Seminar at SMU Delhi

December 14, 2012 (Friday) , 3:30 PM at Webinar
Speaker: Richard Wilson, Caltech (California Institute of Technology), USA.
Title: A zero-sum Ramsey-type problem for hypergraphs and diagonal (Smith) forms of certain incidence matrices.
Abstract of Talk
The Smith normal form (or a diagonal form) of an integer matrix $A$ allows us to easily determine whether an a system $Ax=b$ of equations has an integer solution $x$. We determine a diagonal form for a matrix $N=N_t(H)$ associated with a $t$-uniform hypergraph whenever $H$ has a certain property that we call `primitivity', a previously unstudied property that we show holds almost surely for a random hypergraphs as the number of vertices increases. The binary case of a zero-sum Ramsey-type problem of Alon and Caro is equivalent to solving the congruences $Nx\equiv j\pmod 2$ where $j$ is the vector of all 1's, and so we can solve their problem for primitive hypergraphs. This is joint work with Tony Wong.