Monday, May 18, 2015
Freie Universität Berlin
Takustr. 9
14195 Berlin
room 005
Lecture - 14:15
Abstract:
A finite or infinite matrix M is called `partition regular' if whenever the natural numbers are finitely coloured there exists a vector x, with all of its entries the same colour, such that Mx=0. Many of the classical results of Ramsey theory, such as van der Waerden's theorem or Schur's theorem, may be naturally rephrased as assertions that certain matrices are partition regular. While the structure of finite partition regular matrices is well understood, little is known in the infinite case. In this talk we will review some known results and then proceed to some recent developments. No knowledge of the subject will be assumed.
Colloquium - 16:00
Abstract:
We will deal with a class of integer sequences, the binomial sums, that contains a lot of classical sequences coming from combinatorics or number theory. They basically express as multiple sums of products of binomial coefficients. The generating functions of the binomial sums are very special as they coincide with a certain sort of integrals with a parameter. I will explain this equivalence and its consequences : decidability of equality between binomial sums, arithmetic properties, etc. This will involve computer algebra and algebraic geometry.