International Workshop

Invariant Distances and Metrics in Complex Analysis

July 8 – 10, 2026,
Sofia, Bulgaria

in the frame of the International Conference “Mathematics Days in Sofia – 2026”

The 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 de Toulouse, France

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

Participants

  • Ahmed Yekta Ökten,
    Università di Roma “Tor Vergata”, Italy

  • Anand Chavan,
    Jagiellonian University, Poland

  • Armen Edigarian,
    Jagiellonian University, Poland

  • Feng Rong,
    Shanghai Jiao Tong University, China

  • John Erik Fornæss,
    Norwegian University of Science and Technology, Norway

  • Leandro Arosio,
    Università di Roma “Tor Vergata”, Italy

  • Łukasz Kosiński,
    Jagiellonian University, Poland

  • Marcin Tombiński,
    Jagiellonian University, Poland
  • Matteo Fiacchi,
    Università di Roma “Tor Vergata”, Italy

  • Nikolai Nikolov,
    Institute of Mathematics and Informatics, Bulgaria

  • Pascal J. Thomas,
    Université de Toulouse, France

  • Peter Pflug,
    Carl von Ossietzky Universität Oldenburg, Germany

  • Pouriya Torkinejad-Ziarati,
    Université de Toulouse, France

  • Sławomir Dinew,
    Jagiellonian University, Poland

  • Włodzimierz Zwonek,
    Jagiellonian University, Poland

  • Żywomir Dinew,
    Jagiellonian University, Poland

Program and Abstracts

Hall 278, Institute of Mathematics and Informatics

8th July (Wednesday)
Chair: Pascal J. Thomas
14:00 Sławomir Dinew: Affine Hartogs Figures and Applications
14:50 Matteo Fiacchi: The Pluricomplex Poisson Kernel for Convex Finite Type Domains
15:40 Coffee break
Chair: Pascal J. Thomas
16:10 John Erik Fornæss: Kobayashi Metric on Domains in ℂ²
17:00 Ahmed Yekta Ökten: On Gehring-Hayman Theorem for the Minimal Metric
18:30 Welcome party of the workshop
9th July (Thursday)
Chair: John Erik Fornæss
14:00 Leandro Arosio: The Number of Generators of the Algebra of Continuous Functions on a Compact Manifold
14:50 Pouriya Torkinejad-Ziarati: Cyclicity in Dirichlet-Type Spaces Dα(𝔹²) on the Unit Ball of ℂ²
15:40 Coffee break
Chair: John Erik Fornæss
16:10 Marcin Tombiński: Caratheodory Surfaces and Lempert Theory
17:00 Żywomir Dinew: Determining Sets for Subharmonic and Plurisubharmonic Functions
18:30 Sightseeing tour – Sofia historical center
20:00 Official dinner, Sofia Balkan Palace Hotel
10th July (Friday)
Chair: Peter Pflug
10:00 Feng Rong: On the Schwarz Constant and the Lu Function of Bounded Symmetric Domains
10:50 Armen Edigarian: Kobayashi Isometry and Holomorphic Coverings
11:40 Lunch break
Chair: Peter Pflug
13:00 Anand Chavan: Burns-Krantz Rigidity
13:50 Włodzimierz Zwonek: Reinhardt Domains Determined by Their Endomorphisms

Plenary talk

We shall discuss a classical interpolation problem that was solved many decades ago and explain why it remains both important and fascinating today. We will describe its origins in engineering and present modern approaches to the subject. We shall also discuss its deep connections with Operator Theory and the Theory of Several Complex Variables.

Presentation

Workshop talks

The classical Gehring-Hayman theorem states that on simply connected planar domains, the Euclidean lengths of hyperbolic geodesics are bounded above up to a multiplicative constant by Euclidean lengths of any other curve joining their end points. When the domain is convex, this means that hyperbolic geodesics are quasi-geodesics for the Euclidean distance. With methods of the Lempert theory, Kosiński, Nikolov and Thomas extended the Gehring-Hayman theorem to regular enough strongly pseudoconvex domains endowed with the Kobayashi distance.

The minimal distance, introduced recently by Forstnerič and Kalaj, is the real analogue of the Kobayashi distance. In this talk, we discuss our work in progress with Matteo Fiacchi and Nikolai Nikolov on the Gehring-Hayman theorem on strongly convex domains endowed with the minimal distance. Our approach relies on Gromov hyperbolicity methods and global estimates of the minimal distance obtained by Fiacchi and Nikolov.

Presentation

In this talk, we will discuss an approach based on Lempert theory to study Burns-Krantz rigidity. In particular, we will prove Burns-Krantz rigidity for certain special convex complex ellipsoids, including the n-dimensional diamond, at all boundary points, irrespective of smoothness.

Presentation

We consider the following problem. Assume that π : X → Y is a holomorphic covering and that any 𝔻 → X (Kobayashi/Lempert) isometry is holomorphic
or anti-holomorphic. Whether any 𝔻 → Y (Kobayashi/Lempert) isometry is holomorphic or anti-holomorphic? We show that in some cases it is true
(e.g. X is a bounded strictly convex domain).

Presentation

In a 1958 paper of K.H. Look (Q.K. Lu), he introduced the invariant “Schwarz constant” on bounded homogeneous domains and made explicit computations for classical Cartan domains of type I-IV. In the same paper, Lu also presented his famous inequality that the Bergman metric dominates the Caratheodory metric. In this talk, we give the Schwarz constant of all bounded symmetric domains. We also introduce and study the Lu function (in relation with the Lu inequality) of bounded symmetric domains.

This is a joint work with Zhilin Liu.

Presentation

Fatou components basically never have smooth boundary. This makes it difficult to estimate the boundary behaviour of invariant metrics. We consider the problem about Kobayashi density near the boundary of the backward orbit of a given point in a Fatou component.

This is joint work in progress with Mi Hu (Monash University, Melbourne) and Feng Rong (Shanghai Jiao Tong).

Presentation

Given a smooth compact manifold X of dimension n, what is the minimal number of smooth functions that generate a dense subalgebra of the algebra of complex-valued continuous functions? Topological considerations show that this number is at least n+1. I will show that this number is exactly n+1 if n is smaller than or equal to 11. To prove this, we will study the minimal dimension N such that X admits an embedding in CN with polynomially convex image.

This is based on joint work with Håkan Samuelsson Kalm and Erlend Fornaess Wold.

We study the relationship between non-degenerate three-point Pick interpolation problems, Carathéodory surfaces, and uniqueness varieties in the polydisc. Given interpolation data generating a uniqueness variety

U(a1, …, an) ⊂ 𝔻n,

we investigate its realization as a Carathéodory surface of the form

Lα = {(x, y, α3(x, y), …, αn(x, y)) : (x, y) ∈ Dα},

where the coordinate functions αj arise from rational inner maps. We establish a correspondence between the geometry of these surfaces and the combinatorics of the interpolation data by proving that the number of faces of Lα coincides with the number of sides of the polygon

conv(a1, …, an).

This provides a geometric characterization of uniqueness varieties through Carathéodory geometry and leads naturally to the notion of basic Roman surfaces. Using this framework, we analyze the structure and uniqueness of complex geodesics, showing how extremal problems for the Carathéodory metric encode rigidity phenomena for interpolation. These results reveal a deep interplay between Pick interpolation, convex-geometric structures, and the global geometry of Carathéodory surfaces.

Presentation

Bracci-Patrizio-Trapani introduced the pluricomplex Poisson kernel in strongly convex domains as a generalization of the classical Poisson Kernel in the disk. This kernel is a solution to a homogeneous Monge-Ampère problem with a simple singularity at the boundary, and it turns out to be (minus) the normal derivative at the boundary of the Green function. Furthermore, its sublevel sets are the horospheres with respect to the Kobayashi distance. I will show how to generalize this kernel in convex finite type domains, using a new approach based on metric geometry.

This is a joint work with L. Arosio and F. Bracci.

Presentation

Motivated by cyclicity results for stable polynomials, we construct non-polynomial examples with prescribed critical cyclicity thresholds. The constructions are based on compact boundary zero sets lying in three different geometric situations: transversal curves, complex tangential curves, and totally real sets. In each case, we build holomorphic functions with precise estimates in terms of the Korányi distance to the zero set, using interpolation results of Bruna–Ortega and Chaumat–Chollet. These estimates allow us to determine exactly for which α the resulting functions are cyclic in Dα(𝔹2).

The different cases can be unified by the Korányi Hausdorff dimension: the critical index satisfies αc = 2 – dimH,K(Z(f) ∩ ∂𝔹2).

This gives critically cyclic functions realizing a continuum of critical indices in Dirichlet-type spaces on the unit ball in the range [1/2, 2].

One of the classical characterizations of pseudoconvexity is through (holomorphic images of) Hartogs figures. In an ongoing project with T.
Pawlaschyk (Wuppertal) we consider affine rather than holomorphic images of (standard) Hartogs figures. The aim of the talk will be to describe
some geometric and function theoretic phenomena in such a setting.

The following result will be presented. Pseudoconvex Reinhardt domains (not necessarily bounded) in dimension two with isomorphic semigroups of holomorphic endomorphisms are biholomorphically or anti-biholomorphically equivalent.

Presentation

We describe which sets are determining for the families of subharmonic and plurisubharmonic functions, as well as for some subfamilies of these classes of functions. We discuss the differences between the subharmonic and plurisubharmonic settings, and provide some examples.

Presentation

Venue and General Information

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

Arrival day: 7th of July, Departure day: 11th of July, 2026.

The Event is Supported by: