Citation
Lieber, Joshua Franklin (2021) Études in Homotopical Thinking: F₁-geometry, Concurrent Computing, and Motivic Measures. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/a4zm-1f28. https://resolver.caltech.edu/CaltechTHESIS:06092021-045504824
Abstract
This thesis weaves together three papers, each of which provides a use of homotopical intuition in a different field of mathematics. The first applies it to the study of various models of F₁-geometry, focusing mainly on the Bost-Connes algebra. The second endeavors to compare two homotopical models for concurrent computing before introducing a new one as well. Finally, the last paper provides a construction for obtaining derived motivic measures from an abstract six functors formalism and, in particular, applies this idea to obtain a lift of the Gillet-Soulé motivic measure.
| Item Type: | Thesis (Dissertation (Ph.D.)) | ||||||
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| Subject Keywords: | Homotopy theory; F1-geometry; concurrent computing, motives, motivic measures | ||||||
| Degree Grantor: | California Institute of Technology | ||||||
| Division: | Physics, Mathematics and Astronomy | ||||||
| Major Option: | Mathematics | ||||||
| Thesis Availability: | Public (worldwide access) | ||||||
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| Defense Date: | 27 May 2021 | ||||||
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| Record Number: | CaltechTHESIS:06092021-045504824 | ||||||
| Persistent URL: | https://resolver.caltech.edu/CaltechTHESIS:06092021-045504824 | ||||||
| DOI: | 10.7907/a4zm-1f28 | ||||||
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| Default Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
| ID Code: | 14269 | ||||||
| Collection: | CaltechTHESIS | ||||||
| Deposited By: | Joshua Lieber | ||||||
| Deposited On: | 30 Aug 2021 16:19 | ||||||
| Last Modified: | 28 Oct 2021 18:58 |
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