Date: Monday May 10
Location:  Mathematical Institute (Snellius Bldg.), room 401,
Leiden University

Time: 1645h-1730h

Speaker: Professor Igor Shparlinski (Macquarie U, AUS)

Title: Sum-Product Problem: New Generalisations and Applications

Abstract:  We give a brief survey of recent results related to the
sum-product problem which dates back to work of Erdos and
Szemeredi (1983), where it is shown that for any set A of real numbers, at
least one of the sets
A+A = {a_1 + a_2 : a_1,a_2 in A} and A A = {a_1 a_2 : a_1,a_2 in A} is
large. More recently, Bourgain, Katz  and Tao (2006) obtained
similar results for  sets A in prime finite fields.

We outline these and several other recent results in this area
and also present a diverse scope of  their applications  to
several other problems.

Finally we mention several open problems, some of which are
motivated by applications to cryptography.