**
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)

### 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)

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