UW Algebra Seminar

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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