Notre Dame
Student Algebraic Geometry/
Commutative Algebra Seminar
Spring 2009
(3-4pm on Mondays in 258 Hurley)
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Date |
Time/Place |
Speaker |
Title |
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Feb 9 |
usual |
Angela Kohlhaas |
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Feb16 |
usual |
Angela Kohlhaas |
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Feb 23 |
Usual |
Megan Patnott |
The Weak Lefschetz Property and Non-Unimodality in Codimension Three |
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Mar 6-8 |
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Mar 9-15 |
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Spring Break |
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Mar 23 |
usual |
Kuei-Nuan Lin (Purdue) |
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Apr 20 |
usual |
Bernadette Boyle |
Geometric Consequences of Extremal Behavior in a Theorem of Macaulay |
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Apr 27 |
usual |
Bonnie Smith |
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Algebraic Geometry / Commutative
Algebra Seminar.
Abstract of Talks:
Feb 9: Angela Kohlhaas. The core of ideals with reduction number one
Abstract: The multiplicity of a monomial ideal in a polynomial ring can be
calculated as the volume outside its associated convex hull.
This fact will be used to show that monomial ideals of reduction number one in
k[x,y] have a particular shape, giving us enough information to compute the
core of the ideal. We can then show that the core is integrally closed if and
only if it is equal to the adjoint of the square of the ideal.
Feb 16: Angela Kohlhaas. Cores and adjoints
Abstract: This talk will be a continuation from last week. The adjoint of an ideal is a useful tool in algebraic geometry. Understanding its relationship to the core of an ideal is an important topic of study. We will show that under certain conditions, a monomial ideal in k[x,y] has an integrally closed core if and only if the core is equal to the adjoint of the square of the ideal.
Feb 23: Megan Patnott. The Weak Lefschetz Property and Non-Unimodality in Codimension Three
Abstract: We'll discuss level algebras in three variables. Specifically, they can fail to have the Weak Lefschetz Property, and have even can have non-unimodal Hilbert functions.
Apr 20: Bernadette Boyle. Geometric Consequences of Extremal Behavior in a Theorem of Macaulay
Abstract: In this talk I will discuss what information the Hilbert
function can give us about its respective variety. In particular we
will look at the cases in which maximal growth, as given by a Theorem
of Macaulay, occurs, and specifically when we have growth like a
hypersurface or growth like a curve. This talk is based on a paper of
the same title by A. Bigatti, A.V.Geramita, and J.Migliore
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