The Unreasonable Effectiveness of Spectral Graph Theory: A Confluence of Algorithms, Geometry & ...

James R. Lee, University of Washington
Simons Institute Open Lectures
simons.berkeley.edu/events/ope...
Full title: The Unreasonable Effectiveness of Spectral Graph Theory: A Confluence of Algorithms, Geometry, and Physics

[@rbnn]

Great talk. I wish I'd seen that motivation when I was studying this.

[@Onezero675]

great watch, thanks

[@AdamGenesisArt]

Great video! sparked some ideas

[@columbus8myhw]

Can I ask what the protest was about?

[@shashankupadhyay4163]

awesome

[@aidenkim6629]

15:40

[@forheuristiclifeksh7836]

aleinunas kerp lipton lovasz rackoff RandomWalk 25:34

[@roholazandie3515]

this might be the best explanation on spectral graph theory on the internet!

[@thedeathstar420]

Can I get a citation for the proof mentioned in 32:30?

[@astromcd]

annals.math.princeton.edu/wp-content/uploads/annals-v175-n3-p08-s.pdf

[@forheuristiclifeksh7836]

30:00

[@DinHamburg]

what is the exact reason that the random walk was done on a torus and not on a square ?

[@drewduncan5774]

A square with opposite edges identified is a torus.

[@MravojedNaTrotinetu]

Probably because square grid is topologicaly noncompact and that it requires boundary conditions to be specified while setup on torus is topologycaly compact and does not require boundary conditions (reason why it's more generic than finite square grid).

[@augblog]

The grid on a torus is 4-regular.

[@alfatti1603]

Also note that the torus is topologically nontrivial ( genus-1 surface) which impacts the long term diffusion behaviour

[@wayfinder105]

Torii have the easiest boundary conditions to program probably (just have to write every coordinate modulo, no need to write any special cases).