We are happy to announce** fourth meeting of Croatian – Slovenian Seminar for Analysis and Algebra (Alpe – Adria)** that will be held on **Saturday, November 26, 2022, at University of Ljubljana, Faculty of Mathematics and Physics**, according to following schedule:

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**10:00–10:45** **Urban Jezernik**: *Diameters of groups*

__Abstract:__ The diameter of a finite group G equipped with a generating set S is the smallest number k so that every element of G can be written as a product of at most k elements from S. We will take a look at how large or small these diameters can (conjecturally) be, and what the generic situation is like.

**10:50–11:35** **Dražen Adamović**: *On recent realizations of affine Kac-Moody vertex algebras and W-algebras*

__Abstract:__ Vertex operator constructions of affine Kac-Moody Lie algebras, discovered around 1980, represent one of the most important motivations for the development of modern vertex algebra theory. In the last few years, new explicit realizations of affine vertex algebras have been investigated, motivated by the study of modern physical theories and their correspondence with the theory of vertex algebras. We will present our discoveries in this direction, published in several articles, and discuss applications in the representation theory. A particular emphasis will be put on the Inverse quantum Hamiltonian reduction.

**12:00–12:45** **Marko Kandić**: *Prime ideals in vector lattices*

__Abstract:__ In this talk we consider the set of all prime ideals in vector lattices and how the properties of the prime ideals structure the vector lattice in question. The different properties that will be considered are firstly, that there are only finitely many prime ideals, secondly, that every prime ideal is principal, and lastly, that every ascending chain of prime ideals is stationary.

**12:50–13:35** **Dijana Ilišević**: *On isometries and related mappings*

__Abstract:__ An isometry is a mapping between metric spaces which preserves distances between elements. The study of isometries can be considered as one of the principal mathematical topics from the earliest times, and it is still a very active research topic. The study of isometries between Banach spaces began at the very beginnings of the theory of Banach spaces, with the classical Banach-Stone theorem. Today there are many Banach-Stone type results in various settings. Other classical (but revived) theorems in this research field are Mazur-Ulam theorem and Wigner’s theorem.

This talk aims to provide a flavor of a wide variety of problems related to isometries. Introductory material will be combined with several recent results. Joint results with Slovenian mathematicians will be particularly highlighted.

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