Apr

7

Thu

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.

Sep

19

Tue

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.

## University of Hawaiʻi at Mānoa