Aditivní problémy v celistvých prvcích a mřížkách
| Thesis title in Czech: | Aditivní problémy v celistvých prvcích a mřížkách |
|---|---|
| Thesis title in English: | Additive problems in algebraic integers and lattices |
| Academic year of topic announcement: | 2025/2026 |
| Thesis type: | dissertation |
| Thesis language: | |
| Department: | Department of Algebra (32-KA) |
| Supervisor: | doc. Mgr. Vítězslav Kala, Ph.D. |
| Author: |
| Guidelines |
| The additive structure of algebraic integers in totally real number fields has been of great interest in the last ten years, partly due to its connection to universal quadratic forms. While the case of real quadratic fields is fairly well understood, the student will focus on the higher degree case where much less is known. The student will also consider more general problems concerning subsemigroups of lattices, motivated by extending the known results on numerical semigroups, as well as applications of these results to various topics such as quadratic forms. |
| References |
| T. Hejda and V. Kala. Additive structure of totally positive quadratic integers. Manuscripta Math., 163:263–278, 2020.
V. Kala. Universal quadratic forms and indecomposables in number fields: a survey. Commun. Math., 31(2):81–114, 2023. V. Kala and M. Tinková. Universal quadratic forms, small norms and traces in families of number fields. Int. Math. Res. Not. IMRN, 2023(9):7541–7577, 2023. J. Neukirch. Algebraic Number Theory, vol. 322. Grundlehrender Mathematischen Wissenschaften. Berlin, Heidelberg: Springer, 1999. J. C. Rosales, P. A. García-Sánchez, Finitely generated commutative monoids, Nova Science Publishers, Inc., Commack, NY, 1999. J. C. Rosales, P. A. García-Sánchez, Numerical semigroups, Dev. Math., 20, Springer, New York, 2009. |