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.

Slides

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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.

slides

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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.

Slides Worksheets Video

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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:

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