What actually is the idea behind the condensed mathematics?

The most basic thing in condensed mathematics is a condensed set. nLab says, "A condensed set is a sheaf of sets on the pro-étale site of a ...

Condensed mathematics - Wikipedia

Condensed mathematics is a theory developed by Dustin Clausen and Peter Scholze which, according to some, aims to unify various mathematical subfields, ...

Getting into condensed mathematics : r/math - Reddit

The first set of notes on condensed math focus on sketching one way to define (through the condensed theory) a 6 functors formalism for coherent ...

Condensed Mathematics and Analysis - Math Stack Exchange

I think that the vision of Clausen and Scholze was to construct a “nice formalism” containing topological spaces (the not-too-pathological ones, ...

Condensed Mathematics and Complex Geometry Dustin Clausen ...

In fact, the notion of qs condensed set exactly matches the notion of compactological space developed by Waelbrock, [Wae06]. Via this description in terms ...

Applications of Condensed mathematics? - Math Stack Exchange

This question is probably premature. In challenging the formalization community to prove a fundamental theorem in the theory, Scholze admits ...

condensed mathematics - nForum

Probably easier and conceptually clearer ways to do it will be found in the future; it is really quite a natural idea to try to treat real analysis ...

Categorical Foundations of Formalized Condensed Mathematics

... in the theory of condensed mathematics ... of condensed mathematics ... The notion of an indexed family of morphisms over X is not exactly ...

Lectures on Condensed Mathematics Peter Scholze (all results joint ...

... condensed mathematics taught in ... theory of completion for condensed abelian groups ... 10 However, as the current notion does not exactly match the classical ...

Session 8: Masterclass in Condensed Mathematics - YouTube

... Condensed mathematics" currently being developed by Dustin Clausen and Peter Scholze. This theory holds the promise of vastly expanding the ...

'condensed-mathematics' tag wiki - MathOverflow

Condensed mathematics of Clausen and Scholze. Closely related to the pyknotic ... What actually is the idea behind the condensed mathematics? Clausen ...

oberseminar: condensed mathematics

Condensed mathematics redefines the notion of topological ... allowing all rings and modules to be condensed if not stated otherwise, i.e. by D(A) we actually ...

The Foundations of Condensed Mathematics - Dagur Asgeirsson

The above notion of cohomology is really a cohomology of the condensed set S associated to the topological space S. We might as well define ...

condensed mathematics in nLab

1. Idea. Condensed mathematics aims to provide a more convenient framework in which to treat algebraic objects which are equipped with a ...

Algebraic geometry and its plot to take over the (analytic) world.

Recently, Peter Scholze posted a challenge to the Xena project to formalize a result in condensed mathematics. The motivation for this result is ...

Liquid tensor experiment | Xena - WordPress.com

(Besides some general topos theory and homological algebra (and, for one point, a bit of stable homotopy theory(!)), the argument mostly uses ...

Chris Lambie-Hanson (CAS, Prague), PHK 16.11.2022 - YouTube

Title: Condensed mathematics and set theory Speaker: Chris Lambie-Hanson (Institute of Mathematics of the Czech Academy of Sciences) ...

Math for Condensed Matter or Materials Science Theory

In summary, a physics major/math minor would benefit from taking upper-level math classes that cover combinatorics, algorithms, ...

An introduction to condensed mathematics

The idea of. Clausen and Scholze is to actually use the site of all (light) profinite spaces S and not ... which is necessary to understand the basics of the ...

notes on solid geometry - Columbia Blogs

ring/module/abelian group/monoid) will be condensed "preferred algebraic structure". The idea behind condensed mathematics follows the philosophy of ...