Manchester Number Theory Seminar - Sam Streeter (Bristol)

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Speaker: Sam Streeter (Bristol) Title: Hilbert property for del Pezzo surfaces of degree one Abstract: Various conjectures in arithmetic geometry predict the abundance of rational points on Fano varieties. In dimension two, these are the well-studied family of del Pezzo surfaces, whose arithmetic and geometric complexity is controlled by their degree, an integer between one and nine, with degree one proving the most challenging. I will report on work with Julian Demeio and Rosa Winter in which we provide the first examples of non-thinness of rational points (the Hilbert property), thus abundance, in certain families of del Pezzo surfaces of degree one and Picard rank one. Room: Frank Adams 1, Alan Turing Building