Page 111 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 111
COMPLEX ANALYSIS AND GEOMETRY (MS-17)
totically Fekete (a slightly weaker concept than Fekete) with respect to all Hermitian ample
line bundles simultaneously. If time permits I will also outline a conjectural picture involving a
related class of point processes and its connection to canonical metrics in complex geometry.
Images of CR manifolds
Jiri Lebl, lebl@okstate.edu
Oklahoma State University, United States
Coauthors: Alan Noell, Sivaguru Ravisankar
We study CR singular submanifolds that have a removable CR singularity, that is, manifolds
that are singular, but whose CR structure extends through the singularity. Bishop surfaces are
trivial examples, but in higher CR dimension, generically the CR singularity is not removable.
In particular, we study real codimension 2 submanifolds in C3. This is joint work with Alan
Noell and Sivaguru Ravisankar.
Strict density inequalities for interpolation in weighted spaces of
holomorphic functions in several complex variables.
Joaquim Ortega Cerdà, jortega@ub.edu
Universitat de Barcelona, Spain
Coauthors: Karlheinz Gröchenig, Antti Haimi, José Luis Romero
I will present a joint work with Karlheinz Gröchenig, Antti Haimi and José Luis Romero were
we solve a problem posed by Lindholm and prove strict density inequalities for sampling and in-
terpolation in Fock spaces of entire functions in several complex variables defined by a plurisub-
harmonic weight.
In particular, these spaces do not admit a set that is simultaneously sampling and interpo-
lating. To prove optimality of the density conditions, we construct sampling sets with a density
arbitrarily close to the critical density.
Parabolic Fatou components with holes
Josias Reppekus, reppekus@mat.uniroma2.it
Università di Roma "Tor Vergata", Italy
Many examples of invariant non-recurrent Fatou components of automorphisms F of C2 arise
from local projections to one variable in which the dynamics are approximately parabolic. After
constructing a local basin B, a critical step is to show that the associated completely invariant
global basin Ω of all orbits ending up in B is not just a proper subset of a Fatou component.
I will present two types of examples in which the initial projection is non-linear and the
resulting Fatou component Ω is biholomorphic to C × C∗, i.e. “has a hole”. The constructions
are based on the dynamics near a fixed point p on the boundary of U such that the eigenvalues
of F at p are complex conjugate irrational rotations. For the first type, all orbits in Ω converge
to p, whereas for the second type the orbits in Ω converge precisely to the points of an entire
curve minus p.
109
totically Fekete (a slightly weaker concept than Fekete) with respect to all Hermitian ample
line bundles simultaneously. If time permits I will also outline a conjectural picture involving a
related class of point processes and its connection to canonical metrics in complex geometry.
Images of CR manifolds
Jiri Lebl, lebl@okstate.edu
Oklahoma State University, United States
Coauthors: Alan Noell, Sivaguru Ravisankar
We study CR singular submanifolds that have a removable CR singularity, that is, manifolds
that are singular, but whose CR structure extends through the singularity. Bishop surfaces are
trivial examples, but in higher CR dimension, generically the CR singularity is not removable.
In particular, we study real codimension 2 submanifolds in C3. This is joint work with Alan
Noell and Sivaguru Ravisankar.
Strict density inequalities for interpolation in weighted spaces of
holomorphic functions in several complex variables.
Joaquim Ortega Cerdà, jortega@ub.edu
Universitat de Barcelona, Spain
Coauthors: Karlheinz Gröchenig, Antti Haimi, José Luis Romero
I will present a joint work with Karlheinz Gröchenig, Antti Haimi and José Luis Romero were
we solve a problem posed by Lindholm and prove strict density inequalities for sampling and in-
terpolation in Fock spaces of entire functions in several complex variables defined by a plurisub-
harmonic weight.
In particular, these spaces do not admit a set that is simultaneously sampling and interpo-
lating. To prove optimality of the density conditions, we construct sampling sets with a density
arbitrarily close to the critical density.
Parabolic Fatou components with holes
Josias Reppekus, reppekus@mat.uniroma2.it
Università di Roma "Tor Vergata", Italy
Many examples of invariant non-recurrent Fatou components of automorphisms F of C2 arise
from local projections to one variable in which the dynamics are approximately parabolic. After
constructing a local basin B, a critical step is to show that the associated completely invariant
global basin Ω of all orbits ending up in B is not just a proper subset of a Fatou component.
I will present two types of examples in which the initial projection is non-linear and the
resulting Fatou component Ω is biholomorphic to C × C∗, i.e. “has a hole”. The constructions
are based on the dynamics near a fixed point p on the boundary of U such that the eigenvalues
of F at p are complex conjugate irrational rotations. For the first type, all orbits in Ω converge
to p, whereas for the second type the orbits in Ω converge precisely to the points of an entire
curve minus p.
109
