# 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

- Matteo Bordignon (01/2022–01/2023)
- Giacomo Cherubini (from 09/2020)
- Siu Hang “Gordon” Man (from 09/2022)
- Daniel Gil Muñoz (from 08/2021)
- Błażej Żmija (from 10/2021)

###### 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.

*In particular, Vita may accept a new Ph.D. student who would start their studies in October 2023 (an earlier start is not possible). The applications for this position will be accepted from January 1 till January 31, 2023; more information will be listed here by the end of October 2022.*

*We’ll hire a new postdoc with starting date in the first half of 2023 (at latest July 1, 2023), see here. Informal inquiries by strong candidates are welcome (by email to Vita).*

### News

Our students Matěj Doležálek and Martin Raška both got the First Prize at the International Mathematics Competition for University Students.

Apply to our new postdoc opening! (Applications should be received ideally by Sep 15.)

Vita will give an invited series of introductory lectures on universal quadratic forms at XXIII International Workshop for Young Mathematicians in Krakow in September.

Giacomo’s and Pavlo’s paper on the potential energy of algebraic integers is accepted by J. Math. Anal. Appl.

The paper by Ester, Jakub, and Martin on Pythagoras numbers in biquadratic fields got accepted by Expositiones Math.

Pavlo will soon start a new postdoc at Aalto University, where he’ll work with Camilla Hollanti.

Matěj Doležálek received the Award of The Learned Society of the Czech Republic for his work *Quaternions and universal quadratic forms over number fields*.

### 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

- 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)
- Pavlo Yatsyna (01/2020–07/2022)
*next job: postdoc at Aalto University* - 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* - Magdaléna Tinková (PhD student, 2017–2021)
*next job: tenure-track faculty at Czech Technical University, Prague*