# Students

### Students advised

###### Ph.D.

Om Prakash, Representations of algebraic integers by higher degree forms (from 2023)

Ester Sgallová, n-universal quadratic forms over number fields (from 2021)

Mikuláš Zindulka, Arithmetics of number fields: partitions, norms, and quadratic forms (from 2021)

Jakub Krásenský, Universal quadratic forms over orders in number fields (2018–2023)

*next job: assistant professor (tenure track) at Czech Technical University in Prague, Faculty of Information Technology, Department of Applied Mathematics*

Magdaléna Tinková, Arithmetics of number fields and generalized continued fractions (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*

###### Master’s

Matěj Doležálek (from 2023)

Martin Raška (from 2021)

Martin Kuděj, Semilattices and indecomposable elements (2024)

Bára Tížková, Adeles and class fields (2023)

Sára Vyhnalová, Ideal lattices in cryptography (co-advised by Pavlo Yatsyna, 2021)

Kristína Mišlanová, Quaternion algebras and units (2021)

Ester Sgallová, Periodicity of Jacobi-Perron algorithm (co-advised by Magda Tinková, 2021)

*2nd place in SVOC research competition*Lucien Šíma, Finitely generated semirings and semifields (2021)

*Pavel Surý, Local-global principle for quadratic forms (2020)*

Martin Čech, Pretentious approach to analytic number theory (2018)

Kristýna Zemková, Composition of quadratic forms over number fields (2018)

*3rd place in SVOC research competition*

*Dean’s prize*

Dominik Lachman, Bruhat-Tits buildings (2017)

*1st place in SVOC research competition*

*Dean’s prize*

Jakub Hlavnička (FJFI ČVUT), Products of primes in arithmetic sequences and prime number theorem (2016)

Maroš Hrnčiar, Solving diophantine equations by factorization in number fields (2015)

###### Bachelor’s

Natália Bátorová, Arithmetic-geometric mean sequences and elliptic curves over finite fields (co-advised by Stevan Gajović, from 2023)

Jan Kotyk, Congruent numbers, elliptic curves, and L-functions (co-advised by Stevan Gajović, from 2023)

Žaneta Lipertová (from 2023)

Emma Pěchoučková (from 2023)

Anna Růžičková (co-advised by Martin Raška, from 2023)

Tomáš Sklenář, Proving combinatorial identities via formal power series (co-advised by Siu Hang Man, from 2022)

František Couf, Fourier transform on polytopes and tiling with rectangles (co-advised by Mikuláš Zindulka, 2023)

Simona Hlavinková, The structure of generalized Pythagorean triples (2023)

Veronika Jarrahová, Cyclotomic extensions and the Kronecker-Weber theorem (2023)

Filip Kucka, RSA in number fields and on lattices (2023)

David Stern, Partitions of totally positive elements in real quadratic fields (co-advised by Mikuláš Zindulka, 2023)

Matěj Doležálek, Subfields of number field extensions and quadratic forms (2022)

*3rd** place in SVOC research competition*

Daniela Lněničková, Geometric solution of quadratic diophantine equations (2022)

Martin Raška, Sums of squares in number fields (2021)

*Dean’s prize Honorable mention in SVOC research competition*Bára Tížková, Universal quadratic forms and estimates of traces of algebraic integers (2021)

Ondrej Bínovský, Imaginary quadratic fields with class number 1 (2021)

Matěj Doležálek, Quaternions and universal quadratic forms over number fields (2021, unofficial research project)

Award of The Learned Society of the Czech Republic

Award of The Learned Society of the Czech Republic

*1st place in SVOC research competition*

Alexandr Beneš, Counting extensions of imaginary quadratic fields (2020)

*Dean’s prize*

Veronika Hájková, Pythagoras numbers of orders in number fields (2020)

Martin Kuděj, Continued fractions with prescribed period (2020)

Kateřina Bžatková, Visibly irreducible polynomials (2019)

Kristína Mišlanová, Matrix of Legendre symbols (2019)

Sára Vyhnalová, Solovay-Strassen primality test (2019)

Anh Dung Le, Bernoulli numbers and ideal class groups (2017)

Martin Čech, Algebraic proofs of Dirichlet’s theorem on arithmetic progressions (2016)

Josef Svoboda, Universal quadratic forms over number fields (2016)

###### High school (SOC research competition)

Matěj Doležálek, Quaternions and generalizations of four-square theorem (2019)

*1st place in SOC research competition, České hlavičky award*Matěj Doležálek, The congruent number problem (2018)

List of supervised theses at CUNI

### Student articles

See yellow authors here.

### Student grants

Number systems in lattices and number field orders

- J. Krásenský (PI), K. Mišlanová, E. Sgallová, M. Zindulka
- GAUK, 2020–2022

Indecomposable integers and universal quadratic forms

- M. Tinková (PI), M. Čech, J. Krásenský, K. Zemková
- GAUK, 2018–2020
- the outcomes of the grant were evaluated by the grant agency as
*exceptionally good*

Several smaller Student faculty grants

### Tips & links

Jak na doktorát do USA (How to apply for PhD in the US, in Czech)

Na internetu je spousta příruček na to, jak psát matiku v angličtině, třeba tahle.

Teorie čísel na matfyzu

Jak na vybírání vedoucího