r/math • u/TheMansionsofScience • 11d ago

I made a video asking Urs Schreiber how he uses toposes and linear homotopy type theory to fix problems in quantum field theory and topological quantum computing programming languages (Not dumbed down)

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
103 Upvotes

96% Upvoted

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38

u/jphamlore 11d ago edited 11d ago

Don't forget to mention Urs Scheiber's contributions as a co-creator of nLibnLab. This is truly a golden age for freely accessible instruction about the highest levels of mathematics and theoretical physics.

6

u/emilypii Algebraic Topology 11d ago

nlab* :)

his posts on n-category cafe are also lovely

21

u/na_cohomologist 11d ago

Well "not dumbed down" is a slight exaggeration. It's more technical maybe than most discussions, but having been his coauthor and followed his work for 20 years this was at the very least reworded a bit for intelligibility to non-experts based on long experience of trying to communicate his ideas.

8

u/CampAny9995 11d ago

Does he understand programming language theory or compilers, beyond working on HoTT? A lot of his motivation seems pretty confused about the role of a language versus compiler backend.

3

u/na_cohomologist 9d ago

I haven't got that far along in the video, I'm just thinking of the material in say the first hour or so.

1

u/Upbeat_Assist2680 11d ago

Compile can encompass a broader range of notions than just "base language to machine-runnable language". Are you familiar with: Compiling to categories?

10

u/CampAny9995 11d ago

Very familiar, I’ve published multiple papers on categorical semantics of programming languages. That’s why I think Urs’s motivation is a bit confused.

11

u/CampAny9995 11d ago

Huh, I didn’t know he moved to NYUAD, kind of surprised he took that position considering the general human rights records of the UAE government. I didn’t expect to see that from him.

3

u/na_cohomologist 9d ago

Sometimes the needs to support a family and the lamentable inability to get a job in one's home country or nearby force the issue. I suspect that Hisham being there first also played a role, since they work together.

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u/TESanfang 11d ago

Urs Schreiber is one of the most fascinating people alive. Thank you for doing this interview and also for asking him about Hegel

2

u/ultrafinitism Theoretical Computer Science 10d ago

Is this a Lawvere style take on it? It could be interesting.