Research

You can find my work on ORCID and on MathSciNet. Most of my papers are on arXiv, but it does not connect my former and my current surname. I am also on Researchgate.

Publications:

1. Non-universality of ternary quadratic forms over fields containing √2 (with J. Krásenský). arXiv
2. Kitaoka's conjecture and sums of squares (with V. Kala and J. Krásenský). arXiv
3. Vishik equivalence and similarity of quadratic forms over fields of characteristic 2 (with Detlev Hoffmann), J. Algebra (2025). DOI
4. Isotropy indices of Pfister multiples in characteristic two (with Nico Lorenz), J. Pure Appl. Algebra 228(12) (2024). arXiv, DOI
5. Vishik equivalence and similarity of p-forms and totally singular quadratic forms, Pacific J. Math. 329(2) (2024). arXiv, DOI
6. Isotropy and full splitting pattern of quasilinear p-forms, J. Algebra 657 (2024). arXiv, DOI
7. Isotropy of quadratic forms over function fields in characteristic 2, Comm. Algebra 52(10) (2024). arXiv, DOI
8. Composition of Bhargava's Cubes over Number Fields, Expo. Math., 41.4 (2023) arXiv, DOI
9. Integers represented by ternary quadratic forms (with B. Faye, L. Matthiesen, D. Schindler and M. Tinková), published in Women in Numbers Europe III: Research Directions in Number Theory (2021), 207–231. Springer, DOI
10. Composition of Binary Quadratic Forms over Number Fields, published in Math. Slovaca, 71(6) (2021), 1339–1360. arXiv, DOI
11. There are no universal ternary quadratic forms over biquadratic fields (with J. Krásenský and M. Tinková), published in Proc. Edinburgh Math. Soc., 63(3) (2020), 861–912. arXiv, DOI
12. Universal quadratic forms and indecomposables over biquadratic fields (with M. Čech, D. Lachman, J. Svoboda, M. Tinková), published in Math. Nachr. 292 (2019), 540–555. arXiv, DOI

Talks:

• Equivalence relations of quadratic forms in characteristic two, Al@Bicocca seminar, Università degli Studi di Milano-Bicocca, Milan, Italy
• Isotropy of quadratic forms in characteristic two, PIMS Postdoctoral Fellow Seminar
• Equivalence relations of quadratic forms, mainly in characteristic two, Number theory lunch seminar, MPIM Bonn, Germany
• Isotropy of quadratic forms over function fields, University of Antwerp, Belgium
• Equivalence relations of quadratic forms in characteristic two, Oberseminar Algebra und Geometrie, Dortmund, Germany (online) -- presentation, video recording
• Isotropy of quadratic forms in characteristic two, Autumn School of Algebra (organized by the Department of Algebra at the Charles University) -- presentation
• Guest lecture on quadratic forms in characteristic two, Charles University, Prague, Czech Republic (online) -- presentation
• Non-normal number fields, Number Theory Seminar, Prague, Czech Republic
• Composition of quadratic forms over number fields, Oberseminar Algebra und Geometrie, Dortmund, Germany
• Composition of quadratic forms over number fields, Number Theory Seminar, Prague, Czech Republic
• Composition of binary quadratic forms, 20th International Workshop for Young Mathematicians "Number Theory", Kraków, Poland
• The existence of the Euclidean norm in quadratic number fields, Number Theory Seminar, Prague, Czech Republic

Conferences, summer schools & workshops:

• ALGAR 2025: Algebras with involution and linear algebraic groups, University of Antwerp, Belgium
• 2024 CMS Summer meeting, Saskatoon, Canada
• Motives and Invariants: Theory and Applications to Algebraic Groups and their Torsors, BIRS, Banff, Canada
• Young Number Theorists in Bonn, MPIM, Bonn, Germany
• ALGAR 2023: Local-global principles for quadratic forms, University of Antwerp, Belgium
• Motives in Ratisbona, University of Regensburg, Germany
• ALGAR 2022: Constructive mathematics, University of Antwerp, Belgium
• ALGAR 2021: Systems of quadratic forms over arithmetic fields, University of Antwerp, Belgium
• ALGAR 2020: Valuations, quadratic forms and definability, digital edition
• Women in Numbers Europe 3, Rennes, France
• ALGAR 2019: Algebras with involution, University of Antwerp, Belgium
• Quadratic Forms and Axial Algebras, Lens, France
• ALGAR 2018: Sums of squares in fields, University of Antwerp, Belgium
• 20th International Workshop for Young Mathematicians "Number Theory", Kraków, Poland
• ICCGNFRT 2017, Prayagraj (Allahabad), India

Some other texts:

• Equivalence relations of quadratic forms in characteristic 2 and quasilinear p-forms, 2022, Dissertation, supervisor D. W. Hoffmann. DOI
• Composition of Quadratic Forms over Number Fields, 2018, Master thesis, supervisor V. Kala
• Introduction to Witt vectors, 2016, semester project in Commutative algebra (from Barcelona)
• Norm-euclidean quadratic extensions of the field of rational numbers, 2015, undergraduate thesis, supervisor J. Šaroch (in Czech)