Students

Students advised

Ph.D.

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 (from 2018)
Magdaléna Tinková, Arithmetics of number fields and generalized continued fractions (2017–2021)
     next job: assistant professor (tenure track) at Czech Technical University in Prague, Faculty of Information Technology, Department of Applied Mathematics

Master’s

Martin Kuděj (from 2021)
Martin Raška (from 2021)
Bára Tížková (from 2021)
Sára Vyhnalová, Ideal lattices in cryptography (co-advised by Pavlo Yatsyna, 2021)
Kristína Mišlanová, Quaternion algebras and units (2021)
Lucien Šíma, Finitely generated semirings and semifields (2021)
Ester Sgallová, Periodicity of Jacobi-Perron algorithm (co-advised by Magda Tinková, 2021)
     2nd place in SVOC research competition
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

František Couf, Fourier transform on polytopes and tiling with rectangles (co-advised by Mikuláš Zindulka, from 2021)
Matěj Doležálek, Subfields of number field extensions and quadratic forms (2022)
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

     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

(without me as a co-author)
Last updated June 5, 2022

J. Glivická, E. Sgallová, J. Šaroch, Controlling distribution of prime sequences in discretely ordered principal ideal subrings of Q[x], arxiv
J. Krásenský, P. Yatsyna, On quadratic Waring’s problem in totally real number fieldsarxiv
M. Raška, Representing multiples of m in real quadratic fields as sums of squares,
arxiv
J. Krásenský, M. Raška, E. Sgallová, Pythagoras numbers of orders in biquadratic fields, arxiv
M. Tinková, Trace and norm of indecomposable integers in cubic orders, arxiv
M. Tinková, On the Pythagoras number of the simplest cubic fields, arxiv
M. Doležálek, Quaternions and universal quadratic forms over number fields, arxiv
M. Tinková, E. Waxman, M. Zindulka, Artin Twin Primes, arxiv
K. Zemková, Composition of Bhargava’s Cubes over Number Fields, arxiv
D. Lachman, Distance formulas in Bruhat-Tits building of SL_d(Q_p), arxiv
J. Krásenský, A cubic ring of integers with the smallest Pythagoras number, Arch. Math. (Basel) 118 (2022), 39–48, arxiv, journal
M. Tinková, Arithmetics in number systems with cubic base, Publ. Math. Debrecen 99 (2021), 25–50, arxiv, journal
K. Zemková, Composition of binary quadratic forms over number fields, Math. Slovaca 71 (2021), 1339–1360, arxiv, journal
B. Faye, L. Matthiesen, D. Schindler, M. Tinková, K. Zemková, Integers represented by ternary quadratic forms, WINE III, Springer International Publishing (2021), 207–231, book
J. Krásenský, M. Tinková, K. Zemková, There are no universal ternary quadratic forms over biquadratic fields, Proc. Edinb. Math. Soc. 63 (2020), 861–912, arxiv, journal
M. Tinková, P. Voutier, Indecomposable integers in real quadratic fields, J. Number Theory 212 (2020), 458–482, arxiv, journal
M. Čech, D. Lachman, J. Svoboda, M. Tinková, K. Zemková, Universal Quadratic Forms and Indecomposables over Biquadratic Fields, Math. Nachr. 292 (2019), 540–555, arxiv, journal

Student grants

Number systems in lattices and number field orders

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

above Gondla village