Dr Adam Piggott

Senior Lecturer

School of Mathematics and Physics
Faculty of Science
adam.piggott@uq.edu.au
+61 7 336 52321

Overview

Research Interests

  • Combinatorial and Geometric Group Theory
    My research is in combinatorial and geometric group theory, with a particular focus on the automorphism groups of groups, and the groups which can be defined by nice rewriting systems.

Qualifications

  • Doctor of Philosophy, Oxf.

Publications

View all Publications

Available Projects

  • The symmetries of an object have an algebraic structure. Group theory is the study of such structures. In combinatorial group theory, groups are specified via group presentations. This means that we specify an alphabet of symbols, often only a few symbols, and some algebra rules which hold in the group. Everything else about the group must be deduced from the rules we specify. In geometric group theory, we exploit deep connections between groups and geometric structures. There is a sense in which a group itself is a geometric object, and every geometric object comes equipped with a group of symmetries (the isometries). We can use geometry to learn about groups, and we can learn about geometric structures using group theory.

    I will be happy to talk to any honours, masters or Ph.D. student interested in combinatorial and/or geometric group theory to see if we can find a topic which suits their interests. An interested student may wish to peruse the book Office Hours with a Geometric Group Theorist, edited by Matt Clay & Dan Margalit to get a feel for some of the topics in geometric group theory. For combinatorial group theory I suggest browsing through Combinatorial Group Theory by Lyndon and Shupp.

View all Available Projects

Publications

Featured Publications

Book Chapter

  • Piggott, Adam (2018). Coxeter groups. In Dan Margalit and Matt Clay (Ed.), Office hours with a geometric group theorist () Princeton, NJ, United States: Princeton University Press. doi:10.23943/princeton/9780691158662.003.0013

Journal Article

Possible Research Projects

Note for students: The possible research projects listed on this page may not be comprehensive or up to date. Always feel free to contact the staff for more information, and also with your own research ideas.

  • The symmetries of an object have an algebraic structure. Group theory is the study of such structures. In combinatorial group theory, groups are specified via group presentations. This means that we specify an alphabet of symbols, often only a few symbols, and some algebra rules which hold in the group. Everything else about the group must be deduced from the rules we specify. In geometric group theory, we exploit deep connections between groups and geometric structures. There is a sense in which a group itself is a geometric object, and every geometric object comes equipped with a group of symmetries (the isometries). We can use geometry to learn about groups, and we can learn about geometric structures using group theory.

    I will be happy to talk to any honours, masters or Ph.D. student interested in combinatorial and/or geometric group theory to see if we can find a topic which suits their interests. An interested student may wish to peruse the book Office Hours with a Geometric Group Theorist, edited by Matt Clay & Dan Margalit to get a feel for some of the topics in geometric group theory. For combinatorial group theory I suggest browsing through Combinatorial Group Theory by Lyndon and Shupp.