# Dr Adam Piggott

## Areas of expertise

- Pure Mathematics 0101
- Group Theory And Generalisations 010105

## Research interests

Geometric Group Theory; Groups presented by rewriting systems; Automorphism groups of groups.

## Biography

Adam was an undergraduate at the University of Wollongong (B.Math, Honours first class, and B.CompSci) and a graduate student at the University of Oxford (D.Phil. Mathematics). Working as a mathematician in the USA for 13 years (three years at Tufts University and ten years at Bucknell University), he gained considerable experience teaching undergraduate mathematics within the liberal arts model. He returned to Australia in 2018, spending two and half years at the University of Queensland before moving to the Australian National University in 2021 to become the First-year Coordinator in the Mathematical Sciences Institute.

## Researcher's projects

Geodetic groups: foundational problems in algebra and computer science.

A project with Prof. Murray Elder (Univeristy of Technology Sydney) and Prof. Volker Diekert (University of Stuttgart). This project is funded via an ARC Discovery Project grant **DP210100271**.

The project aims to resolve important and longstanding open problems in Geometric Group Theory and Theoretical Computer Science. Since the 1980s researchers have conjectured that the geometric property of admitting a geodetic Cayley graph is equivalent to several purely algebraic, algorithmic, and language-theoretic characterisations of groups. The project requires expertise in geodesic properties of groups, the interaction between formal languages and groups, and the theory of rewriting systems.

## Available student projects

Make an appointment and we can talk about some projects related to rewriting systems in groups, automophism groups of groups, or geometric group theory in general.

## Publications

- Eisenberg, A & Piggott, A 2019, 'Gilman's conjecture', Journal of Algebra, vol. 517, pp. 167-185.
- Cunningham, C, Eisenberg, A, Piggott, A et al. 2016, 'Recognizing right-angled Coxeter groups using involutions', Pacific Journal of Mathematics, vol. 284, no. 1, pp. 41-77.
- Cunningham, C, Eisenberg, A, Piggott, A et al. 2016, 'CAT(0) Extensions of Right-angled Coxeter Groups', Topology proceedings, vol. 48, pp. 277-287.
- Piggott, A 2015, 'On groups presented by monadic rewriting systems with generators of finite order', Bulletin of the Australian Mathematical Society, vol. 91, no. 3, pp. 426-434.
- Koban, N & Piggott, A 2014, 'The Bieri-Neumann-Strebel invariant of the pure symmetric automorphisms of a right-angled artin group', Illinois Journal of Mathematics, vol. 58, no. 1, pp. 27-41.
- Brooksbank, P & Piggott, A 2012, 'On the Derived Length of Coxeter Groups', Communications in Algebra, vol. 40, no. 3, pp. 1142-1150.
- Gutierrez, M, Piggott, A & Ruane, K 2012, 'On the automorphisms of a graph product of abelian groups', Groups, Geometry, and Dynamics, vol. 6, no. 1, pp. 125-153.
- Piggott, A 2012, 'The symmetries of McCullough-Miller space', Algebra and Discrete Mathematics, vol. 14, no. 2, pp. 239-266.
- Piggott, A & Ruane, K 2010, 'Normal forms for automorphisms of universal coxeter groups and palindromic automorphisms of free groups', International Journal of Algebra and Computation, vol. 20, no. 8, pp. 1063-1086.
- Piggott, A, Ruane, K & Walsh, G 2010, 'The automorphism group of the free group of rank 2 is a CAT(0) group', Michigan Mathematical Journal, vol. 59, no. 2, pp. 297-302.
- Gutierrez, M & Piggott, A 2008, 'Rigidity of graph products of abelian groups', Bulletin of the Australian Mathematical Society, vol. 77, no. 2, pp. 187-196.
- Piggott, A 2007, 'The manifestation of group ends in the todd-coxeter coset enumeration procedure', International Journal of Algebra and Computation, vol. 17, no. 1, pp. 203-220.
- Piggott, A 2007, 'Andrews-Curtis groups and the Andrews-Curtis conjecture', Journal of Group Theory, vol. 10, no. 3, pp. 373-387.

## Projects and Grants

Grants information is drawn from ARIES. To add or update Projects or Grants information please contact your College Research Office.

- Geodetic groups: foundational problems in algebra and computer science (Secondary Investigator)