# UFOCLAN

UFOCLAN (**U**niversal quadratic **fo**rms and **cla**ss **n**umbers) is the number theory research group at Charles University, Faculty of Mathematics and Physics, Department of Algebra.

### Team members

- Vita Kala (PI)

###### Postdocs

- Nicolas Daans (01–11/2023)
- Stevan Gajović (from 03/2023)
- Daniel Gil Muñoz (08/2021–06/2023)
*next job: postdoc at University of Barcelona* - Siu Hang “Gordon” Man (from 09/2022)
- Mentzelos Melistas (from 01/2023)
- Błażej Żmija (10/2021–06/2023)
*next job: postdoc at Polish Academy of Sciences*

###### PhD students

Jakub Krásenský (from 2018)

Ester Sgallová (from 2021)

Mikuláš Zindulka (from 2021)

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

### News

Two of our postdocs will soon start their new jobs – Błażej at the Polish Academy of Sciences, and Daniel at the University of Barcelona.

Vita was elected chair of the evaluation panel for mathematics and computer science at Czech Science Foundation.

Giacomo Cherubini, our recent postdoc, received the Bolzano Award for his work on *Prime geodesic theorem*.

In our perhaps best paper so far, Blazej, Pavlo, and Vita proved that real quadratic fields with a universal form of given rank have density zero. This result concludes a part of the story that started eight years ago when Valentin Blomer and Vita constructed the first very sparse sequence of quadratic fields without n-ary universal forms.

Vita wrote a survey paper that gives a (hopefully) accessible overview of our research in the last few years – have a look!

### Funding

###### GAČR Junior Star project

from the Czech Science Foundation GAČR, 2021–2025

success rate 9%, total budget 1 000 000 USD

###### Primus grant

*Universal quadratic forms: geometry and analysis*from Charles University, 2020–2022

###### GAČR Junior grant

*Quadratic forms and numeration systems over number fields*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 Jan Krajíček*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

- 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* - Alessandro Fazzari (09–12/2021)
*next job: postdoc at American Institute of Mathematics* - Tomáš Hejda (01/2017–12/2019)
*next job: work for Overleaf* - 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* - Magdaléna Tinková (PhD student, 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*