# 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)
- Pavlo Yatsyna (PI)

###### Postdocs

- Nicolas Daans (from 01/2023)
- Stevan Gajović (from 03/2023)
- Siu Hang “Gordon” Man (from 09/2022)
- Dayoon Park (from 03/2024)

###### PhD students

- Om Prakash (from 2023)
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

Four of us (Gordon, Pavlo, Stevan, Vita) are enjoying the 8th Rome Number Theory Symposium.

Martin Widmer has visited us in Prague, mainly for discussions about infinite extensions, Northcott property, and quadratic forms.

Gordon and Vita finished an exciting paper 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.

Pavlo’s and Vita’s recent job call was won by Martin Čech, Subham Roy, and Robin Visser – they will join our team during the Summer.

Dayoon Park, an expert in quadratic lattices and m-gonal forms, joined UFOCLAN as a new postdoc.

### Funding

###### GAČR Junior Star project

from the Czech Science Foundation GAČR, 2021–2025

success rate 9%, total budget 1 000 000 USD

###### Primus grant

*Statistical properties of totally real number fields*

PI Pavlo Yatsyna

postdocs (partly) supported: Nicolas Daans, Siu Hang “Gordon” Man

from Charles University, 2024–202*7*

###### 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 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* - Alessandro Fazzari (09–12/2021)
*next job: postdoc at American Institute of Mathematics* - 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*