Tipo di tesi
Tesi di laurea magistrale
Titolo
Decoupling theory: the case of the parabola
Corso di studi
MATEMATICA
Parole chiave
- decoupling
- Fourier analysis
- harmonic analysis
- Vinogradov conjecture
Data inizio appello
24/10/2025
Riassunto (Italiano)
In this theses, I will discuss the decoupling theory of J.Bourgain and C.Demeter in the 2-dimensional setting. In particular I will discuss the case of the parabola. Moreover, I will explain some limits and the numerology of the result.
Finally, I will show how this theory, initially born in the field of harmonic analysis, is related to the apparently distant field of number theory. In particular, the Vinogradov's conjecture for Diophantine equations will be derived from the main result after appropriately reformulate the statement in terms of harmonic analysis.
