**UNION OF BULGARIAN MATHEMATICIANS**

**INSTITUTE OF MATHEMATICS AND INFORMATICS, BULGARIAN ACADEMY OF SCIENCES**

**NATIONAL MATHEMATICS COLLOQUIUM**

The next meeting of the National Mathematics Colloquium will be held on **September 4, 2019 (Wednesday) at 16:15 in the Conference Room **of the Institute of Mathematics and Informatics, Acad. G. Bonchev Street, Block 8

A talk on:

**The Squeezing Function**

will be delivered by **Prof. John Erik Fornæss, Norwegian Academy of Science and Letters, Norwegian University of Science and Technology, Trondheim.**

Everybody is invited.

Head of the Colloquium: Acad. P. Popivanov

**Abstract. **In complex analysis the most important domain is the unit disc. In fact all domains (at least simply connected and bounded) are biholomorphic, i.e. analytically equivalent, to the disc.

In higher dimension, the natural analogue is the unit ball. But in higher dimension, the general domain is not biholomorphic to the ball. A basic question is then how well a general domain can be approximated by the ball. If we have a ball 𝔹_{𝑟} of radius 𝑟<1 contained in the unit ball 𝔹_{1}, then a domain 𝑈 with 𝔹_{𝑟} contained in 𝑈 contained in 𝔹_{1} is said to be squeezed between the two balls. The larger we can choose 𝑟 the closer the domain 𝑈 is to the ball.