The author is interested in various types of uniform behavior for commutative Noetherian rings. This is probably best illustrated by just quoting his two main results. \textit{Uniform Artin-Rees}: Let \(S\) be a Noetherian ring. Let \(N\leq M\) be two finitely generated \(S\)-modules. If \(S\) satisfies at least one of the conditions below, then there exists an integer \(k\) such that for all ideals \(I\) of \(S\), and for all \(n\geq k\) we have \(I^ nM\cap N\leq I^{n- k}N\). (i) \(S\) is essentially of finite type over a Noetherian local ring. (ii) \(S\) is a ring of characteristic \(p\), and \(S\) is module-finite over \(S^ p\). (iii) \(S\) is essentially of finite type over \(\mathbb{Z}\). \textit{Uniform Briançon-Skoda theorem}: Let \(S\) be a Noetherian reduced ring. If \(S\) satisfies at least one of the following conditions then there exists a positive integer \(k\) such that for all ideals \(I\) of \(S\), we have \(\overline {I^ n}\leq I^{n-k}\). (i) \(S\) is essentially of finite type over an excellent Noetherian local ring. (ii) \(S\) is of characteristic \(p\) and \(S^{1/p}\) is module-finite over \(S\). (iii) \(S\) is essentially of finite type over \(\mathbb{Z}\). The author conjectures that these two conclusions hold under weaker hypotheses.