Completed PhD Students
1.
Mei Chee SHUM
Thesis title: Tortile Tensor Categories (Macquarie
University, November 1989); published in full in Journal of Pure and Applied Algebra 93 (1994) 57-110.
2.
Scott R. JOHNSON died 8 December 1988; posthumous PhD 1994;
Thesis title: Cauchy Completion in Enriched Categories
(Australian National University, 1993).
Publications forming
the thesis:
1. Monoidal Morita
equivalence, Journal of Pure & Appl.
Algebra 59 (1989) 169-177;
2. Small Cauchy
completions, Journal of Pure & Appl.
Algebra 62 (1989) 35-45;
3. Modulated
bicategories (with A. Carboni, R. Street and D.
Verity), Journal of Pure & Appl.
Algebra 94 (1994) 229-282.
Book by Steve Johnson on Scott’s life and the circumstances of his
death:
Steve Johnson, A
Thousand Miles from Care (HarperCollins, 2024).
Thesis title: Categories of Representations of Balanced Coalgebroids (Macquarie University, 22 February 1999) ; awarded a Letter
of Commendation from the Dean of Graduate Students.
Publications arising
from the thesis:
1. Balanced coalgebroids, Theory
and Appl. of Categories 7 (2000) 71-147;
2. Categories of
Representations of Coalgebroids, Advances in Math. 154 (2000) 299-332;
3. Tannaka
duality for Maschkean Categories, Proceedings of the
Category Theory Conference in Coimbra (July 1999), J. Pure. Appl. Algebra 168 (2002) 265-367.
4.
Mark WEBER
Thesis title: Symmetric Operads for Globular
Sets (Macquarie University, May 2001).
5. Isar
STUBBE
Thesis title: Categorical structures enriched in a quantaloid: categories and semicategories (Principal
Supervisor Francis Borceux, Universit\'e
Catholique de Louvain, Belgium, 2003).
Thesis title: Categories of Mackey Functors
(Macquarie University, 10 April 2007; http://hdl.handle.net/1959.14/119).
7.
Craig PASTRO
Thesis title: Hopf algebras and related structures in a categorical
environment (Macquarie University, 10 June 2008).
8.
Dimitri CHIKHLADZE
Thesis title: Elements of enriched and quantum category
theory (Macquarie University, submitted 2 July 2010; PhD awarded 28 September
2010).
Publications arising
from the thesis:
1. Barr's Embedding
theorem for enriched categories, Journal
of Pure and Applied Algebra 215 (2011) 2148-2153.
2. Category of quantum
categories, Theory and Applications of
Categories 25 (2011) 1-37.
3. (with S. Lack and
R. Street) Hopf monoidal comonads,
Theory and Applications of Categories
24 (2010) 554-563.
4. The Tannaka representation theorem for separable Frobenius functors, Algebras
and Representation Theory (accepted on 22 February 2011).
9.
David OURY
Thesis title: Duality for Joyal's
category $\Theta $ and homotopy concepts for ${\Theta }_{2}$-sets (Macquarie University, submitted 18
March 2011; PhD awarded 4 October 2011).
Publication arising
from the thesis:
10.
Thomas BOOKER
Thesis title: Structures in and on monoidal categories
with a view towards Tannaka duality
(Macquarie
University, submitted 15 December 2011; PhD awarded 3 April 2012).
Publication arising
from the thesis:
11.
Camell KACHOUR
Thesis title: Aspects of Globular Higher Category Theory
(Principal Supervisor Michael Batanin; Macquarie
University, PhD awarded 5 November 2013).
12.
Mitchell A. BUCKLEY
Thesis title: Three studies in higher category
theory: fibrations, skew monoidal structures and
excision of extremals (Main Supervisors Dominic Verity and Richard
Garner; Macquarie University, PhD awarded 2015).
Thesis title: A higher categorical approach to
Giraud's non-abelian cohomology (Macquarie
University, PhD awarded 6 October 2016).
14.
Ram\'on ABUD ALCAL\'A
Thesis title: Oplax actions and enriched icons with
applications to coalgebroids and quantum categories
(Principal Supervisor Stephen Lack; Macquarie University, PhD awarded ~November
2017).
15.
Christopher NGUYEN
Thesis title: Parity structure on associahedra
and other polytopes (Principal Supervisor Stephen Lack; Macquarie
University, PhD awarded March 2018).
16.
Branko NIKOLI\'C
Thesis title: Morphisms of 2-dimensional structures with
applications (Macquarie University, PhD awarded May 2018).
17.
Charles R. WALKER
Thesis title: Structures in two dimensional
category theory and applications to polynomial functors (Principal
Supervisor Richard Garner; Macquarie University, PhD awarded March 2019).
18.
Yuki MAEHARA
Thesis title: The
Gray tensor product for 2-quasi-categories (Principal supervisor Dominic
Verity; Macquarie University, PhD awarded September 2020).
Partially supervisor of: Tim
Brook PhD ANU 1974; Greg
Bird PhD USyd 1984; Andrew
Solomon PhD USyd 1997. Geoffrey Lewis PhD
UNSW 1974 was a student of Max Kelly
Current PhD Students (Macquarie University)
Hardy Hulley (Principal supervisor Richard Garner)
Eli Hazel (Principal supervisor Richard Garner who also supervised the MRes: Stone and Priestley
dualities via the ultrafilter and prime filter monads)
Ruben Zilibowitz (Principal supervisor Richard Garner)
Visiting Masters Students
Steve Bennoun (\'Ecole Polytechnique F\`ed\'erale de
Lausanne), Tannaka Duality for Comodules over a Hopf Algebra (October 2006 -- March 2007)
Jean-Baptiste Boyer (\'Ecole Normale
Superieure de Cachan, antenne de Bretagne), Categories and Algebraic Topology (June 2010 -- July 2010)
Basile Pillet (\'Ecole Normale Superieure
de Cachan, antenne de
Bretagne), Tangle with categories: Presentation and
Report
(July 2011 -- August 2011)
Honours and MRes Students
Frank Sharpe, Sheaves as Generalized
Sets (1973)
Colin Hill, Sets with Operations
from a Categorical Point of View (1974)
Mark Weber, A Mathematical Analogy
(1996)
Amy Young, Traced Monoidal Categories
(June 1998)
Dilshara Abayasekara, Species of
Structure (1999)
Simon Byrne, Groupoids and
Stuff Types (2005)
Thomas Booker, Non-Standard
Numbers as Global Sections of a Dedekind Reals Object (2007)
Mitchell Buckley, Lawvere
Theories (2008)
Ruben Zilibowitz (MResYear2; Principal supervisor Richard
Garner), The Game Semantics of Free Cartesian Closed
Categories: a Syntactic Derivation (2023)
Vacation Scholars
1994: Heidi Manning (Knot theory)
1995: Paddy McCrudden (Quantum groups) and Stephen Warburton (Links formed
in fencing wire)
1996: Stuart Lawrence (String diagrams in linear algebra)
1997: Daniel O'Neil and Paul Batten (Representations of the finite
general linear groups)
2001: Ryan Crompton and Thi Minh Tam Pham (The
Taylor expansions of tanx and secx; also see http://www.maths.mq.edu.au/~street/Boustroph.pdf
)
2002: Ben Odgers and Hanh Nguyen Vo (Efficient development of number
systems and trigonometry)
2004: James Douglas and Rony Kirollos (Number
systems, TeX and categories)
2005: Simon Byrne (Quantum groups)
2006: Mitchell Buckley (String diagrams in algebra)