Finding the roots to polynomial equations with several complex variables using a homotopy proceedure from a system of polynomials with known roots to the system of given polynomials with unknown roots. At time = 0, the proceedure begins with the known system of roots. As time increments by a time step of dt, the current roots are used as the next guess in Newton's method. When time = 1, we arrive at the given system and have a good approximation of the roots. Complications involve root collisions, however, this is circumvented by means of a guess of collision time and a flip of the roots by 90 degrees. Document includes one nontrivial example. Code is currently unavailable for the several variable algorithm.

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Date	Location
November, 1999	Graduate Student Colloquium, University of Utah
January, 2000	Undergraduate Student Colloquium, University of Utah

Self Avoiding Walks (SAWs) are finite length paths, typically in a lattice topology of dimension d, which do not intersect themselves. For example, one may think of taking a walk in a city without crossing or back-tracking your route. In biology, SAWs come up in the context of protein formation. Of particular interest and currently unknown, we wish to find the number of SAWs of length n for a given lattice dimension. A seemingly simple problem, this paper presents an overview of results to date and some ideas at finding a solution.

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Date	Location
December, 2000	Graduate Student Colloquium, University of Utah