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Introduction: Jeb Collins

edited April 2018 in Chat

I'm an assistant professor at the University of Mary Washington. I am an applied computational mathematician, but I've always been interested in combining pure mathematics with applied. Making a bridge between the two to use a pure mathematical idea in an applied setting. Because of my love of these bridges, category theory in general interests me, but applied category theory particularly interests me.

Most of my work has to do with computationally solving differential equations, so I'm interested to see if these techniques can be applied in a setting with PDEs. I have basically no experience with Category theory, aside from what I've learned from Tia-Danae on Math3ma blog. But I like to learn new things and I'm interested to read through the book.

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  • 1.
    edited April 2018

    Hi - nice to see you here! I'm interested in combining the study of ordinary differential equations with category theory; my best effort so far is this:

    I'm just flying back from Wisconsin right now, where I was talking to Gheorghe Craciun and David Anderson about much more detailed problems about the dynamics of open reaction networks. They're experts on differential equations of this sort, so I can do much better work with them than by myself!

    One could also use category theory to study PDE. In physics people already do it for quantum field theory, but I haven't seen it done much for classical field theory, also known as PDE.

    Comment Source:Hi - nice to see you here! I'm interested in combining the study of ordinary differential equations with category theory; my best effort so far is this: * John Baez and Blake Pollard, [A compositional framework for reaction networks](https://arxiv.org/abs/1704.02051). I'm just flying back from Wisconsin right now, where I was talking to Gheorghe Craciun and David Anderson about much more detailed problems about the dynamics of open reaction networks. They're experts on differential equations of this sort, so I can do much better work with them than by myself! One could also use category theory to study PDE. In physics people already do it for quantum field theory, but I haven't seen it done much for _classical_ field theory, also known as PDE.
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