Home page of the research group of
Katarzyna and Franz-Viktor Kuhlmann
Institute of Mathematics,
University of Szczecin,
ul. Wielkopolska 15,
Email: katarzyna.kuhlmann [at] usz.edu.pl,
fvk [at] usz.edu.pl, fvk [at] math.usask.ca
Our research interests:
valuation theory, real algebra and ordered structures, model theoretic algebra;
- 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,
- ultrametric spaces,
- fixed point theory of contracting functions (ball spaces).
The Ph.D. students in our research group:
Hanna Stojałowska (Hanna did her Masters degree on "Totally positive units of a real
holomorphy ring" in 2019 with Katarzyna)
Piotr Szewczyk (Piotr did his Masters degree on the "Continuity of roots of polynomials over
valued fields" in 2019 with FV)
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)
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
- 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)
- Alessandro Linzi and Hanna Stojałowska: Hypervaluations on hyperfields and ordered canonical hypergroups, to appear in the Iranian journal of mathematical sciences and informatics
- Hanna Ćmiel, Franz-Viktor Kuhlmann and Piotr Szewczyk: On the continuity of roots
of polynomials over valued fields, submitted
- Katarzyna Kuhlmann, Alessandro Linzi and Hanna Stojałowska: Orderings and
valuations in hyperfields, submitted
Currently suggested topics for Master's and Ph.D. studies in our group:
- Valuations on rational function fields in one variable: comparison of key polynomials,
minimal pairs, generating sequences and other means of their classification and description,
with applications to local uniformization.
- Valuations on rational function fields in several variables: their construction and description.
- Valuations on algebraic function fields: properties of their Zariski spaces, structure of valued function fields with defect.
- The valuation theory of deeply ramified fields, generalizations of the theory of tame fields.
- Algebra and model theory of extremal fields.
- Quantifier elimination in valued fields.
- Decidability of Laurent series fields over finite fields, and of their perfect hulls.
- Theorems on the continuity of roots.
- Which topological spaces can be realized as spaces of real places?
- General properties and classification of ball spaces, application to fixed point and coincidence theorems in various mathematical areas.
- Topological fixed point theorems.
Support for young mathematicians:
We 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 are
actively participating in the conferences and workshops we organize, such as:
Workshop on "Valuations on Rational Function
organized by Franz-Viktor Kuhlmann and Katarzyna Kuhlmann
Institute of Mathematics, University of Szczecin, May 8-13, 2018
Graduate Students' Workshop
organized by Franz-Viktor Kuhlmann, Katarzyna Kuhlmann and Franciszek Prus-Wiśniowski
Institute of Mathematics, University of Szczecin, May 31 to June 3, 2019
Second Graduate Students'
We organized and led a working group on Fixed Point Theory for young mathematics students at a
summer school of the Deutsche Studienstiftung, August 6-18, 2017. This resulted in a
joint paper with one of the participants,
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),
joint paper with A. Dutta,
and quite a number of joint papers with FV's former PhD student Anna Blaszczok
(see FV's list of papers).
International connections and collaborations:
We have connections to individual researchers and mathematical centers at the following
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:
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 the year 2010 the Colloquiumfest joined forces with the Czech, Polish and Slovak Conferences
on Number Theory to form the biannual
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?
Last update: February 20, 2022