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AG as studied by mathematicians has produced an incredible amount of applications that would not exist without that level of abstract tooling. And it's highly

AG as studied by mathematicians has produced an incredible amount of applications that would not exist without that level of abstract tooling. And it's highly nontrivial to learn those tools (as someone that has worked through Hartshorne... And then put 20 years into applications).

auggierose 4y ago
What are some of those applications?
- SideQuark 4y ago
  Besides the other list, places results from AG have uses in tech include statistics, control theory, robotics, error-correcting codes, phylogenetics, geometric modelling, string theory, game theory, graph matchings, solitons , integer programming, computer vision, computer aided design..... Some of these are likely why Blinn decided to make an entire course on using it just in computer graphics alone.
  - auggierose 4y ago
    Thanks, I am aware of the general uses, I was just wondering what you in particular have used it for :-)
    - SideQuark 4y ago
      I've used it professionally for error correcting code design, robotic control, crypto (ecc and multivariate polynomial), lots of computer vision uses, grobner bases to simplify algorithms, and geometric modeling. Perhaps more if I look over lists of past projects...
- matt-noonan 4y ago
  Here are a few off the top of my head, as a mathematician-turned-programmer who never has been an algebraic geometer. - Elliptic curve cryptography (https://en.wikipedia.org/wiki/Elliptic-curve_cryptography https://en.wikipedia.org/wiki/Elliptic-curve_cryptography) - Grobner bases, with many applications. Example domains: coding theory, robotics, signal processing... (https://math.stackexchange.com/questions/32421/applications-of-gröbner-bases https://math.stackexchange.com/questions/32421/applications-...) - Physics [solitons] (https://kasmana.people.cofc.edu/SOLITONPICS/ https://kasmana.people.cofc.edu/SOLITONPICS/) - Physics [string theory] (https://royalsociety.org/~/media/people/new-fellows-2014/Presentation-slides/Bridgeland.pdf https://royalsociety.org/~/media/people/new-fellows-2014/Pre...) - Automata theory, via "tropical" algebraic geometry (https://link.springer.com/article/10.1007/s00233-019-09999-8 https://link.springer.com/article/10.1007/s00233-019-09999-8) This is not even considering applications of AG to other areas of pure mathematics, which are extensive.

auggierose 4y ago

What are some of those applications?

SideQuark 4y ago
Besides the other list, places results from AG have uses in tech include statistics, control theory, robotics, error-correcting codes, phylogenetics, geometric modelling, string theory, game theory, graph matchings, solitons , integer programming, computer vision, computer aided design..... Some of these are likely why Blinn decided to make an entire course on using it just in computer graphics alone.
- auggierose 4y ago
  Thanks, I am aware of the general uses, I was just wondering what you in particular have used it for :-)
  - SideQuark 4y ago
    I've used it professionally for error correcting code design, robotic control, crypto (ecc and multivariate polynomial), lots of computer vision uses, grobner bases to simplify algorithms, and geometric modeling. Perhaps more if I look over lists of past projects...
matt-noonan 4y ago
Here are a few off the top of my head, as a mathematician-turned-programmer who never has been an algebraic geometer. - Elliptic curve cryptography (https://en.wikipedia.org/wiki/Elliptic-curve_cryptography https://en.wikipedia.org/wiki/Elliptic-curve_cryptography) - Grobner bases, with many applications. Example domains: coding theory, robotics, signal processing... (https://math.stackexchange.com/questions/32421/applications-of-gröbner-bases https://math.stackexchange.com/questions/32421/applications-...) - Physics [solitons] (https://kasmana.people.cofc.edu/SOLITONPICS/ https://kasmana.people.cofc.edu/SOLITONPICS/) - Physics [string theory] (https://royalsociety.org/~/media/people/new-fellows-2014/Presentation-slides/Bridgeland.pdf https://royalsociety.org/~/media/people/new-fellows-2014/Pre...) - Automata theory, via "tropical" algebraic geometry (https://link.springer.com/article/10.1007/s00233-019-09999-8 https://link.springer.com/article/10.1007/s00233-019-09999-8) This is not even considering applications of AG to other areas of pure mathematics, which are extensive.