Hi, I’m Mori. I like to approach complex questions via deep mathematical structures

Suppose someone hands you a complex system in a black box, what do you do to try to understand it?
A. You try to see what it does (Representation theory)
B. You try to see how it changes (Deformation theory)
Often the answer to A informs the answer to B, and vice versa - via some form of Duality.
Top-down
Some big pictures [How questions tend to be asked in my mental landscape]
Linearization + boundary conditions = categorified representation theory
Analytic vs Algebraic deformations of a system
Eidostates and categorification
Bottom-up
Structures I'm investigating [Building blocks of my mental landscape]
Infinitesimal geometry over the sphere spectrum
Tannaka duality in (infinity, infinity) -categories
Koszul Duality as the salient structure underlying both areas above
Living questions
Some questions I find to be generative as of late (updated: Apr 15 2024)
- How do formal group laws arise in nature/complex systems?
- How to encode the synchronization/resonance of different clocks in an organism using cyclotomic structures/genuine circle actions?
- What does an adaptive system look like as a structure on a moduli space of functors?

I’m best reached via email, or in person - for the moment - in Montreal, Canada