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Introduction: Kristoffe Zehr

Hello everyone. I got my bachelors in Computer Science and Cognitive science at RPI. For a few years after this I worked as a software engineer, and it was during this time that I was first exposed to category theory through Bartosz Milewski's excellent series of blog posts.

I'm currently a graduate student at UIC, preparing to apply to PhD programs in mathematics this fall. I plan to study category theory for my PhD, but I am not yet sure what sort of problems to work on.

At the moment I happen to be organizing an informal course in category theory for programmers while studying for the GRE math test over the summer.

Comments

  • 1.

    Hi, Kristoffe. Fellow RPI alumnus here (BS/MS physics). Now live in Boston, starting part-time grad work in CS in the fall, interested in AI, developmental/cognitive robotics, and teaching robots to learn analogy and metaphor. I'm a bit over my head here with the math, but I'm trying to self-learn Cat Theory. My intuition tells me it will be useful (but not exactly sure how!). I'm also very interested in Conceptual Spaces Theory and concepts as applied to AI. There are a number of papers applying Cat Theory to Conceptual Space theory. Have you thought about applying Cat Theory to AI?

    Comment Source:Hi, Kristoffe. Fellow RPI alumnus here (BS/MS physics). Now live in Boston, starting part-time grad work in CS in the fall, interested in AI, developmental/cognitive robotics, and teaching robots to learn analogy and metaphor. I'm a bit over my head here with the math, but I'm trying to self-learn Cat Theory. My intuition tells me it will be useful (but not exactly sure how!). I'm also very interested in Conceptual Spaces Theory and concepts as applied to AI. There are a number of papers applying Cat Theory to Conceptual Space theory. Have you thought about applying Cat Theory to AI?
  • 2.

    Welcome, Kristoffe! There's a lot of great stuff to do in category theory, but not many math professors who call themselves category theorists in the US. Most people doing serious category theory in the US are homotopy theorists, homotopy type theorists, algebraic geometers... or computer scientists. I'm one of the few who calls myself a "category theorist".

    (By the way, I'm not accepting new grad students - too many already. Not that you asked, but it's sort of an obvious question.)

    Comment Source:Welcome, Kristoffe! There's a lot of great stuff to do in category theory, but not many math professors who call themselves category theorists in the US. Most people doing serious category theory in the US are homotopy theorists, homotopy type theorists, algebraic geometers... or computer scientists. I'm one of the few who calls myself a "category theorist". (By the way, I'm not accepting new grad students - too many already. Not that you asked, but it's sort of an obvious question.)
  • 3.

    Hi Howard, nice to meet you. I've put a bit of thought into applications of category theory to AI - particularly deep learning - after being inspired by some posts on Chris Olah's blog. The direction I'm exploring is considering deep neural networks as morphisms in some subcategory of the category of 1-differentiable manifolds (sufficiently restricted to allow you to do gradient descent). For now this is just a surface-level analysis, I don't yet have the mathematical sophistication to really dive deep into that.

    John, I have noticed that there aren't many 'category theorists' in general - not just in the US. Among other places, I'm looking at Dalhousie University in Halifax, there seem to be several people there working with category theory. I'm only applying to a few schools this fall since I'm still catching up in terms of core undergraduate math courses. Thanks for the heads up though!

    Comment Source:Hi Howard, nice to meet you. I've put a bit of thought into applications of category theory to AI - particularly deep learning - after being inspired by some posts on [Chris Olah's blog](https://colah.github.io/). The direction I'm exploring is considering deep neural networks as morphisms in some subcategory of the category of 1-differentiable manifolds (sufficiently restricted to allow you to do gradient descent). For now this is just a surface-level analysis, I don't yet have the mathematical sophistication to really dive deep into that. John, I have noticed that there aren't many 'category theorists' in general - not just in the US. Among other places, I'm looking at Dalhousie University in Halifax, there seem to be several people there working with category theory. I'm only applying to a few schools this fall since I'm still catching up in terms of core undergraduate math courses. Thanks for the heads up though!
  • 4.

    I really should go back to school. Though I don't know how much a CS masters would really get me given that's all that's stopping me from just doing CS things is motivation and dedication. Math I need a teacher.

    Comment Source:I really should go back to school. Though I don't know how much a CS masters would really get me given that's all that's stopping me from just doing CS things is motivation and dedication. Math I need a teacher.
  • 5.

    Sorry not to reply for a while...

    Kristoffe wrote:

    John, I have noticed that there aren't many 'category theorists' in general - not just in the US.

    That's true, but Canada has more category theorists than the US, which is bizarre if you compare it to any other branch of math.

    Among other places, I'm looking at Dalhousie University in Halifax, there seem to be several people there working with category theory.

    Yes, I'm friends with Peter Selinger (who got a huge NSA grant to design a quantum programming language using category theory and then to help design a quantum computer), and Dorette Pronk (who does good work with cospan categories). They are both quite well-known. The big annual world-wide category theory conference was in Dalhousie a few years ago.

    You should take a look at this, to see who else you might meet in Dalhousie:

    If you're looking for category theory in Canada you should also look at McGill:

    though some of the people there are getting old (despite the picture) and Lambek has died, and also Ottawa:

    Pietr Hofstra is very energetic these days.

    Comment Source:Sorry not to reply for a while... Kristoffe wrote: > John, I have noticed that there aren't many 'category theorists' in general - not just in the US. That's true, but Canada has more category theorists than the US, which is bizarre if you compare it to any other branch of math. > Among other places, I'm looking at Dalhousie University in Halifax, there seem to be several people there working with category theory. Yes, I'm friends with Peter Selinger (who got a huge NSA grant to design a quantum programming language using category theory and then to help design a quantum computer), and Dorette Pronk (who does good work with cospan categories). They are both quite well-known. The big annual world-wide category theory conference was in Dalhousie a few years ago. You should take a look at this, to see who else you might meet in Dalhousie: * [Atlantic Category Theory Group](https://www.mathstat.dal.ca/~selinger/atcat/). If you're looking for category theory in Canada you should also look at McGill: * [Category Theory at McGill](http://www.math.mcgill.ca/bunge/ctatmcgill.html). though some of the people there are getting old (despite the picture) and Lambek has died, and also Ottawa: * [Logic and Foundations of Computing Group](http://www.site.uottawa.ca/~phil/lfc/). Pietr Hofstra is very energetic these days.
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