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Seminar

DDC Junior Seminar: Definability Results in Global Fields and Connections with Central Simple Algebras September 01, 2020 (09:00 AM PDT - 10:00 AM PDT)
Parent Program:
Location: MSRI: Online/Virtual
Speaker(s) Philip Dittmann (TU Dresden)
Description

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

The seminar will feature research talks by the six postdoctoral scholars appointed to the Fall 2020 DDC program, along with talks by students and other pre-tenure researchers associated with this program.  Since seminar attendees will have disparate backgrounds, we plan that these talks will not be too advanced, nor will they assume substantial background knowledge.  Our postdocs include number theorists, model theorists, and computable structure theorists, and talks can be expected to span all of these areas.

Video

Definability Results In Global Fields And Connections With Central Simple Algebras

Abstract/Media

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

 

Much recent work in relation to Hilbert's Tenth Problem over the rational numbers has been concerned with building a library of "interesting" diophantine subsets of Q, and more generally of global fields. I will survey some of these results and their geometric content, and give an introduction to the theory of central simple algebras over global fields, which is behind the published proofs either explicitly or implicitly. I also hope to demonstrate how use of this theory allows an efficient treatment of many of these results simultaneously, and speculate on further directions.

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Definability Results In Global Fields And Connections With Central Simple Algebras

H.264 Video 25148_28646_8463_Definability_Results_in_Global_Fields_and_Connections_with_Central_Simple_Algebras.mp4