• Mathematics has a long track record of refining the concepts by which we make sense of the world. For example, mathematics allows one to speak about different senses of "sameness", depending on the larger context. Phenomenology is the name of a philosophical discipline that tries to systematically investigate the first-personal perspective on reality and how it is constituted. Together, mathematics and phenomenology seem to be a good fit to derive statements about our experience that are, at t…Read more
  • Motivated by Scholze and Fargues' geometrization of the local Langlands correspondence using perfectoid diamonds and Clausen and Scholze's work on the K-theory of adic spaces using condensed mathematics, we introduce the Efimov K-theory of diamonds. We propose a pro-diamond, a large stable (infinity,1)-category of diamonds D^{diamond}, diamond spectra and chromatic tower, and a localization sequence for diamond spectra.