Page 110 - 8th European Congress of Mathematics ∙ 20-26 June 2021 ∙ Portorož, Slovenia ∙ Book of Abstracts
P. 110
COMPLEX ANALYSIS AND GEOMETRY (MS-17)
The Density Property for Calogero–Moser Spaces
Rafael Andrist, ra332@aub.edu.lb
American University of Beirut, Lebanon
A Calogero–Moser space describes the (completed) phase space of a system of finitely many
particles in classical physics. Since the past two decades, these spaces are also an object of
ongoing study in pure mathematics. In particular, a Calogero–Moser space of n particles is
known to be a smooth complex-affine variety, and to be diffeomorphic to the Hilbert scheme of
n points in the affine plane. We establish the density property for the Calogero–Moser spaces
and describe their group of holomorphic automorphisms.
“Levi core”, Diederich-Fornaess index, and D’Angelo forms
Gian Maria Dall’Ara, dallara@altamatematica.it
Istituto Nazionale di Alta Matematica “F. Severi", Italy
Coauthor: Samuele Mongodi
We introduce the notion of “Levi core” of a CR manifold M of hypersurface type, and prove
that, whenever M is the boundary of a smoothly bounded pseudoconvex domain Ω, the Diederich-
Fornaess index of Ω equals a numerical invariant of the Levi core. This line of research is
connected and extends recent results of B. Liu, M. Adachi, and J. Yum.
Metric geometry of domains in complex Euclidean spaces
Hervé Gaussier, herve.gaussier@univ-grenoble-alpes.fr
Université Grenoble Alpes, France
The boundary geometry of a domain strongly constrains the asymptotic behaviour of invariant
metrics and of their curvatures, as shown in important contributions. I will present recent results
that, conversely, give metric characterizations of the boundary geometry of some domains.
Fekete Configurations, Products of Vandermonde Determinants and
Canonical Point Processes
Jakob Hultgren, hultgren@umd.edu
University of Maryland, United States
The asymptotic behavior of Fekete configurations is a classical topic in complex analysis. By
definition, Fekete configurations are arrays of points that maximize Vandermonde determinants.
From a complex geometric perspective, any Hermitian ample line bundle over a compact Kähler
manifold defines a sequence of Vandermonde determinants of increasing dimension and thus a
notion of Fekete configurations. In this talk we will consider a collection of Hermitian ample
line bundles over a fixed compact Kähler manifold. I will present two results. One regarding
the product of the associated Vandermonde determinants and the asymptotic behavior of its
maximizers and one regarding existence of sequences of point configurations which are asymp-
108
The Density Property for Calogero–Moser Spaces
Rafael Andrist, ra332@aub.edu.lb
American University of Beirut, Lebanon
A Calogero–Moser space describes the (completed) phase space of a system of finitely many
particles in classical physics. Since the past two decades, these spaces are also an object of
ongoing study in pure mathematics. In particular, a Calogero–Moser space of n particles is
known to be a smooth complex-affine variety, and to be diffeomorphic to the Hilbert scheme of
n points in the affine plane. We establish the density property for the Calogero–Moser spaces
and describe their group of holomorphic automorphisms.
“Levi core”, Diederich-Fornaess index, and D’Angelo forms
Gian Maria Dall’Ara, dallara@altamatematica.it
Istituto Nazionale di Alta Matematica “F. Severi", Italy
Coauthor: Samuele Mongodi
We introduce the notion of “Levi core” of a CR manifold M of hypersurface type, and prove
that, whenever M is the boundary of a smoothly bounded pseudoconvex domain Ω, the Diederich-
Fornaess index of Ω equals a numerical invariant of the Levi core. This line of research is
connected and extends recent results of B. Liu, M. Adachi, and J. Yum.
Metric geometry of domains in complex Euclidean spaces
Hervé Gaussier, herve.gaussier@univ-grenoble-alpes.fr
Université Grenoble Alpes, France
The boundary geometry of a domain strongly constrains the asymptotic behaviour of invariant
metrics and of their curvatures, as shown in important contributions. I will present recent results
that, conversely, give metric characterizations of the boundary geometry of some domains.
Fekete Configurations, Products of Vandermonde Determinants and
Canonical Point Processes
Jakob Hultgren, hultgren@umd.edu
University of Maryland, United States
The asymptotic behavior of Fekete configurations is a classical topic in complex analysis. By
definition, Fekete configurations are arrays of points that maximize Vandermonde determinants.
From a complex geometric perspective, any Hermitian ample line bundle over a compact Kähler
manifold defines a sequence of Vandermonde determinants of increasing dimension and thus a
notion of Fekete configurations. In this talk we will consider a collection of Hermitian ample
line bundles over a fixed compact Kähler manifold. I will present two results. One regarding
the product of the associated Vandermonde determinants and the asymptotic behavior of its
maximizers and one regarding existence of sequences of point configurations which are asymp-
108
