I'm broadly interested in algebraic & analytic number theory, including higher degree forms, quadratic forms, generalized quadratic forms, analytic properties of algebraic integers represented by higher degree forms, arithmetic of finite or infinite extensions of number fields, class numbers and genre of algebraic number fields, geometry of numbers, rational points on elliptic and hyperelliptic curves, the circle method, and sieve methods.
(with O. Chwiedziuk, M. Doležálek, S. Hlavinková, E. Pěchoučková, Z. Pezlar, A. Růžičková and M. Zindulka) No proper generalized quadratic forms are universal over quadratic fields, submitted.
(with O. Chwiedziuk, M. Doležálek, E. Pěchoučková, Z. Pezlar, G. Romeo, A. Růžičková and M. Zindulka) Representing rational integers by generalized quadratic forms over quadratic fields, submitted.
Northcott property and universality of higher degree forms, Int. J. Number Theory, 21 (2025), no. 03, 675-694.
(with V. Kala) There is no 290-Theorem for higher degree forms, Math. Nachr. 297 (2024) , no. 11, 4322-4332.
A note on the class number of certain real cyclotomic fields, Indian J. Pure Appl. Math., 2024.
(with K. Chakraborty) Generalized fruit Diophantine equation and hyperelliptic curves, Monatsh. Math. 203 (2024), no. 3, 667-676.
Principal investigator of GAUK grant Universality of generalized higher degree forms over number fields (2025-2028).
Team member of UFOCLAN: Universal quadratic forms and class numbers, PI: Vítězslav Kala (2023-2025).