题目:Generalized Ehrhart polynomial (广义的Ehrhart多项式)
报告人: Nan Li 麻省理工学院(MIT)
时 间: 6月8日（星期二）10:30--11:30
地 点：数学楼102报告厅
摘 要：Let $P$ be a polytope with rational vertices. A classical theorem
of Ehrhart states that the number of lattice points in the dilations
$P(n) = nP$ is a quasi-polynomial in $n$. We generalize this theorem
by allowing the vertices of P(n) to be arbitrary rational functions in
$n$. In this case we prove that the number of lattice points in P(n)
is a quasi-polynomial for $n$ sufficiently large. Our work was
motivated by a conjecture of Ehrhart on the number of solutions to
parametrized linear Diophantine equations whose coefficients are
polynomials in $n$, and we explain how these two problems are related.