Mathematics Feed

Quantum Gravity Lesson 38

Every math undergraduate loves their torus, with the 18 triangles needed to compute homology. With quantum cubes, we automatically label axes discretely with powers of a letter. 
So when does a square include a 2-cell? Look at the bottom left square. 


A category theorist will immediately see that this is a limit diagram for the product of X and Y. But the square defined by the generator of H1 does not yield a nice square, although it does commute.


Prismatic Cohomology


When I was working in Los Angeles last year, my main focus was thinking about motivic cohomology with Michael Rios. Other quantum gravity colleagues were less mathematically inclined, and only Michael and I appreciated the depth of the new theory and its potential for deriving classical spaces. Mike likes to wear Pink Floyd T-shirts with prisms on them, and he put the picture on an arxiv paper some time ago.

This week at UCLA (oh, Los Angeles) a mathematician is talking about a new theory of motivic cohomology, which is called Prismatic Cohomology, after the Pink Floyd album cover (for the Dark Side of the Moon). 

Terence Tao blog post

Columbia lecture notes

Terence Tao links to new seminar notes by anonymous audience members. Take a look.


As you know, q-deformations are what happens to classical algebras when we go to braided structures. And from quantum gravity, we determined that the cohomology underlies the emergence of coordinates.