Thomas Garrity (Williams College),
Using algebraic geometry to factor polynomials
Multi-variable polynomials with rational coefficients can be factored over
the complex numbers relatively efficiently using some basic algebraic
geometry and some recent work on topological algorithms from robotics.
The steps involve first translating the algebra problem of factoring into
a topological problem (involving the finding of the number of connected
components of a real semi-algbraic set; this are the sets that many people
in robotics care about). Then the topology problem is in turned
translated into finding the number of connected components of a graph,
which is is easy to compute. The efficiency of this algorithm will be
discussed. The talk should be accessible to all graduate students.