GReTA seminar #10: 'Hypergraph Rewriting and the Wolfram Model'

Speaker: Jonathan Gorard (University of Cambridge and Wolfram Research, UK)

Abstract:

This talk will summarize some recent results obtained in connection with the Wolfram Physics Project: a systematic attempt to reduce fundamental physics to the problem of hypergraph rewriting. Specifically, we will discuss the construction of an efficient hypergraph rewriting scheme using the formalism of Wolfram model multiway systems, with a categorical semantics defined via double-pushout rewrites over selective adhesive categories, and equipped with a dagger-symmetric monoidal structure that exhibits surprising formal connections to categorical quantum mechanics. We will also demonstrate that, by equipping such a multiway system with an additional notion of causal structure (defined via the semantics of precausal categories), we are able to introduce new inference rules of selective resolution, paramodulation and factoring that generalize the standard Knuth-Bendix completion rules for term rewriting systems, and significantly improve the efficiency of automated diagrammatic reasoning algorithms over hypergraphs. Time permitting, we will discuss some near-term practical applications of these methods for quantum information theory (allowing for more efficient diagrammatic simplification of quantum circuits), as well as numerical general relativity (allowing for more explicit numerical simulation of graph-theoretic models of space and time).

About the GReTA seminars:

[tarkajedi]

A Nobel prize is in this mans future along with Wolfram and the entire team....
It will only expand this year !!!! If you don't know this exciting and profound work take the time to understand .... This has profound implications for our entire understanding of the universe and offers us hope of exciting new advances!!!

[tarkajedi]

Masterful presentation!!!! This is making exciting advances.... I am watching this again!!!!

[tarkajedi]

The Wolfram Model has already made unbelievable connections between GR and Quantum Mechanics!!! Surprising and revolutionary... For years I believed we were in the dark ages of understanding gravity and space-time and now I have hope for a profound change.... Share this with your friends!!!

[tarkajedi]

The Wolfram Project has already done what has not been done for decades.... So many exciting advances to follow methinks !!!! It has taken me twice as long and lots of work to follow and it is a beautful mathematical thing....

[tarkajedi]

People who understand Categry Theory are Wizards!!!!

[StephenPaulKing]

Jonathan, check out the work of Marius Buliga!

[tassomatr]

Understood about 1% of what was said, but couldn't stop watching

[dakrontu]

He says 'ok' the same way Wolfram does.

[nolan]

Inverting the rules doesn't turn back the clock?

[silberlinie]

Ungücklicherweise brennt Jonathan sein
Leben an mehr denn drei Enden ab.