Seminar
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| Location: | SLMath: Online/Virtual |
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.
Torsors And Topology In Diophantine Problems
To participate in this seminar, please register here: https://www.msri.org/seminars/25206
I will give an introduction to two of my specific research areas, both of which hinge on an application of ideas from topology to Diophantine problems. A key notion is that of a torsor, a more algebraic version of principal bundles from topology. A torsor in this context is a set with an action of a finite or algebraic group along with an auxiliary action of the absolute Galois group of the field in question. I will explain in a simple case how Kummer theory may be phrased in terms of torsors. Then I will discuss how they apply in two of my research projects: one about the Brauer-Manin and etale homotopy obstructions and their limits, another about Kim's non-abelian Chabauty's method for provably finding the (finite) set of integral points on certain varieties.
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Slides
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Torsors And Topology In Diophantine Problems
| H.264 Video | 25147_28645_8446_Torsors_and_Topology_in_Diophantine_Problems.mp4 |