Community Research and Development Information Service - CORDIS

Final Report Summary - PECTA (Extremal Problems in Combinatorics and Their Applications)

The main objective of the present CIG grant was to facilitate my integration into Tel-Aviv University as a permanent faculty member and to help me build a successful research group. As I elaborate below, I think that in both cases the outcomes were positive. First, I was promoted to the rank of Associate Professor with tenure about 3 years ago. Second, last year I received an ERC-Starting grant. Third, I now have 2 PhD students, 2 Post-doc researchers and 2 MSc students. Our joint projects have resulted in publications in some of the top mathematical journals. Let me describe 4 of the main results we obtained in the past 2 years.

1. In a joint work with my PhD student G. Moshkovitz and with Lovett-Hosseini we improved a result of B. Greene by proving a tight lower bound for the arithmetic regularity lemma.

2. I a joint work with my PhD student G. Moshkovitz we proved a general result on the limitations of partions of a graph into expanding subgraphs. This general result allowed us to prove that numerous results in pure and algorithmic graph theory are optimal.

3. In a joint work with my MSc student L. Gishboliner we resolved an open problem of Lovasz and Vesztergombi regarding efficient algorithms called property testers. This is related to the fastly growing are of graph limits.

4. In a joint work with my PhD student G. Moshkovitz we resolved an open problem raised by Fox-Pach-Sudakov-Suk regarding a general Ramsey-type problem in the theory of hypergraphs.

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