Fri Mar 14, 2008
60 Evans Hall, 4:10–6 PM
Matthias Aschenbrenner (Mathematics, UCLA)
Uniform Degree Bounds for Groebner Bases
I will address some topics concerning algorithms and bounds for polynomial rings over Noetherian coefficient rings. These issues essentially go back to Kronecker’s ideology of constructive mathematics. I’ll explain some of the history, state a natural conjecture on degree bounds for Groebner bases, and provide evidence for its truth. I’ll also give a characterization (proved using elementary nonstandard analysis) of those Noetherian commutative rings for which there exist uniform degree bounds for Groebner bases of ideals of polynomial rings over these rings.