UFOCLAN

UFOCLAN (Universal quadratic forms and class numbers) is the number theory research group at Charles University, Faculty of Mathematics and Physics, Department of Algebra.

Team members

  • Vita Kala
PIs
Postdocs
Ph.D. students

We regularly have funding for hiring new postdocs and Ph.D. students. Interested very strong candidates are welcome to email Vita with informal inquiries.

In particular, we

  • have two 3-year postdoc openings, and
  • may hire a few Ph.D. students from October 2025. Please see here for more information.

News

January 4, 2025

Jongheun Yoon joined UFOCLAN as our newest postdoc and Stevan Gajovic left for a position at MPIM Bonn.

December 17, 2024

Selecta Math. accepted the paper by Gordon and Vita that establishes a new connection between sails, a key notion in the geometric theory of generalized continued fractions, and arithmetic of totally real number fields, specifically, universal quadratic forms and indecomposables.

October 24, 2024

We finally took a new team photo! (Well, three years after the previous one, let’s hope we’ll be faster next time.)

October 5, 2024

Vita will give an invited talk at the conference Recent advances in Mathematics and related areas at SRM AP, India, in January 2025. Just like at the previous two editions, there will be many excellent speakers!

September 27, 2024

Lots of recent progress on universal forms and Northcott property over infinite extensions: With Martin Widmer, we’ve finished a paper showing that they exist only very rarely, and our first paper on the topic was accepted by JLMS.

September 13, 2024

Two papers on the universality of higher degree forms written by our first year Ph.D. student Om Prakash were recently accepted for publication – one to Math. Nachr. (joint with Vita) and one to Int. J. Number Theory.

September 13, 2024

Our students were very active and successful in the Student NT Seminar last year: They wrote two papers on the universality of generalized quadratic forms.

July 28, 2024

Vita was invited to give a talk at the 8th Number Theory Meeting in Torino, Italy.

Show all news.

Funding

Universal quadratic forms and class numbers

GAČR Junior Star project
PI Vita Kala
from the Czech Science Foundation GAČR, 2021–2025
success rate 9%, total budget 1 000 000 USD

Multiple Dirichlet series and analytic number theory

Primus grant
PI Martin Čech
postdocs (partly) supported: TBA
from Charles University, 2025–2028

Automorphic forms for symplectic groups via trace formula

Primus grant
PI Siu Hang “Gordon” Man
postdocs (partly) supported: TBA
from Charles University, 2025–2028

Statistical properties of totally real number fields

Primus grant
PI Pavlo Yatsyna 
postdocs (partly) supported: Martin Čech, Nicolas Daans, Siu Hang “Gordon” Man, Robin Visser
from Charles University, 2024–2027

Universal quadratic forms: geometry and analysis

Primus grant
PI Vita Kala
from Charles University, 2020–2022

Quadratic forms and numeration systems over number fields

GAČR Junior grant
PI Vita Kala
from the Czech Science Foundation GAČR, 2017–2019
outcomes of the grant were evaluated by the grant agency as excellent (top 20%)

University research center UNCE

Our seminars

Number Theory Seminar
Algebra Colloquium
If you want to give a talk in either of these seminars, please let one of the organizers (eg Vita) know!
We have mailing lists for both seminars with weekly talk announcements – if you want to join them, please also let Vita know.

Team publications

See here.

Past team members

Postdocs
  • Matteo Bordignon (01/2022–01/2023)
    next job: postdoc at KTH Stockholm
  • Giacomo Cherubini (09/2020–10/2022)
    next job: permanent position at Sapienza University of Rome
  • Nicolas Daans (01/2023–09/2024)
    next job: postdocs at KU Leuven and University of Mons
  • Alessandro Fazzari (09–12/2021)
    next job: postdoc at American Institute of Mathematics
  • Stevan Gajović (03/2023–12/2024)
    next job: postdoc at MPIM Bonn
  • Daniel Gil Muñoz (08/2021–06/2023)
    next job: postdoc at University of Barcelona
  • Tomáš Hejda (01/2017–12/2019)
    next job: work for Overleaf
  • Mentzelos Melistas (01/2023–08/2023)
    next job: tenure track lecturer at University of Twente
  • Eric Nathan Stucky (08/2021–08/2022)
    next job: adjunct faculty member at Champlain College
  • Tomáš Vávra (01/2017–08/2020)
    next job: postdoc at University of Waterloo
  • Ezra Waxman (08/2018–07/2019)
    next job: postdoc at Dresden University with Minerva Fellowship
  • Pavlo Yatsyna (01/2020–07/2022)
    next job: postdoc at Aalto University
  • Błażej Żmija (10/2021–06/2023)
    next job: postdoc at Polish Academy of Sciences
Ph.D. students