Abstract
In this contribution we give incidence bounds for arrangements of curves in F q 2. As an application, we prove a new result that, if (x, f (x)) is a Sidon set, then either A+A or f(A)+f(A) should be large. The main goal of the paper is to illustrate the use of graph spectral techniques in additive combinatorics. This is an extended version of the talks I gave in the Additive Combinatorics DocCourse held at the CRM in Barcelona and at the conference “Fete of Combinatorics” held in Keszthely.
The research was conducted while the author was a member of the Institute for Advanced Study. Funding provided by The Charles Simonyi Endowment. The research was supported by NSERC and OTKA grants and by Sloan Research Fellowship.
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Solymosi, J. (2009). Incidences and the spectra of graphs. In: Combinatorial Number Theory and Additive Group Theory. Advanced Courses in Mathematics - CRM Barcelona. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8962-8_22
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