Research

Curriculum Vitae

MathSciNet
Google Scholar
arXiv
ORCID
Web of Science

Grants and awards

Sailing to criterion sets for quadratic forms
UFOCLAN: Universal quadratic forms and class numbers
Universal quadratic forms: geometry and analysis
Quadratic forms and numeration systems over number fields

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

Service (selected)

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

Chair of the Committee of programs for the support of science at Charles University for Natural Sciences, Mathematics, and Computer Science, evaluating Primus and UNCE grant proposals (from 2024; previously member 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 (2026–2029, 2020–2023)

Editorial board member of International Journal of Number Theory, Open Mathematics, Commentationes Mathematicae Universitatis Carolinae, and Communications in Mathematics

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

Articles

Five of my best recent papers are highlighted in bold.
My Erdős number is 2.

50. V. Kala, O. Prakash, There are consecutive cubic fields with large class numbers, when ordered by discriminant, 10 pp., submitted

49. V. Kala, K. Kramer, J. Krásenský, Kitaoka’s Conjecture and sums of squares, 15 pp., submitted

48. V. Kala, J. Krásenský, D. Park, P. Yatsyna, B. Żmija, Kitaoka’s Conjecture for quadratic fields, 27 pp., submitted

47. V. Kala, J. Krásenský, G. Romeo, Universality criterion sets for quadratic forms over number fields, 19 pp., submitted

46. V. Kala, P. Yatsyna, Even better sums of squares over quintic and cyclotomic fields, 19 pp., submitted

45. V. Kala, P. Yatsyna, B. Żmija, Real quadratic fields with a universal form of given rank have density zero, Amer. J. Math. (to appear), 18 pp.

44. V. Kala, D. Kim, S. H. Lee, Universality lifting from a general base field, Rev. Mat. Iberoam. 41 (2025), 2379–2400, journal

43. N. Daans, V. Kala, S. H. Man, P. Yatsyna, M. Widmer, Most totally real fields do not have universal forms or Northcott property, Proc. Natl. Acad. Sci. USA 122 (2025), article e2419414122, 8 pp., journal

42. N. Daans, V. Kala, J. Krásenský, P. Yatsyna, Failures of integral Springer’s Theorem, Proc. Amer. Math. Soc. 153 (2025), 2369–2379, journal

41. V. Kala, E. Sgallová, M. Tinková, Arithmetic of cubic number fields: Jacobi-Perron, Pythagoras, and indecomposables, J. Number Theory 273 (2025), 37–95, journal

40. V. Kala, S. H. Man, Sails for universal quadratic forms, Selecta Math. (N.S.) 31 (2025), article 26, 31 pp., journal

39. N. Daans, V. Kala, S. H. Man, Universal quadratic forms and Northcott property of infinite number fields, J. Lond. Math. Soc. 110 (2024), article e70022, 20 pp., journal

38. V. Kala, O. Prakash, There is no 290-Theorem for higher degree forms, Math. Nachr. 297 (2024), 4322–4332, journal

37. H. Řada, Š. Starosta, V. Kala, Periodicity of general multidimensional continued fractions using repetend matrix form, Expo. Math. 42 (2024), article 125571, 36 pp., journal

36. V. Kala, L. Šíma, On minimal semiring generating sets of finitely generated commutative parasemifields, Algebra Universalis 85 (2024), article 24, 19 pp., journal, pdf

35. V. Kala, M. Melistas, Universal quadratic forms and Dedekind zeta functions, Int. J. Number Theory 20 (2024), 1833–1847, journal, pdf

34. V. Kala, M. Zindulka, Partitions into powers of an algebraic number, Ramanujan J. 64 (2024), 537–551, journal, pdf

33. V. Kala, T. Kepka, M. Korbelář, Congruence-simple matrix semirings, Internat. J. Algebra Comput. 34 (2024), 407–424, journal

32. V. Kala, P. Miska, On continued fraction partial quotients of square roots of primes, J. Number Theory 253 (2023), 215–234, journal

31. G. Cherubini, A. Fazzari, A. Granville, V. Kala, P. Yatsyna, Consecutive real quadratic fields with large class numbers, Int. Math. Res. Not. IMRN (2023), 12052–12063, journal

30. V. Kala, Universal quadratic forms and indecomposables in number fields: A survey, Commun. Math. 31 (2023), Special issue: Euclidean lattices: theory and applications, 81–114, journal
Won Communications in Mathematics Best Paper Award 2023

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

8. A. Drápal, C. Hämäläinen, V. Kala, Latin bitrades, dissections of equilateral triangles and abelian groups, J. Comb. Des. 18 (2010), 1–24

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

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

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

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

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

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

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

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.

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

Theses

Arithmetic of small elements in totally real fields, 2024, research professor dissertation (for DSc. title)

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

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

Popular

2018 Abel Prize awarded for Langlands program (in Czech), Pokroky matematiky, fyziky a astronomie, 63 (2018), 78–90

Dividing a treasure (in Czech), Rozhledy matematicko-fyzikální 92 (2017), 35–36

Kye monastery