UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

August 25, 2009

939 Evans Hall

3:45PM: Integral Closure, Pure and Applied

David Eisenbud

Location: Evans 939

Among the most fundamental operations in commutative algebra and algebraic geometry is \emph{integral closure}, or \emph{normalization} as it is often called. I'll give an introduction to this idea and its uses, and I'll discuss the computational problem of finding the integral closure of a ring or an ideal, demonstrating how to do it in the Macaulay2 symbolic computation system.

5:00PM: Arrangements of Hyperlanes, Lines and Conics

Adam Boocher

Location: Evans 939

A hyperplane arrangement is simply a union of hyperplanes. Much is known about these arrangements, yet many basic questions remain open. For example, Terao's conjecture states that the freeness of a hyperplane arrangement (a simple algebraic condition) depends only on the combinatorics of the arrangement. This conjecture is still open even for arrangements of lines in the plane. The analogous conjecture for arrangements of lines and conics is false. In this talk I will give a general introduction to the theory of line arrangements and discuss related work for conic-line arrangements.

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