UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

March 31, 2015

939 Evans Hall

3:45PM: Eigenconfigurations of Tensors

Anna Seigal

Diagonalizing a matrix is extremely useful in many applications, and so would be finding an equivalent way to decompose a tensor. We will discuss ways to generalize eigenvectors to the case of tensors, and the possible configurations of points in projective space that can occur as the eigenvectors of some tensor. We also discuss what it means for a tensor eigenvector to be robust and the applications of such eigenvectors. It is based on ongoing work with Bernd and Hirotachi Abo at the University of Idaho.

5:00PM: The Riemann Singularity Theorem and a Cancellation Theorem for Segre Classes

Daniel Lowengrub

The Riemann Singularity theorem is a classical theorem relating two important objects associated to smooth curves. It says that the multiplicity of a point on the theta divisor of the curve is equal to the dimension of the fiber of the Abel Jacobi map from the Hilbert scheme of points to the Jacobian. Sebastian Casalania-Martin and Jesse Kass proved an analog of this for nodal curves and conjectured what the formula should be for general planar curves. In this talk, we will prove a theorem about Segre classes which will allow us to generalize Fulton's proof of the Riemann Singularity theorem to arbitrary planar curves, and thus obtain the conjectured formula.

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