UC Berkeley

Commutative Algebra and Algebraic Geometry Seminar

October 02, 2007

939 Evans Hall

3:45PM: Recent Results in Numerical Algebraic Geometry

Andrew Sommese

Following an overview of Numerical Algebraic Geometry, some recent work will be presented: a) work with J. Hauenstein and C. Wampler on regeneration, a new equation-by equation approach to solving large polynomial systems. b) work with D. Bates, J. Hauenstein, and C. Wampler on adaptive multiprecision and Bertini, our new software for doing numerical algebraic geometry computations. c) work with D. Bates, C. Peterson, and C. Wampler on numerical computation of the geometric genus of curve components of algebraic sets.

5:00PM: Over-constrained mechanisms and curves of genus 7

Frank-Olaf Schreyer

I will describe the algebraic geometry behind certain kinds of "mechanisms" -- those made from rigid rods, hinged together and attached to the "ground" at some points. A mechanism is called over-constrained if the dimension of the variety of movements it can make exceeds the "expected dimension", computed from the number of objects that can move, and the number of constraints satisfied, much as one would compute the "expected dimension" of a variety as the dimension of the ambient space minus the number of equations. I will present a general approach to the discovery of over-determined mechanisms, and study a specific kind of "platform robot" -- basically a table that sits on top of rods of various lengths attached to the floor and hinged so that they can meet floor and table at any angle -- that is connected to algebraic curves of genus 7.

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