The Hebrew University of Jerusalem Einstein Institute of Mathematics |
The Hebrew University of Jerusalem The Rachel and Selim Benin School of Computer Science & Engineering |
Jozsef Solymosi (UBC)
The lectures will be held at the Edmond Safra Campus Givat Ram, Jerusalem
First talk:
Thursday, May 4, 14:30--15:30
Math colloquium talk
Mathematics building, Lecture hall 2
The sum-product problem
The incompatibility of multiplicative and additive structures in various fields and rings is an important phenomena. In this talk I will talk about a special case of it. Let us consider a finite subset of integers, A. The sum set of A is the set of pairwise sums of elements of A and the product set is the set of pairwise products. Erdős and Szemeredi conjectured that either the sum set or the product set should be large, almost quadratic in size of A. The conjecture is still open. Similar questions can be asked over any ring or field. We will review some recent results, further problems and conjectures. |
Second talk:
Sunday, May 7, 11:00--13:00
Combinatorics seminar
Rothberg building B, Room 221 Polynomial methods in incidence geometry
Several exciting new results in discrete geometry and additive combinatorics were proved using basic properties of a well chosen polynomial. In these cases the polynomial captures some of the key features of the problem. We will analyse the results searching for common elements in the proofs. |
Third talk:
Wednesday, May 10, 10:30--12:00
CS theory seminar
Rothberg building B, Room 220 Geometric incidences
This talk is a continuation of the previous two. We will translate various mathematical problems to questions about geometric incidences. Then, we give bounds on the number of incidences between curves and points over real, complex, and finite fields. |