Luka Carroll
On a Class of Right Restriction Monoids Related to Diagram Monoids and Transformation Semigroups
“Investigate a new family of right restriction (diagram) monoids, including:
1. Obtaining a presentation (by generators and relations) using recently-established techniques.
2. Gaining an understanding of the underlying combinatorial structures built from the idempotents of these monoids and their ideals.
3. Answering questions about minimal generating sets.
4. Using computational experiments to investigate their congruences.”
Luka Carroll
Western Sydney University
Luka Carroll is an undergraduate student in his second year of a Bachelor of Mathematics, majoring in Computational Mathematics, at Western Sydney University. Initially working as an estimator for a mid-sized construction company, Luka then pursued a degree in philosophy before rediscovering his love for mathematics.
Luka doesn’t just enjoy finding the solution to a problem; rather, he wants to know why a solution works and how it can be generalised. This has led him to focus on mathematical proofs and algorithms, especially in the fields of abstract algebra and combinatorics.
He also has a philosophical interest in mathematics, particularly how the unreasonable effectiveness of its applications and the frequent occurrence of pure mathematical discoveries preceding any real-world analogue, seem to suggest the existence of a coherent, abstract universe parallel to our own.
In his spare time, Luka enjoys cooking elaborate meals, going for long runs and observing the native birds in his local area of Emu Plains.
Once he has completed his degree, Luka hopes to pursue a career in pure mathematics research, algorithm design or machine learning.
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