Seminar at SMU Delhi

September 17, 2014 (Wednesday) , 3:30 PM at Webinar
Speaker: Jean-Marc Deshouillers, Institut de Math\'{e}matique de Bordeaux, Bordeaux INP, France
Title: Pseudo s-th powers are a basis of order $s+\epsilon$
Abstract of Talk
In order to understand what could be expected for Waring's problem (I.e. expressing integers as sums of a bounded number of s-th powers), Erd\H{o}s and R\'{e}nyi introduced a random model for sums of s-th powers of integers. We shall present this model to an audience which is not supposed to know much about Probability Theory nor Number Theory. We shall present the history of the model and the latest developments concerning the possibility to represent - almost surely - any large integer as a sums of $s+1$ pseudo $s$-th powers, one of them being drastically limited in size. A general underlying theme of the lecture is: how good or bad are probabilistic models to mimic real life? This is joint work with J. Cilleruelo, V. Lambert and A. Plagne.