Robert J. Graham

About

I am a Ph.D. student in mathematics at McGill University studying homotopy type theory and various other things. My supervisor is Mikael Pichot.

Contact

robert.graham2@mail.mcgill.ca
1020 Burnside Hall

Papers

[pdf] Approximate Convex Hulls: sketching the convex hull using curvature (with Adam Oberman)


We compute approximate convex hulls by finding the points with high curvature. We provide justification for this method and extend it to finding the hyperplanes of a convex hull.


[pdf] Synthetic Homology in Homotopy Type Theory (Draft)


The basics of homology formulated in homotopy type theory


[pdf] Universal entropy invariants (with Mikael Pichot)


We describe how one can define an "entropy" invariant for many mathematical structures. This is a generalization of a procedure that has already occurred multiple times in the literature most notably in the work of Dan Voiculescu on free probability and Lewis Bowen on Bernoulli shifts (and technically classical entropy). In essence, it is a way to measure the number of approximations to your structure.


[pdf] A free product formula for the sofic dimension (with Mikael Pichot)


This is a technical result computing the sofic dimension of an amalgamated free product of pmp groupoids. It contains a straightforward generalization of results by Lewis Bowen on Bernoulli shifts from groups to groupoids.