Now showing items 1-5 of 5

• #### Algebraic Approaches to State Complexity of Regular Operations ﻿

(University of Waterloo, 2019-10-15)
The state complexity of operations on regular languages is an active area of research in theoretical computer science. Through connections with algebra, particularly the theory of semigroups and monoids, many problems ...
• #### Contributions to the Theory of Radicals for Noncommutative Rings ﻿

(University of Waterloo, 2017-06-20)
We consider several radical classes of noncommutative rings. In particular, we provide new results regarding the radical theory of semigroup-graded rings, monomial algebras, and Ore extensions of derivation type. In ...
• #### On Hopf Ore Extensions and Zariski Cancellation Problems ﻿

(University of Waterloo, 2020-04-29)
In this thesis, we investigate Ore extensions of Hopf algebras and the Zariski Cancellation problem for noncommutative rings. In particular, we improve upon the existing conditions for when $T=R[x; \sigma, \delta]$ is a ...
• #### Recurrence in Algebraic Dynamics ﻿

(University of Waterloo, 2020-07-28)
The Dynamical Mordell--Lang Conjecture states that if a polynomial orbit has infinite intersection with a closed set in an algebraic variety, then the intersection must occur periodically. Although this problem is unsolved ...
• #### Sparse Automatic Sets ﻿

(University of Waterloo, 2020-11-26)
The theory of automatic sets and sequences arises naturally in many different areas of mathematics, notably in the study of algebraic power series in positive characteristic, due to work of Christol, and in Derksen's ...

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