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Études in Homotopical Thinking: F₁-geometry, Concurrent Computing, and Motivic Measures


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.


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.))
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)
Research Advisor(s):
  • Marcolli, Matilde
Thesis Committee:
  • Flach, Matthias (chair)
  • Marcolli, Matilde
  • Mantovan, Elena
  • Graber, Thomas B.
Defense Date:27 May 2021
Funding AgencyGrant Number
Perimeter Institute for Theoretical PhysicsUNSPECIFIED
Foundational Questions InstituteFQXi-RFP-1 804
Record Number:CaltechTHESIS:06092021-045504824
Persistent URL:
Lieber, Joshua Franklin0000-0002-6936-5054
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:14269
Deposited By: Joshua Lieber
Deposited On:30 Aug 2021 16:19
Last Modified:28 Oct 2021 18:58

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