Title:
Analyzing walks with combinatorics and automata theory

Abstract:
The enumeration theorem by Chomsky and Schützenberger revealed
a significant intersection between the theory of automata and
enumerative combinatorics. Since then, much progress has been made in
both fields. However, their intersection remains unchanged in the sense
that no further enumeration theorem emerged beyond that of
Chomsky-Schützenberger. We survey the literature in both fields and
picture what it would look like to expand the intersection between them.

Kuykendall Hall 210

Title: Low($Pi^0_1$-IM) = $Delta^0_1$

Abstract: My dissertation investigated $Pi^0_1$-immune sets, i.e. those
that have no co-enumerable subset. This talk continues that work, first
connecting it to modern notions of computability-theoretic lowness. Then
I settle (in the affirmative) a conjecture that my dissertation left
open: only the computable sets fail to co-enumerate a $Pi^0_1$-immune
set.