3:45PM: Almost CohenMacaulay AlgebrasPaul RobertsOne of the classical topics in Commutative Algebra is the study of CohenMacaulay rings and algebras. In addition to their intrinsic interest, they have important applications to other questions, such as the Homological Conjectures. A few years ago Heitmann showed that a weaker condition, which we call the property of being almost CohenMacaulay, has many of the same implications and is much more likely to hold. In this talk I will define almost CohenMacaulay rings, give several examples, and discuss some of the implications of their existence.

5:00PM: Counting lattice points and the number 2i+7Steven SamLet P be a lattice ddimensional polytope. A theorem of E. Ehrhart states that the number of lattice points of nP (the nth dilate of P), as a function of positive integers n, agrees with a polynomial of degree d (the Ehrhart polynomial of P). In this talk, I will give a review of Ehrhart polynomials and discuss a paper of C. Haase and J. Schicho that classifies all such polynomials for d=2. If we replace ``lattice polytope'' by ``rational polytope,'' the word ``polynomial'' becomes ``polynomial with periodic coefficients'' (quasipolynomials). I will discuss known bounds for the periods of Ehrhart quasipolynomials, but show that in some cases, they are ordinary polynomials. I will also show that the classification for d=2 is incomplete if we consider rational polygons whose Ehrhart quasipolynomial is a polynomial, and present some conjectures that I like about why some polytopes have smaller period than the known bounds suggest.
