UFOCLAN
UFOCLAN (Universal quadratic forms and class numbers) is our number theory research group at Charles University, Faculty of Mathematics and Physics, Department of Algebra.
Team members
Faculty
- Vita Kala (associate professor from 2022)
- Martin Čech (assistant professor from 2025; postdoc 09–12/2024)
PIs
- Siu Hang “Gordon” Man (PI from 01/2025; postdoc 09/2022-12/2024)
- Pavlo Yatsyna (from 01/2024)
Postdocs
- Dayoon Park (from 03/2024)
- Giuliano Romeo (from 07/2025)
- Subham Roy (from 08/2024)
- Robin Visser (from 10/2024)
- Jongheun Yoon (from 01/2025)
- Kristýna Zemková (from 06/2025)
- Błażej Żmija (from 07/2025)
Ph.D. students
- Om Prakash (from 2023)
Mikuláš Zindulka (from 2021)
We regularly have funding for hiring new postdocs and Ph.D. students. Interested very strong candidates are welcome to email Vita with informal inquiries.
News
The excellent American Journal of Mathematics accepted one of our best papers, in which Blazej, Pavlo, and Vita proved that real quadratic fields with a universal form of given rank have density zero.
Our joint paper with Martin Widmer appeared in the prestigious multidisciplinary journal PNAS. In the paper, we show that most totally real fields (of infinite degree over Q) do not have universal forms or the Northcott property.
Daejun Kim, Seok Hyeong Lee, and Vita proved several foundational results on the general lifting problem for universal quadratic forms in a paper that was accepted by Revista Matemática Iberoamericana.
Akash Singha Roy and Stylianos Sachpazis won our recent postdoc job call. They will join our group to work on the Primus projects of Gordon and Martin.
Martin was hired for a tenure track assistant professor position at the Department of Mathematical Analysis (at our university).
With Félicien Comtat and Didier Lesesvre, Gordon established an effective version of Kuznetsov trace formula for GSp(4). The results developed in this major breakthrough will be of tremendous help in understanding the statistics of automorphic forms on GSp(4).
After too many years, Blazej, Dayoon, Kuba, Pavlo, and Vita finally finished a paper on Kitaoka’s conjecture for real quadratic fields. Combining a careful theoretical work with non-trivial computations, we prove that there are at most 13 real quadratic fields that have a universal ternary quadratic form.
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
- PI Libor Barto, 2024–2029
Intersections of algebra, geometry, and informatics - PI Jan Krajíček, 2018–2023
Methods of algebra and logic
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
- Jakub Krásenský (2018–2023)
next job: assistant professor (tenure track) at Czech Technical University in Prague, Faculty of Information Technology, Department of Applied Mathematics - Magdaléna Tinková (2017–2021)
next jobs: assistant professor (tenure track) at Czech Technical University in Prague, Faculty of Information Technology, Department of Applied Mathematics; and postdoc at TU Graz funded by Postdoc grant from Czech Science Foundation
