Rte 81 2009

The 19^th Annual Route 81 Conference on Algebraic Geometry and Commutative Algebra will take place on Saturday, October 17, 2009, hosted by the Mathematics Department of Syracuse University.

Talks

8:30–9:00

Breakfast (donuts, bagels, coffee provided)

9:00–9:30

Jennifer Bierman (Cornell): Reverse lex ideals
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In this talk, I will introduce the notion of reverse lex ideals in a polynomial ring, and compare their properties to those of lex ideals. In particular I provide an analogue of Green's Theorem for reverse lex ideals. I also compare the Betti numbers of Borel and square-free Borel monomial ideals to those of reverse lex ideals.

9:40–10:10

Gwyn Whieldon (Cornell): Regularity of edge ideals
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Connecting algebraic invariants of edge ideals (projective dimension, regularity, types of betti diagrams possible, etc.) to combinatorial properties of the original graph allows us to better characterize possible resolutions of edge ideals in terms of these bits of data. In the case of edge ideals of trees, for example, the regularity of I(G) is exactly one higher than the largest number of edges which are restriction disjoint - and regularity of all edge ideals is bounded from below by this number, eInd(G). However, we can construct a large class of examples where the regularity is higher than eInd(G) - and we provide a characterization of possible reg(I(G)) in terms of eInd(G). Finally, we can also give some characterization of possible "lower edges" of betti diagrams.

10:50–11:20

Kyungyong Lee (Purdue): Hilbert schemes of points
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The famous n! conjecture can be stated in an elementary language. In fact it asserts that the dimension of the vector space spanned by all derivatives of a certain bivariate analogue of the n ?n Vandermonde determinant is equal to n!. Earlier results of Haiman and Garsia had shown that the n! conjecture implied the Macdonald positivity conjecture. Later Haiman proved the n! conjecture by showing that isospectral Hilbert schemes of points on the plane are normal and Cohen-Macaulay. I'll discuss how the properties in the plane case can or cannot be generalized to the higher dimensional case.

11:30–12:00

Thuy Pham (Toronto): On the computation of jdeg of blowup algebras
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For a graded algebra A, its jdeg(A) is a global degree that can be used to study complexity of the normalization. In this talk, we discuss methods to estimate jdeg using symmetric algebras and approximation complexes. This is joint work with Wolmer Vasconcelos.

12:00–2:00

Lunch

2:00–2:30

Janet Striuli (Fairfield): Homological properties of almost Gorenstein rings
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In this talk we will present some of the homological properties of a class of ring that were first defined by Vraciu-Huneke. In particular we will talk about the existence of totally reflexive modules and the syzygies of the canonical module.

2:40–3:10

Allen Knutson (Cornell): Frobenius splitting, point counting and degeneration
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3:50–4:20

Suanne Au (Le Moyne): The equivariant K-theory of toric varieties
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4:30–5:00

Valdemar Tsanov (Queen's): Embeddings of flag varieties and cohomological components in representations of semisimple Lie Algebras
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Location, Map, Parking