### UW Algebra Seminar

Abstracts

**Speaker:**
Nikos Tziolas

**Title:**
Families of D-minimal models and applications to 3-fold
divisorial contractions

**Date:**
January 25

**Abstract:**
Let X be a projective algebraic variety and let D be a Weil
divisor on it. One of the fundamental constructions in birational
geometry is the D-minimal model. The D-minimal model of X is a
birational map f:Y-->X such that f is an isomorphism in codimension 1
and the birational transform of D in Y is Q-Cartier and f-ample. I will
discuss when the D-minimal model exists and in particular if D-minimal
models form families. As an application i will classify certain 3-fold
terminal divisorial contractions.

**Speaker:**
Zachary Treisman, University of Washington

**Title:**
Counting lines with jet spaces

**Date:**
February 1

**Abstract:**
The framework of intersection theory on projective jet spaces
allows for
some interesting computations, such as a quick way to see the 27
lines
on a cubic surface. This particular computation gerneralizes
easily to
higher dimensions. Generalization to higher degree, though perhaps
expected, is not as apparent. I'll describe the setup and some
interesting features of these calculations.

**Speaker:**
Dan Krashen, Institute for Advanced Study

**Title:**
Zero cycles on homogeneous varieties

**Date:**
February 8

**Abstract:**
The computation of Chow groups of projective homogeneous varieties
has had interesting applications in the theory of quadratic forms,
central
simple algebras, and K-theory. In this talk I will describe some
new methods
of computing the Chow group of zero cycles in a projective variety
involving
R-equivalence and symmetric powers. With these tools, I am able to
compute
this group for certain classes of homogeneous varieties, extending
previous
results of Panin, Swan, and Merkurjev. To do this, we explore
connections
between these homogeneous varieties and the problem of
parametrizing
subfields in a central simple algebra.

**Speaker:**
Yu Yuan, University of Washington

**Title:**
Resolving the singularities of the minimal Hopf cones

**Date:**
February 22

**Abstract:**
We resolve the singularities of the minimal Hopf cones by
families of regular minimal graphs.
In justifying the equivariance of the
Hopf map (in particular, S^15--->S^8),
we establish the partial Moufang identity and alternativity for the
partially normed algebra of sedenions, the direct sum of two
copies of the octonions (Cayley numbers).

*To request disability accommodations, contact the Office of the ADA
Coordinator, ten days in advance of the event or as soon as possible:
543-6450 (voice); 543-6452 (TDD); 685-3885 (FAX); access@u.washington.edu (E-mail).
*

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