International Workshop

Invariant distances and metrics in complex analysis

July 11 – 15, 2023,
Sofia, Bulgaria

in the frame of the International Conference “Mathematics Days in Sofia”

T

he workshop will bring together researchers around a central theme of the geometric properties of various distances and metric of domains in Cn (squeezing function, Gromov hyperbolicity, visibility of geodesics) as well as related subjects.

Organizing Committee

  • Nikolai Nikolov (Institute of Mathematics and Informatics, Bulgaria)
  • Pascal J. Thomas (Université Paul Sabatier, France)

  • Krassimira Ivanova (Institute of Mathematics and Informatics, Bulgaria) – scientific secretary

Participants

  • Ahmed Yekta Ökten, Institut de Mathématiques de Toulouse, France

  • Anand Chavan, Jagiellonian University, Poland

  • Andrew Zimmer, University of Wisconsin-Madison, USA

  • Erlend Fornæss Wold, University of Oslo, Norway

  • Filippo Bracci, Università di Roma “Tor Vergata”, Italy

  • Gautam Bharali, Indian Institute of Science, India
  • Hervé Gaussier, Université Grenoble 1, France

  • John Erik Fornæss, NTNU Trondheim, Norway

  • Krassimira Ivanova, Institute of Mathematics and Informatics, Bulgaria

  • Lukasz Kosinski, Jagiellonian University, Poland

  • Marcin Tombinski, Jagiellonian University, Poland

  • Matteo Fiacchi, University of Ljubljana, Slovenia

  • Nikolai Nikolov, Institute of Mathematics and Informatics, Bulgaria

  • Omar Bakkacha, Université Grenoble Alpes, France

  • Pascal Thomas, Université Paul Sabatier, France

  • Slawomir Dinew, Jagiellonian University, Poland

  • Włodzimierz Zwonek, Jagiellonian University, Poland

  • Zehao Sha, Université Grenoble Alpes, France

  • Zywomir Dinew, Jagiellonian University, Poland

Program and Abstracts:

  • Matteo Fiacchi

    Gromov hyperbolicity in backward dynamics

    In this talk we study the backward dynamics of non-expanding self-maps of a proper geodesic Gromov hyperbolic metric space. To do so, we introduce the notion of stable dilation at a boundary regular fixed point of the Gromov boundary, whose value is related to the dynamical behaviour of the fixed point. As an application, we obtain new results for holomorphic self-maps of bounded domains D, where D is either strongly pseudoconvex, convex finite type, or pseudoconvex finite type in C2, solving several open problems from the literature. This is a joint work with L. Arosio, L. Guerini and A. Karlsson.

  • Slawomir Dinew

    Complex nonlinear equations, weak solutions and admissible domains

    We report on recent progress in the study of nonlinear elliptic equations in domains in Cn. Existence of weak solutions to those, if suitable boundary behavior is assumed, forces geometric properties of the domain.

  • Wlodzimierz Zwonek

    2-proper holomorphic images of the Cartan domains

    The ideas that generalize the construction of the symmetrized bidisc and the tetrablock as 2-proper holomorphic images of the Cartan domains will be presented. The new domains have many geometric properties that will be presented in the lecture. That will contain description of automorphisms, properties of the Bergman kernel, (non)-convexity of the domains. The talk is based on the common research with Gargi Ghosh.

  • Zywomir Dinew

    Aspects of B-regularity

    The notion of B-regularity was introduced by Sibony in his famous Duke paper from 1987. For compact sets it means that one can approximate uniformly an arbitrary continuous function by continuous plurisubharmonic functions defined on (varying) neighborhoods. We will present some new properties of B-regular compacts and domains and provide some examples. This is an ongoing research with Sl awomir Dinew.

Venue and General Information:

The workshop will be held at Institute of Mathematics and Informatics at the Bulgarian Academy of Sciences (Sofia, Acad. Georgi Bontchev Str., Block 8).

Arrival day: 11th of July, Departure day: 15th of July.

The Event is Supported by: