This is a research proposal submitted to FAPESP for Hiêp Hàn's application for a postdoctoral fellowship at the Institute of Mathematics and Statistics of the University of São Paulo (IME/USP). Hàn's stay in São Paulo is initially planned for 24 months, from 4 January 2011. This researcher will be a member of the combinatorics and theory group at IME/USP and of NUMEC, Núcleo de Modelagem Estocástica e Complexidade, a research centre of USP.The main themes of the proposed research are quasi-randomness of graphs and hypergraphs, and extremal problems for hypergraphs. More specifically, problems along three lines of research are proposed: (i) weak notions of quasi-randomness for hypergraphs and applications, (ii) quasi-randomness for sparse structures, including graphs with given degree sequences and (iii) extremal problems for spanning subhypergraphs, such as Hamilton cycles. Several of the proposed problems involving quasi-randomness suggest accompanying regularity lemmas and applications.
News published in Agência FAPESP Newsletter about the scholarship: