Asymptotic Hilbert series

Algebra Seminar
Monday, August 27, 2012 - 3:00pm for 1 hour (actually 50 minutes)
Skiles 005
Gregory G. Smith – Queens University
Greg Blekherman
How does one study the asymptotic properties for the Hilbert series of a module? In this talk, we will examine the function which sends the numerator of the rational function representing the Hilbert series of a module to that of its r-th Veronese submodule. As r tends to infinity, the behaviour of this function depends only on the multidegree of the module and the underlying multigraded polynomial ring. More importantly, we will give a polyhedral description for the asymptotic polynomial and show that the coefficients are log-concave.