# Seminar SAAAJ, Ljubljana 26.11.

Dragi kolegi!

Obveščava vas, da bo Seminar za analizo in algebro Alpe-Jadran (SAAAJ) imel ponovno srečanje v soboto, 26.11.2202, na FMF v Ljubljani. Med 10.00 in 13.30 se bodo zvrstila predavanja naslednjih predavateljev:

Urban Jezernik Dražen Adamović Marko Kandić Dijana Ilišević (Naslovi + povzetki so spodaj)

Po predavanjih bo organizirano skupno kosilo v Via Bona.

Prosim, da do srede, 23.11, označite svojo udeležbo v tabeli: https://docs.google.com/spreadsheets/d/1kS3AIWg4hm68Fwle-GxsIbgC8q_qguFzYl5CMASGBik/edit?usp=sharing https://docs.google.com/spreadsheets/d/1kS3AIWg4hm68Fwle-GxsIbgC8q_qguFzYl5CMASGBik/edit?usp=sharing

Lep pozdrav, Igor in Marjeta

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Speaker: Urban Jezernik Title: 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.

Speaker: Dražen Adamović Title: 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.

Speaker: Marko Kandić Title: 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.

Speaker: Dijana Ilišević Title: 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.