Thesis supervisor: Sándor Kiss
Location of studies (in Hungarian): Department of Algebra, Institute of Mathematics, BME Abbreviation of location of studies: BME
Description of the research topic:
The investigation of the sumsets and difference sets is a very important topic in Additive Number Theory. Among the plenty of beautiful and interesting results in this topic one of the oldest is the famous theorem of Cauchy and Davenport. There is some unsolved problems in this field as well. An immediate question arises when the size of the sumset and difference set is small: what can one say about the size of the original set? Another classical problem is to estimate the cardinality
of a subset of the finite field of p elements with the property that the difference of any two elements from the subset is a quadratic residue modulo p. To handle these problems and similar questions there are new and exciting methods developed by outstanding research mathematicians
recently. The task of the PhD student is to learn and improve the known methods and try to solve
some problems in this field. The student have to publish his results in high quality journals.
Required language skills: English Further requirements: Basic knowledge of Algebra, Analysis and Combinatorics are needed.
The PhD student should like to read and learn new tools from several fields of mathematics.
Number of students who can be accepted: 1
Deadline for application: 2017-05-31
2024. IV. 17. ODT ülés Az ODT következő ülésére 2024. június 14-én, pénteken 10.00 órakor kerül sor a Semmelweis Egyetem Szenátusi termében (Bp. Üllői út 26. I. emelet).
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