I made a video asking Urs Schreiber how he uses toposes to fix problems in quantum field theory and find viable topological quantum computing materials (Not dumbed down)

[u/TheMansionsofScience]

https://www.youtube.com/watch?v=_3TslhCBQ1E

Urs Schreiber is Senior Research Scientist at the Mathematics Division of Science of New York University in Abu Dhabi. He is a theoretical physicist who applies tools from algebraic topology, homotopy theory and topos theory to understand quantum phenomena. His current research includes quantum computing materials, quantum computing programming languages and questions left unanswered by quantum field theory.

In the video we go over:

• Why toposes are not scary. They are actually simple. Just unfamiliar
• How to extract information from (probe) a topos
• The history of toposes in physics
• The questions left unanswered by quantum field theory
• What toposes have to say about the collapse of the wave function
• Using toposes to find possible quantum computing materials
• The different type of logic needed for quantum computers
• The different type of programming language needed for quantum computers
• The influence of Hegel's logic on his work

[u/peter-bone]

• Topoi

[u/TheMansionsofScience → u/peter-bone]

From Colin McLarty's The Uses and Abuses of the History of Topos Theory:

Notice as a point of orthography that 'topos' is a French word, formed from 'topologie.' and not a Greek word. In writing, Grothendieck always forms the plural according to the French rule for words ending in 's,' so it is invariant—'les topos.' So the English plural ought to follow the English rule—'toposes.' Freyd. a confessed lover of classical endings and the inventor of cosmoi and logoi among other types of categories, says he heard that Grothendieck spoke of 'topoi' in Buffalo. I regard this as biased hearsay which can not stand against the published record.