I think I finally understand pushouts and pullbacks from your tutorial.

An example I like is a radomissed algorithm to approximate the Sierpinski Gasket by starting with a set consitting of the vertices of an equilateral triangle then, starting from 1 vertex, of the set choose another vertex at random, move 2/3 of the stright line distance to that point, create a new vertex and add it to the set. In the limit this produces the Sierpinski Gasket. I think this belongs to deterministic results from randomised algorithms but it may not fit your definition exactly.

In optimization sometimes people use randomized algorithm to solve the max cut problem with very good performance.

thank u for this

There is so much lore. I am a little scared of taking AG next semester. But I want to start sometime. 😅

thank you. I'm researching basic nets in projective plane and facing cw complex this is helpful

Do we have numerical groebner bases

One of the strongest application of algebraic geometry in this field is the application of algebraic method for constructing sum of square optimization. These sum of square optimization can then be solved by using semidefinite programming

I watched , 2024 biggest breakthroughs in computer science, by quanta magazine kzbin.info/www/bejne/nIWwfqaomqakjpI It mentions difficulty of making sense of overall calculated Hamiltonians , so let's do sum of squares and polynomial relaxation :)

Thank you! Now all what I read makes much more sense!

I want you to know I was yelling "What!? How?" at my screen while watching this lol, mind blown.

I hope you have a video explain fiber bundle I could not find it, I am also interested in why we need it and how it is useful with use cases, thx

Extremely useful, Thanks!

Thank you! Exactly what I wasn't understanding

bro aging backward

EIGENVALUES

This QR algorithm sounds a lot like an application of the Helmholtz decomposition of vector field into a solenoid vector field and an irrotational vector field.

8:47 Oh, that's really cute. You're kind of beating M into two matrices Q and R such that QR=RQ?

Where would you point me to if I want to learn more about how fixed points work generally in math? You seem to have fixed point intuition that I want lol

how can a line become a point, i think alot of lines should become a plane

Another typo: at 2:12, in order to match the graph, equation (2) should evidently be x + y = 1/2

I love the fact you link books/resources of the topics you cover, amazing work! Your lie theory video blew kinda up (atleast algorithmic 3k views in 3 days)!

Nice video and explanation! Subscribed!

Im very interested in the concept of groups associated with partial differential equations. Especially how those groups may evolve or deform a little bit as the parameters in the differential equations vary for example the heat diffusion coefficient in the heat equation. Have you heard of others studying this concept and have any pointers on how to study this? In artificial intelligence there is a crowd how approximate operators using neural networks and the deep O nets/fourier neural operators do use this concept of parameter variation as a tunable parameter in part of their training algorithm. However, I haven’t seen them study algebra or operator algebras tangential to doing operator approximations in that way. And that’s what I’d like to study and research in more detail.

9:00 I've personally seen a guy (I think he was from the ENS Paris) effortlessly use the fraktur typeface, in chalk, on a blackboard. I was so in awe

Lie theory is nice when applied to nt

Beautiful and informative video. Thanks!

Damn, I need to catch up on the previous content haha...By then you will hopefully have said a few words about Topos Theory and its potential to unify all of math (and even physics?). I am currently experimenting with it...Thanks for your tireless work

You have an absolutely lovely way to explain the essentials of these topics.

Great content as always

Yeah! It’s here! Yours videos at weekend are One of my favorite times of the week😊

Probably my favorite topic, automated discovery of math.

The natural transformation at 9:53 , is this from (the composition of the hom bifunctor from \calD \times \calD to Set, with F \times id_\calC ), to (the composition of the bifunctor from \calC \times \calC to Set , with id_\calD \times G ) ? And then this natural transformation is an adjunction if all of the morphisms comprising it are isomorphisms (in particular, bijections) ?

The way you've defined SL_n(K), as a set of particular matrices whose determinant is 1 led me to think that SL_n it's not in fact the variety, but actually the set of loci of zeroes of the determinants of these matrices is in fact the set of varieties , not SL_N(K) . Am I correct, or is there something I'm not seeing ? I'm not a mathematician, so it's important for me to get the precise idea....

skein is not a made up word - it comes from knitting

Oh I am so looking forward to taking an AG class next semester. :D

Outstanding approch and explanation. Your examples are superb

Nice video thanks

im a third year uni student and im really enjoying your series. thanks for making the videos :D

Where can i get lots of examples of modular representations? Any book recommendations?

Your work has been noted. It has aided my understanding and will aid humanity as a whole.

Hilariously, it seems group theory is a natural extension of linear algebra. This is the equivalent to coordinate transformations!

In my Graph Theory course, we were told that complete graphs are denoted with K for Kuratowski, who proved that a graph was planar if and only if it had no subgraph that could be homomorphically reduced to K_5 or K_3,3

Any source providing a diagrammatic representation of Hecke algebras? Like the relevant diagrams arising in Temperley-Lieb algebras.

What will you do with your time once you've been replaced by computers?

Got understood with ur nice explanation still for me much is left to go

Thank you!

Thank you so much!!

A very good video! Thank you.

Is this notion of module the same as modules over rings? a generalisation of vector space? Why do you choose module and not vector space? Since you keep promoting linear algebra which is the study of vector spaces.