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Phone: (407) 823-6284;   Fax: (407) 823-6253;   MAP  207 2005-2006 MATHEMATICS COLLOQUIUM SERIES 11/10/05 Colloquium Dr. Joseph P. Brennan North Dakota State University Computing With Invariants Abstract:  A critical question in computational invariant theory is that of the existence of a finite sagbi basis for the ring of invariants. This is the computational analogue of the 14th problem of Hilbert. This talk will examine joint work of the speaker with R. Fossum on the analogue of the result of Wetizenbock for finiteness of rings of invariants for the additive group through the proof of a conjecture of McClintock. This presentation will also contain an independent sub-talk on the mathematical modeling of nanoparticle formation with particular emphasis on estimation of the polydispersity of the nanoparticles involved.