh.de
Technische Universität Hamburg and CAU Kiel, Germany
We consider the Korteweg-de Vries equation on metric star graphs. After reviewing suitable
coupling conditions at the vertex for the linearised equation, i.e. an Airy-type evolution equa-
tion, we investigate coupling conditions at the vertex such that the system allows for solitary
waves.
This is joint work with Delio Mugnolo (Hagen) and Diego Noja (Milan).
394
Subordinacy theory on star-like graphs
Netanel Levi, netanel.levi@mail.huji.ac.il
Hebrew University of Jerusalem, Israel
The notion of subordinacy was introduced by Gilbert and Pearson, and it enables one to separate
the singular and absolutely continuous parts of the spectrum of Schroedinger operators on the
line via asymptotic properties of solutions to the eigenvalue equation. Informally speaking, a
solution is called subordinate if it decays faster than any other linearly independent solution. We
present a generalization of the Gilbert-Pearson subordinacy theory to Schroedinger operators
on star-like graphs, which are graphs that consist of a compact component C, to which a finite
number of half-lines are attached. We use our result to draw conclusions on the multiplicity of
the singular spectrum of such operators.
Asymptotics of Green functions: Riemann surfaces and Graphs
Noema Nicolussi, noema.nicolussi@univie.ac.at
École Polytechnique (CMLS), France
Analysis on graphs and Riemann surfaces admits many interesting parallels. Both settings admit
a canonical measure (the Arakelov–Bergman and Zhang measures) and an associated canonical
Green function reflecting crucial geometric information.
Motivated by the question of describing the limit of the Green function on degenerating
families of Riemann surfaces, we introduce new higher rank versions of metric graphs and
their Laplace operators. We discuss how these limit objects describe the asymptotic of the
Green function on metric graphs and Riemann surfaces close to the boundary of their respective
moduli spaces.
Based on joint work with Omid Amini (École Polytechnique).
Solitons for the KdV equation on metric graphs
Christian Seifert, christian.seifert@tuhh.de
Technische Universität Hamburg and CAU Kiel, Germany
We consider the Korteweg-de Vries equation on metric star graphs. After reviewing suitable
coupling conditions at the vertex for the linearised equation, i.e. an Airy-type evolution equa-
tion, we investigate coupling conditions at the vertex such that the system allows for solitary
waves.
This is joint work with Delio Mugnolo (Hagen) and Diego Noja (Milan).
394
