Research

ORCID, Researchgate, Web of Science, Scopus

Publications

1. Z. Masáková and M. Tinková, Finiteness in real cubic fields, Acta Math. Hungar. 153, (2017) 318-333.

2. M. Čech, D. Lachman, J. Svoboda, M. Tinková and K. Zemková, Universal quadratic forms and indecomposables over biquadratic fields, Math. Nachr. 292, (2019) 540-555.

3. M. Tinková and P. Voutier, Indecomposable integers in real quadratic fields, J. Number Theory 212, (2020) 458-482.

4. J. Krásenský, M. Tinková and K. Zemková, There are no universal ternary quadratic forms over biquadratic fields, Proc. Edinb. Math. Soc. 63 (3), (2020) 861-912.  

5. M. Tinková, Arithmetics in number systems with cubic base, Publ. Math. Debrecen 99, (2021) 25-50.

6. B. Faye, L. Matthiesen, D. Schindler, M. Tinková and K. Zemková, Integers Represented by Ternary Quadratic Forms, Women in Numbers Europe III: Research Directions in Number Theory, Association for Women in Mathematics Series, vol 24, Springer, (2021) 207-231.

7. M. Tinková, E. Waxman and M. Zindulka, Artin twin primes, J. Number Theory 245, (2023) 203-232. 

8. V. Kala and M. Tinková, Universal quadratic forms, small norms and traces in families of number fields, Int. Math. Res. Not. IMRN 2023, (2023) 7541-7577.

9. M. Tinková, Trace and norm of indecomposable integers in cubic orders, Ramanujan J. 61, (2023) 1121-1144.

10. M. Tinková, On the Pythagoras number of the simplest cubic fields, Acta Arith. 208, (2023) 325-354. codes

11. D. Gil Muñoz and M. Tinková, Additive structure of non-monogenic simplest cubic fields, submitted. code 

12. V. Kala, E. Sgallová and M. Tinková, Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables, submitted. codes

13. D. Gil Muñoz and M. Tinková, The lifting problem for universal quadratic forms over simplest cubic fields, to appear in Bull. Aust. Math. Soc. 

14. M. Tinková, Bounds on the Pythagoras number and indecomposables in biquadratic fields, submitted.

Talks

• Units with Property (F) in cubic number  fields, Combinatorial and Algebraic Structures Seminar, Prague, Czech Republic

• Finiteness in real cubic  fields, Combinatorics on Words 2017, Janov nad Nisou, Czech Republic

• Finiteness in real cubic  fields, Numeration 2017, Rome, Italy

• Arithmetics in number systems with cubic base, Number Theory Seminar, Prague, Czech Republic

• Indecomposable integers and universal quadratic forms, Numeration 2018, Paris, France

• Indecomposable integers and universal quadratic forms, wds-m 2018, Prague, Czech Republic

• Universal quadratic forms and indecomposables over biquadratic  fields, Number Theory Seminar, Prague, Czech Republic

• Universal quadratic forms and indecomposables over biquadratic  fields, Combinatorics on Words 2018, Janov nad Nisou, Czech Republic

• Arithmetics in number systems with cubic base, ALANT 5, Bedlewo, Poland

• Greedy expansions and property (F), Autumn School of the Department of Algebra 2018, Rybniště, Czech Republic

• Indecomposable integers in real quadratic fields of odd discriminant, Number Theory Seminar, Prague, Czech Republic 

• Jacobi-Perron algorithm and indecomposable integers in the simplest cubic fields, wds-m 2019,  Prague, Czech Republic 

• Indecomposable integers in real quadratic fields, Combinatorics on Words 2019, Janov nad Nisou, Czech Republic

• Jacobi-Perron algorithm and indecomposable integers in the simplest cubic fields, Numeration 2019, Vienna, Austria

• Jacobi-Perron algorithm and indecomposable integers in the simplest cubic fields, 24th Central European Number Theory Conference, Komárno, Slovakia

• Jacobi-Perron algorithm and indecomposable integers in the simplest cubic fields, Oberseminar Algebra und Geometrie, Dortmund, Germany 

• Universal quadratic forms, small norms and traces in families of number fields, Zahlentheoretisches Kolloquium, Graz, online  

• On the Pythagoras number of the simplest cubic fields, ALGAR 2021, Antwerp, Belgium

• Universal quadratic forms, small norms and traces in families of number fields, One World Numeration Seminar, online 

• Trace and norm of indecomposable integers in cubic orders, Number Theory Conference 2022, Debrecen, Hungary 

• Universal quadratic forms, small norms and traces in families of number fields, ELAZ 2022, Poznań, Poland 

• Additive structure of non-monogenic simplest cubic fields, WINGs 2023, Chesterfield, United Kingdom  

• Additive structure of non-monogenic simplest cubic fields, Numeration  2023, Liège, Belgium 

• Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables, Zahlentheoretisches Kolloquium, Graz, Austria

• Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables, Journées Arithmétiques 2023, Nancy, France

• Additive structure of non-monogenic simplest cubic fields, 25th Central European Number Theory Conference, Sopron, Hungary

• Trace and norm of indecomposable integers in cubic orders, Young Number Theorists in Bonn, Bonn, Germany

Summer Schools, Workshops & Other Conferences

• 2nd French-German Summer School, Dresden, Germany

• Women in Numbers Europe 3, Rennes, France

• Front Range Number Theory Day, Spring 2021, online

• ALGAR 2021, Antwerp, Belgium

• Arithmetic Statistics and Local-Global Principles, Vienna, Austria

• ALGAR 2022, Antwerp, Belgium

• ALGAR 2023, Antwerp, Belgium

Grants

• Principal investigator of GAUK grant Indecomposable integers and universal quadratic forms, 2018-2020 (with Martin Čech, Kristýna Zemková, Ester Sgallová and J. Krásenský)

• Principal investigator of GAČR grant Local-global problems over number fields, 2022-2025 (Postdoc Individual Fellowship – Outgoing, including a stay in Graz for two years)