WORKSHOP
on
"VALUATIONS ON RATIONAL FUNCTION FIELDS"


Department of Mathematics and Physics
University of Szczecin
ul. Wielkopolska 15
70-451 Szczecin, Poland


Dates:
Monday to Sunday, May 7-13, 2018

Organized by:
Katarzyna and Franz-Viktor Kuhlmann (Institute of Mathematics, University of Szczecin, Poland),

with the generous support of:
the Faculty of Mathematics and Physics and the Institute of Mathematics of the University of Szczecin


The purpose of the workshop was:
1) to gather comprehensive information about the extension of valuations from a field K to the rational function field K(x) and to arrive at a synthesis of the various approaches and tools (key polynomials, generating sequences, minimal pairs, pseudo Cauchy sequences and approximation types, power series);
2) to discuss the open problems about extensions to rational function fields in several variables and related objects (such as e.g. R((x,y)) ).

Poster for the Workshop: A3 - A4


The list of participants included:

Eberhard Becker (University of Dortmund, Germany)
Anna Blaszczok (University of Silesia at Katowice, Poland)
Olga Kashcheyeva (University of Illinois at Chicago, USA)
Hagen Knaf (Hochschule Rhein Main, Wiesbaden, Germany)
Wael Mahboub (Beirut, Lebanon)
Edward Mosteig (Loyola Marymount University, USA)
Josnei Novacoski (Sao Paulo, Brazil)
Miguel Ángel Olalla Acosta (Sevilla, Spain)
Giulio Peruginelli (University of Padova, Italy)
Bernd Schober (Hannover, Germany)
Bernard Teissier (Institut Mathématique de Jussieu-Paris Rive Gauche, France)
Michel Vaquié (Université Paul Sabatier, Toulouse, France)


Schedule

Abstracts

Conference photo 1
Conference photo 2



Materials

Hanna Cmiel and Piotr Szewczyk: A short introduction to notions and results by Alexandru, Popescu, Zaharescu and Khanduja (Beamer presentation)
Sudesh Kaur Khanduja: Interplay between augmented valuations, key polynomials and minimal pairs (Beamer presentation)
Ed Mosteig: Reversely Well-Ordered Valuations on Polynomial Rings in Two Variables (Beamer presentation)
Ed Mosteig: Well-Ordered Valuations on Rational Function Fields in Two Variables preprint on arXiv
Josnei Antonio Novacoski: Key Polynomials and Minimal Pairs (pdf file)
Michel Vaquié: Famille admise associée à une valuation de K(x) (pdf file)



ALANT 5 - Joint Conferences on Algebra, Logic and Number Theory
12th Czech, Polish and Slovak Conference on Number Theory and 21st Colloquiumfest
Bedlewo (Poland), June 24-29, 2018

The Valuation Theory Home Page


Last update: September 13, 2018 --------- created and maintained by Franz-Viktor Kuhlmann