Szemerédi-Trotter theorem, one of the Erdős-like cornerstone in geometry, states that any arrangement of n points and n lines in the plane determines O(n4/3) incidences. In this workshop, we go over some proofs of Szemerédi-Trotter theorem and also review some applications in combinatorial geometry and additive combinatorics such as unit distance problem and sum-product theorem. We also discuss some major open problems in this direction.
PhD student at the University of California at San Diego
Mozhgan is a last year PhD student at the University of California at San Diego, working under supervision of prof. Andrew Suk. She is interested in Combinatorics and Combinarial Geometry. She got her B.Sc degree in Mathematics from Sharif University of Technology under supervision of prof. Ebadollah Mahmoodian.