Research – Vita Kala

Curriculum Vitae

MathSciNet
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arXiv
ORCID
Web of Science

Grants and awards

Principal investigator of UFOCLAN: Universal quadratic forms and class numbers grant

from the Czech Science Foundation GAČR, 2021–2025
highly selective JUNIOR STAR project (success rate 9%, total budget 1 000 000 USD)
postdocs: Giacomo Cherubini (01/2021–10/2022), Nicolas Daans (01–11/2023), Alessandro Fazzari (09–12/2021), Stevan Gajović (from 03/2023), Daniel Gil Muñoz (08/2021–06/2023), Siu Hang “Gordon” Man (from 07/2023), Mentzelos Melistas (from 01/2023), Eric Nathan Stucky (08/2021–08/2022), Błażej Żmija (10/2021–06/2023), a few more may be hired later

Principal investigator of Primus grant Universal quadratic forms: geometry and analysis

from Charles University, 2020–2022
postdocs: Giacomo Cherubini (09–12/2020), Siu Hang “Gordon” Man (09–12/2022), Tomáš Vávra (05–08/2020), Pavlo Yatsyna (01/2020–07/2022)

Principal investigator of Junior grant Quadratic forms and numeration systems over number fields

from the Czech Science Foundation GAČR, 2017–2019
postdocs: Tomáš Hejda, Tomáš Vávra (both 01/2017–12/2019), Ezra Waxman (08/2018–07/2019)
outcomes of the grant were evaluated by the grant agency as excellent (top 20%)

Neuron Impuls award for the project Semifields in number theory and geometry for 2018–2019

Bolzano Award for 2018 for the work Universal quadratic forms and families of number fields

University Center of Excellence: junior team member, PI Jan Krajíček

Service (selected)

Chair of the Evaluation Panel P202 “Mathematics and Informatics” of Czech Science Foundation GACR (2023–2025; previously vice chair 2021–2023)

Member of the Committee of programs for the support of science at Charles University (evaluating internal grant proposals, from 2023)

Member of the Cooperatio advisory board for mathematics, Charles University (from 2022)

Member of the Academic Senate of the Faculty of Math. and Physics, Charles University (02/2020–01/2023)

Editorial board member of Commentationes Mathematicae Universitatis Carolinae

Editorial board member of Pokroky matematiky, fyziky a astronomie (Advances in mathematics, physics, and astronomy), Czech journal for popularization of math and physics

Articles

Most of my recent papers are on arXiv (although the published versions are typically slightly different). Please email me if you are interested in copies or preprints of my theses and other papers.
Six of my best papers are highlighted in bold.

37. (with M. Zindulka) Partitions into powers of an algebraic number, 8 pp., submitted

36. (with T. Kepka, M. Korbelář) Congruence-simple matrix semirings, 11 pp., submitted

35. (with E. Sgallová, M. Tinková) Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables, 40 pp. (+21 pp. of appendices), submitted

34. (with P. Yatsyna, B. Żmija) Real quadratic fields with a universal form of given rank have density zero, 18 pp., submitted

33. (with P. Miska) On continued fraction coefficients of square roots of primes, 13 pp., submitted

32. (with L. Šíma) On generators of commutative semifields, 12 pp., submitted

31. (with G. Cherubini, A. Fazzari, A. Granville, P. Yatsyna) Consecutive real quadratic fields with large class numbers, Int. Math. Res. Not. IMRN (to appear), 12 pp. journal, arxiv

30. Universal quadratic forms and indecomposables in number fields: A survey, Commun. Math. 31 (2023), Special issue: Euclidean lattices: theory and applications (to appear), 21 pp.

29. (with P. Yatsyna) On Kitaoka’s conjecture and lifting problem for universal quadratic forms, Bull. London Math. Soc. 55 (2023), 854–864. journal

28. Number fields without universal quadratic forms of small rank exist in most degrees, Math. Proc. Cambridge Philos. Soc. 174 (2023), 225–231. journal

27. (with M. Tinková) Universal quadratic forms, small norms and traces in families of number fields, Int. Math. Res. Not. IMRN (2023), 7541–7577. arxiv (not fully updated, use journal link)

26. (with T. Hejda) Ternary quadratic forms representing a given arithmetic progression, J. Number Theory 234 (2022), 140–152. journal

25. (with P. Yatsyna) Lifting problem for universal quadratic forms, Adv. Math. 377 (2021), 107497, 24 pp. journal

24. (with P. Yatsyna) Sums of squares in S-integers, New York J. Math. 26 (2020), 1145–1154. journal

23. (with T. Hejda) Additive structure of totally positive quadratic integers, Manuscripta Math. 163 (2020), 263–278. journal

22. (with J. Svoboda) Universal quadratic forms over multiquadratic fields, Ramanujan J. 48 (2019), 151–157. journal

21. (with T. Vávra) Periodic representations in algebraic bases, Monatsh. Math. 188 (2019), 109–119. journal

20. (with M. Korbelář) Idempotence of finitely generated commutative semifields, Forum Math. 30 (2018), 1461–1474. journal

19. (with A. Dahl) Distribution of class numbers in continued fraction families of real quadratic fields, Proc. Edinb. Math. Soc. 61 (2018), 1193–1212. journal

18. (with V. Blomer) On the rank of universal quadratic forms over real quadratic fields, Doc. Math. 23 (2018), 15–34. journal

17. (with P. Glivický) Fermat’s Last Theorem and Catalan Conjecture in weak exponential arithmetics, Math. Log. Quart. 63 (2017), 162–174. journal

16. Semifields and a theorem of Abhyankar, Comment. Math. Univ. Carolin. 58 (2017), 267–273. journal

15. Lattice-ordered abelian groups finitely generated as semirings, J. Commut. Algebra 9 (2017), 387–412. journal

14. Norms of indecomposable integers in real quadratic fields, J. Number Theory 166 (2016), 193–207. journal; additional info

13. Universal quadratic forms and elements of small norm in real quadratic fields, Bull. Aust. Math. Soc. 94 (2016), 7–14. journal

12. (with V. Blomer) Number fields without universal n-ary quadratic forms, Math. Proc. Cambridge Philos. Soc. 159 (2015), 239–252. journal

11. (with J. Berg, A. Castillo, R. Grizzard, R. Moy, C. Wang) Congruences for Ramanujan’s f and omega functions via generalized Borcherds products, Ramanujan J. 35 (2014), 327–338. journal

10. (with J. Ježek, T. Kepka) Finitely generated algebraic structures with various divisibility conditions, Forum Math. 24 (2012), 379–397

9. (with M. Korbelar) Congruence simple subsemirings of Q^+, Semigroup Forum 81 (2010), 286–296

8. (with A. Drapal, C. Hamalainen) Latin bitrades, dissections of equilateral triangles and abelian groups, J. Comb. Des. 18 (2010), 1–24

7. (with T. Kepka, P. Nemec) Norms on semirings I, Acta Univ. Carolin. Math. Phys. 51 (2010), 29–48

6. (with T. Kepka) Commutative parasemifields finitely generated as semirings, Acta Univ. Carolin. Math. Phys. 51 (2010), 49–56

5. (with T. Kepka, M. Korbelar) Notes on commutative parasemifields, Comment. Math. Univ. Carolin. 50 (2009), 521–533

4. (with A. D. Keedwell) Addendum to “The existence of Buchsteiner and conjugacy-closed quasigroups”, Europ. J. Combin. 30 (2009), 1386

3. (with T. Kepka, M. Korbelar, J. D. Phillips) Various subsemirings of the field Q of the rational numbers, Acta Univ. Carolin. Math. Phys. 50 (2009), 29–59

2. (with T. Kepka) A note on finitely generated ideal-simple commutative semirings, Comment. Math. Univ. Carolin. 49 (2008), 1–9

1. (with V. Flaska, A. Jancarik, T. Kepka) Trees in commutative nil-semigroups of index two, Acta Univ. Carolin Math. Phys. 48 (2007), 81–101

Presentations

Typically I give blackboard talks, so here are just a few of my beamer presentations.

Warning: The slides contain intentional simplification and (certainly some!) unintentional errors. Use with caution!

Universal quadratic forms over number fields — from International Conference on Class Groups of Number Fields and Related Topics 2021. video

Universal quadratic forms over number fields — a (semi)-popular talk from Number theory seminar, Prague, 2021. video

Lifting problem for universal quadratic forms — from XXXI^st Journées Arithmétiques, 2019

Classifications of finitely generated semifields and lattice-ordered groups — from 56th SSAOS, 2018

Universal quadratic forms over number fields — from XXX^th Journées Arithmétiques, 2017

Additively indecomposable integers in number fields — from ALaNT 4, 2016

Theses

Universal quadratic forms over number fields, 2020, habilitation thesis (don’t read – the survey paper gives a better overview of my recent research).

Density of Self-Dual Automorphic Representations of GL_n(A_Q), 2014, PhD thesis, Purdue University, advisor F. Shahidi

Algebraic Substructures in C^m, 2013, PhD thesis, Charles University, advisor T. Kepka

Simple semirings, 2009, Master’s thesis (Mgr.), advisor T. Kepka

Simple semirings, 2007, undergraduate thesis (Bc.), advisor T. Kepka

Prvociselne vzorce (Prime-generating functions), 2004, high school graduation thesis, supervisor R. Kucera

Grants and awards

Service (selected)

Articles

Presentations

Theses

Popular