Mathematics¶

February 13, 2014
in Mathematics
5 min read

Isotopy

Equivalence of algebraic structures

Consider two finite algebras that are the same except for a relabeling of the operations. Our intuition tells us that these are simply different names for the same mathematical structure. Formally, however, not only are these distinct mathematical objects, but also they are nonisomorphic.

Isotopy is another well known notion of "sameness" that is broader than isomorphism. However, I recently proved a result that shows why isotopy also fails to fully capture algebraic equivalence.

February 13, 2014
in Mathematics
1 min read

Overalgebras

In the Overalgebras GitHub repo resides the article Expansions of finite algebras and their congruence lattices, Algebra Universalis, 69, 2013. Also included is the GAP software I wrote for constructing new finite algebras by extending and expanding transitive G-sets, as described in the paper.

February 5, 2014
in Mathematics, Formal verification
2 min read

Diaconescu's Theorem

I learned about Diaconescu's Theorem from Andrej Bauer's lecture.

This post describes the proof as it was presented by Bauer. These notes are rough and intended for my own reference. Please see François Dorais' blog post for a nice discussion of this topic.