UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

September 12, 2017

939 Evans Hall

3:45PM: Changing Views on Curves and Surfaces

Bernd Sturmfels

We present work with Kathlen Kohn and Matthew Trager on visual events in computer vision. Given an algebraic curve or surface in 3-space, the image or contour curve arises by projecting from a viewpoint. Qualitative changes in that curve occur when the viewpoint crosses the visual event surface. The components of this ruled surface are iterated singular loci of the coisotropic hypersurfaces associated with the original curve or surface. We present formulas, due to Salmon and Petitjean, for the degrees of these surfaces, and show how to compute visual event surfaces using algebraic tools.

5:00PM: Evolutions and Second Symbolic Powers

Jana Sotakova

Let K be a field and let R be a local K-algebra. An evolution of R is a surjective homomorphism T->R of K-algebras such that the induced map between the modules of differentials is an isomorphism. We will see that the question of the existence of non-trivial evolutions is related to the Eisenbud-Mazur conjecture on (second) symbolic powers.

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