About me

My name is Jakub Krásenský, since the academic year 2023/2024 an assistant professor of mathematics at Czech Technical University in Prague, Faculty of Information Technology. In September 2023, I obtained my PhD in the field of Number Theory, at Charles University in Prague, Faculty of Mathematics and Physics.  My advisor was Víťa Kala from the algebra department, our research group is called UFOCLAN.

My research topic are universal quadratic forms over orders in number fields. I am particularly interested in Kitaoka's conjecture about ternary quadratic forms, in universal non-free lattices of small rank, and in the Pythagoras number and g-invariants of number field orders. In connection with universal quadratic forms of small rank, I also investigated indecomposable algebraic integers, in particular in real biquadratic fields.

As a part of the TIGR research group, I am also deeply interested in nonstandard positional number systems, in particular in GNSs in lattices, which I investigate in collaboration with Attila Kovács from ELTE in Budapest, and in number systems in quaternions. The relevant papers are in preparation. A summary of some of our results is contained the slides from my talk at the Numeration 2023 conference in Liège.

I also support Barbora Hudcová in her research regarding cellular automata and other discrete dynamical systems, in particular focusing on how to define reasonably well computable parameters which correlate with complexity or chaotic behaviour. Our joint paper about simulation by affine cellular automata got recently accepted in the journal Theoretical computer science.

One of my hobbies is popularising mathematics. I am an organiser of the international team competition for high-school students Náboj. For six years I have organised the Mathematical correspondence seminar a.k.a. PraSe; recently, I have translated two books of mathematical, logical and linguistic riddles for the Portál publishing house: Heuréka! by Heinrich Hemme and 100 mozkocvičných hádanek (100 Maddening Mindbending Puzzles) by Rob Eastaway and David Wells.

Naturally, I have various other hobbies and interests, but I don't see the point of sharing them here, on my research/teaching web page. I enjoy talking to people in person.

Publications:

• N. Daans, V. Kala, J. Krásenský and P. Yatsyna, Failures of integral Springer's theorem, submitted. Available at arXiv.

• B. Hudcová and J. Krásenský, Simulation limitations of affine cellular automata, Theoret. Comput. Sci. (in press). Available at arXiv or as a journal pre-proof at doi: https://doi.org/10.1016/j.tcs.2024.114606.

• J. Krásenský and P. Yatsyna, On quadratic Waring's problem in totally real number fields, Proc. Amer. Math. Soc. 151, 1471–1485 (2023). Available at doi:10.1090/proc/16233 and arXiv.

• J. Krásenský, M. Raška and E. Sgallová, Pythagoras numbers of orders in biquadratic fields, Expo. Math. 40, 1181–1228 (2022). Available at doi:10.1016/j.exmath.2022.06.002 and arXiv.

• J. Krásenský, A cubic ring of integers with the smallest Pythagoras number, Arch. Math. (Basel) 118, 39–48 (2022). Available at doi:10.1007/s00013-021-01662-5 and arXiv.

• J. Krásenský, M. Tinková and K. Zemková, There are no universal ternary quadratic forms over biquadratic fields, Proc. Edinburgh Math. Soc. 63(3), 861–912 (2020). Available at doi:10.1017/S001309152000022X and arXiv.

If you want to contact me, the easiest way is my e-mail adress jakub.krasensky {at} fit.cvut.cz.

I'm very happy for any questions or feedback related to any of my research interests or to the books I've translated.