Research

Publications:

• • Isotropy indices of Pfister multiples in characteristic two (with Nico Lorenz), preprint. arXiv

  • Vishik equivalence and similarity of p-forms and totally singular quadratic forms, preprint. arXiv

  • Isotropy and full splitting pattern of quasilinear p-forms, submitted. arXiv

  • Isotropy of quadratic forms over function fields in characteristic 2, to appear in Comm. Algebra. arXiv

  • Composition of Bhargava's Cubes over Number Fields, Expo. Math., 41.4 (2023)  arXiv, DOI

  • 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

  • Composition of Binary Quadratic Forms over Number Fields, published in Math. Slovaca, 71(6) (2021), 1339–1360. arXiv, DOI

  • 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

  • Quadratic extensions of cyclotomic number fields and a conjecture of Ciolan and Neiss (with P. Moree and C. Pagano), in preparation 

  • 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:

• • Isotropy of quadratic forms in characterictic 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:

• • 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)

Researchgate

ORCID