## The UW Sage Seminar Schedule

The seminar meets at 5pm in Communications B027.

DATE: Monday, December 3, at 5pm TITLE: Status reports

DATE: Monday, November 26, at 5pm Seminar: The Sage Seminar Organizer: William Stein Title: Combinatorial Generation Speaker: Robert Miller, UW Location: 5pm in Communications B027 Abstract: Suppose you want to classify some collection of objects. Optimally, as is often the case if your objects are algebraic, there is some theorem that does all the work. For example, finitely generated abelian groups are determined by a sequence of integers, i.e. the rank and the elementary divisors. On the other end of the spectrum is when your objects are not so well behaved, and there is a "combinatorial explosion" of possibilities- you cannot hope for a theorem, and instead you wish to simply generate those objects one by one, such that each isomorphism class has exactly one representative generated. The naive approach would be to go through each possibility, adding one to the list only after it has been determined to be not isomorphic to those already in the list. There is an alternative approach, involving no isomorphism elimination at all. This approach will be explained, and some new coding theory software will be presented.

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TITLE: Groebner Basics LOCATION: Thomson Hall 215 at ** 4PM ** on November 5, 2007 SPEAKER: Josh Kantor ABSTRACT: Groebner bases are a fundamental tool which allow for efficient algorithmic computation in polynomial rings and modules over such rings. We we will start with the simple question of ideal membership, i.e., given an ideal $I \subset k[x_1,\ldots x_n]$, and $f \in k[x_1,\ldots, x_n]$, how does one check whether or not $f\in I$. We will show how Groebner basis solve this problem, and others.

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Monday, October 29, 2007:

TITLE: Combinatorial Algebras in SAGE TIME: 5-6pm on Monday, October 29, 2007 LOCATION: B027 in the Communications building SPEAKER: Mike Hansen Abstract: A "combinatorial algebra" is an algebra over a ring whose module basis is indexed by a class of combintorial objects with multiplication on basis elements typically determined by some combinatorial operation. Some examples of combinatorial algebras include the symmetric group algebra of order n (indexed by permutations of size n), the algebra of Schubert polynomials (indexed by permutations), partition algebras (indexed by set partitions satisfying certain constraints), and the symmetric function algebra (indexed by integer partitions). In this talk, I will go over support for combinatorial algebras in SAGE with an emphasis on symmetric functions, some issues that have arisen in their implementation, and things still left to do.

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Monday, October 15, 2007:

TITLE: Introduction to Abelian Varieties TIME: 5-6pm on Monday, October 15, 2007 LOCATION: B027 in the Communications building SPEAKER: Robert Miller Abstract: What the heck is an abelian variety? Elliptic curves are the 1-dimensional abelian varieties. What are they in general? Maybe something like an abelian group and an algebraic variety? A complex torus is a complex manifold which is diffeomorphic to an n-torus. All such structures can be obtained as a quotient of CC^n by a lattice, and this procedure gives us a compact complex manifold. For n=1, this is an elliptic curve. For n >= 1, any variety structure on a complex torus must be unique, and Riemann proved that there is such a variety structure if and only if the torus can be embedded in complex projective space. More specifically, CC^n/L is an abelian variety if and only if there is a positive definite Hermitian form whose imaginary part takes integral values on L. After defining abelian varieties as above, William Stein will give an example or two in Sage.

Monday, October 22, 2007:

(no seminar)

Monday, November 5, 2007:

Monday, November 12, 2007: (no seminar -- Sage Days 6)

Monday, November 19, 2007:

Monday, November 26, 2007:

Monday, December 3, 2007: