28th of October - Lucas Slot (UvA) (at 14:00)
Title: Positivity and promptsÂ
Abstract: A Positivstellensatz (named after Hilbert's Nullstellensatz) gives an algebraic certificate of positivity for a multivariate, real polynomial. A substantial literature is devoted to proving degree bounds on these certificates. Recently, optimal bounds were obtained in two or three of the most studied settings by various (groups of) people prompting various AI models (and thinking). These improve upon the state-of-the-art by a lot, and essentially close a line of research going back about two decades. I talk about an experimental, ongoing collaboration aimed at collecting these results and making their proofs accessible to human readers.