Institute of Mathematics,

University of Szczecin,

ul. Wielkopolska 15,

70-451 Szczecin,

Poland

Email: katka314 [at] gmail.com,

fvk [at] usz.edu.pl, fvk [at] math.usask.ca

Our research interests: valuation theory, real algebra and ordered structures, model theoretic algebra;

in particular:

- general valuation theory,
- applications of valuation theory to algebraic and arithmetic algebraic geometry: local uniformization and desingularization in arbitrary characteristic and arbitrary dimension,
- model theory of valued fields (generalizations of the Ax-Kochen-Ershov Theorem, quantifier elimination, decidability),
- valuations on function fields, Zariski spaces of places,
- spaces of real places,
- ordered sets, abelian groups and fields,
- hyperfields,
- ultrametric spaces,
- fixed point theory of contracting functions (ball spaces).

The present and former Ph.D. students in our research group:

Hanna Ćmiel. She obtained her PhD in June of 2022 with a thesis on "Continuity of
roots and values for valued fields".

Alessandro Linzi. He obtained his PhD in June of 2022 with a thesis on "Algebraic
hyperstructures in the model theory of valued fields".

Piotr Szewczyk. Piotr did his Masters degree on the "Continuity of roots of polynomials
over valued fields" in 2019 with FV. He is now continuing his PhD studies at the Institute
of Algebra of the TU Dresden under the supervision of Arno Fehm and the cosupervision of
Sylvy Anscombe.

Hanna Stojałowska. Hanna did her Masters degree on "Totally positive units of a real
holomorphy ring" in 2019 with Katarzyna. Under her supervision, she is now preparing a PhD
thesis on real hyperfields.

Piotr Błaszkiewicz. Piotr did his Bachelor degree on "Algebraic Structures used for
Quantifier Elimination in Valued Fields" in 2019, and his Masters degree on
"Quantifier Elimination in valued fields with respect to the corresponding hyperfields"
in 2021, both with FV. He is now continuing his PhD studies at the Institute of Mathematics
of the University of Wroclaw under the supervision of Piotr Kowalski and the cosupervision
of FV.

Publications with participation of our Ph.D. students:

- Hanna Ćmiel, Alessandro Linzi, Piotr Szewczyk and Piotr Błaszkiewicz:
*Caristi-Kirk and Oettli-Théra ball spaces, and applications*, J. Fixed Point Theory Appl.**21**(2019), no. 4, Paper No. 98

(pdf file) - Hanna Ćmiel, Franz-Viktor Kuhlmann and Katarzyna Kuhlmann:
*A generic approach to measuring the strength of completeness/compactness of various types of spaces and ordered structures*, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas**115**, Article number: 156 (2021)

(pdf file) - Alessandro Linzi and Hanna Stojałowska:
*Hypervaluations on hyperfields and ordered canonical hypergroups*, to appear in the Iranian journal of mathematical sciences and informatics

(pdf file) - Hanna Ćmiel, Franz-Viktor Kuhlmann and Piotr Szewczyk:
*On the continuity of roots of polynomials over valued fields*, Communications in Algebra**51**(2023), 1383-1412

(pdf file)

- Katarzyna Kuhlmann, Alessandro Linzi and Hanna Stojałowska:
*Orderings and valuations in hyperfields*, J. Algebra**611**(2022), 399-421

(arXiv) - Alessandro Linzi and Pierre Touchard:
*On the hyperfields associated to valued fields*

(arXiv) - Alessandro Linzi:
*Notes on valuation theory for Krasner hyperfields*

(arXiv)

Support for young mathematicians:

We were and still are particularly active in the support of mathematicians early on in their career, giving advice on their research projects and articles in preparation. We invite them to visit us for these purposes at our Institute, and we organize conferences and workshops specially geared towards young mathematicians. Everyone who is interested in learning about our projects and areas of expertise is cordially invited to visit us or to contact us by email.

We support our students in building up connections with other researchers around the world, either by visiting them, or by inviting these researchers to visit us. Our students have been actively participating in the conferences and workshops we organize, such as:

organized by Franz-Viktor Kuhlmann and Katarzyna Kuhlmann

Institute of Mathematics, University of Szczecin, May 8-13, 2018

12th Czech, Polish and Slovak Conference on Number Theory and 21st Colloquiumfest

Bedlewo (Poland), June 24-29, 2018

organized by Franz-Viktor Kuhlmann, Katarzyna Kuhlmann and Franciszek Prus-Wiśniowski

Institute of Mathematics, University of Szczecin, May 31 to June 3, 2019

organized by Franz-Viktor Kuhlmann and Franciszek Prus-Wiśniowski

Institute of Mathematics, University of Szczecin, March 24 and 25, 2022

Other papers written with mathematicians early in their career are:

joint paper with C. Visan,

joint paper with J. Dobrowolski,

joint paper with S. Durhan (formerly Azgin),

joint paper with S. Anscombe,

joint paper with I. Vlahu (former Masters student of FV),

joint paper with F. Sonaallah (former Masters student of FV and Katarzyna),

joint paper with K. Pal (former postdoctoral fellow of FV on a scholarship from PIMS),

joint paper with A. Naseem (former postdoctoral fellow of FV),

joint paper with J. Novacoski (former PhD student of FV),

a first joint paper and a second joint paper with A. Dutta,

and quite a number of joint papers with FV's former PhD student Anna Rzepka (formerly Blaszczok) (see FV's list of papers).

International connections and collaborations:

We have connections to individual researchers and mathematical centers at the following
universities:

Brazil: ICMC - USP Sao Carlos,

Czech Republic: Institute of Mathematics of the Czech Academy of Sciences,

France: Institut Mathématique de Jussieu - Paris Rive Gauche, Toulouse,

Germany: Münster, Dresden, Hochschule RheinMain,

Poland: University of Wroclaw, University of Silesia at Katowice,

USA: University of Missouri - Columbia, University of Pennsylvania, University of Hawaii,
Graduate Center New York.

The Valuation Theory Home Page:

We are maintaining a web site that gives information on what is going on in valuation theory, announces conferences andcontains a preprint repository:

Conferences:

We have organized and are organizing a number of conferences and workshops. Detailed information
and links can be found on The Valuation Theory Home Page. Since the year
2000, FV has organized the Colloquiumfest, a small and mostly low budget conference, with various
co-organizers. It also has taken place at various universities and venues: University of
Saskatchewan, CUNY Graduate Center in New York, IHP Paris, Bogazici University in Istanbul,
University of Valladolid, University of Central Lancashire, University of Szczecin, Federal
University of São Carlos in Brazil, Institute of Mathematics of the Czech Academy of Sciences
in Prague.

Would you like to co-organize a Colloquiumfest at your institution? Just contact us!

Furthermore, FV initiated and co-organized two big international Valuation Theory Conference, each of which was followed by the publication of proceedings volumes. The third one is to follow in the next years - perhaps in Poland?

Saskatoon, Canada, 1999

Segovia, Spain, July 18 to 30, 2011

*Last update: May 24, 2023*