Logo

Mathematical Sciences Research Institute

Home » DDC - Valuation Theory: Everywhere local solubility for hypersurfaces in products of projective spaces

Seminar

DDC - Valuation Theory: Everywhere local solubility for hypersurfaces in products of projective spaces November 11, 2020 (09:00 AM PST - 10:00 AM PST)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Jennifer Park (Ohio State University)
Description

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Video

Everywhere Local Solubility For Hypersurfaces In Products Of Projective Spaces

Abstract/Media

Valuation theory plays a major part in the interaction between number theory and logic. In this seminar, a variety of topics from valuation theory, and in particular connections to model theory, will be discussed. There will be a strong emphasis on results involving the definability of valuations.

To participate in this seminar, please register here: https://www.msri.org/seminars/25206

Abstract: Poonen and Voloch proved that the Hasse principle holds for either 100% or 0% of most families of hypersurfaces (specified by degrees and the number of variables). In this joint work with Tom Fisher and Wei Ho, we study one of the special families of hypersurfaces not accounted for by Poonen and Voloch, and we show that the explicit proportion of everywhere locally soluble (2,2)-curves in P^1 x P^1 is about 87.4%.

No Notes/Supplements Uploaded

Everywhere Local Solubility For Hypersurfaces In Products Of Projective Spaces

H.264 Video 25219_28733_8623_Everywhere_Local_Solubility_for_Hypersurfaces_in_Products_of_Projective_Spaces.mp4