contents

Research Projects
Invited lecture series
Reading courses
Lecture courses
Expository lectures and outreach

research projects

If you are interested in doing a research project either as an Honours thesis, a higher degree thesis or over summer, please come and talk to me. Possible topics include:

Low-dimensional topology (knot theory, 3-manifolds, geometric structures)
Hyperbolic geometry (hyperbolic manifolds, invariants)
Group theory (representations of finitely generated groups, group actions on trees)
Computational algebraic geometry
Tropical geometry (foundation, algorithms and applications)

supervision of postgraduate students

Dickson Annor, MPhil (started 2016)
Dominic Tate, PhD (started 2016)
Alex Casella, PhD (started 2015)
Montek Gill, MSc (2015)

supervision of honours students

The University of Sydney
• Grace Garden: The Mapping Class Group and its Action on the Character Variety of the Once-Punctured Torus (2015)
• Dominic Tate: Parametrising the Teichmüller Space of the Punctured Torus (2015)
• Montek Gill: The Hyperbolic Gluing Equations Over Commutative Rings and a Residual Property of 3-Manifold Groups (2014)
• Sampson Wong: Algorithms for the Epstein-Penner decomposition of a cusped surface (2014)
• Alex Casella: Toric varieties associated to ideal triangulations (2013-2014)
The University of Queensland
• Samuel Mellick: Alexander invariants and the Thurston norm (2011)
• Mitchell Watt: Morse Theory: Smooth and Discrete (2011)
The University of Melbourne
• Tharatorn Supasiti: Serre's tree for SL(2,F) (2008)
• James Wan: Projective Geometry, Projective Structures, and the Hex Metric (2008)

supervision of undergraduate research projects

The University of Sydney
• Colin Huang, Jongmin Lim, Zac Sanchez, Will Stewart, Max Tobin, Alec Zhang with Leo Jiang as mentor: TSP Showcase Project (SCTP1907): Births and Deaths of Singularities (2017)
• Asem Wardak (3rd year), AMSI Vacation Research Project: Negatively curved structures in dimensions three and four via discrete geometry (2016/17)
• Mahan Ghobadi (2nd year), Summer Vacation Research Project: Hyperbolic and Projective Arithmetic Fuchsian Groups (2016/17)
• Ennes Mehmedbasic and Edwin Spark (3rd year), Summer Vacation Research Project (co-supervised with Alex Casella): The toric geometry of the hyperbolic gluing equations (2015/16)
• Abdul Zreika (2nd year), AMSI Vacation Research Project, together with Courtney Darville, Lachlan Mcpheat and Asem Wardak (2nd year), Summer Vacation Research Project (co-supervised with Robert Haraway): The space of closed essential normal surfaces in knot complements (2015/16)
• Kieran Ballurkar, Chunxi Jiao, Cecilia Li, Rachel Wong with Joshua Ciappara as mentor: TSP Showcase Project (SCTP1907) Unravelling the Dodecahedral Spaces (2014)
• Julien Sedro (Ecole Normale Superieure de Cachan), 2-month masters internship: The Epstein-Penner construction (2013)
• Courtney Darville, Jack Gregan, Gavin Lee, Nick Miltchinov, Ankur Paul, George Polonski with Sampson Wong as mentor: TSP Showcase Project (SCTP1907) Space: Appearance, Imagination and the Fourth Dimension (2013)
• Montek Gill (2nd year), AMSI Vacation Research Project: Cross ratios and Thurston's gluing equations over rings (2012/13)
The University of Queensland
• Tom Chappell (2nd year), Advanced Study Program in Science: Low-dimensional topology (2010)
• Samuel Mellick (3rd year), Summer Research Project: Gromov norm and scl (2010)
The University of Melbourne
• Stephen Muirhead, Summer Vacation Project (co-supervised with Craig Hodgson). Title: Projective structures on surfaces (2008)
Columbia University in the City of New York
• Co-supervised three students in a VIGRE Undergraduate Summer Research Experience (with Walter Neumann and Abhijit Champanerkar). Title: A-polynomials of hyperbolic 3-manifolds (2000)

invited lecture series

Triangulations and combinatorial differential geometry, MSC Tsinghua University, China (July 2014)
Real projective manifolds, MSC Tsinghua University, China (July 2012)
Geometry & Groups, AMSI Summer School, University of New South Wales (January 2012)
Varieties associated to 3-manifolds, Melbourne Summer School, The University of Melbourne (January 2001)

reading courses

Reading courses are tailored to the interests and background knowledge of the participants. Assessment typically consists of exercises or presentations (40%) and a short report (60%).

The University of Sydney
• Jack Gregan, Knot theory, SCTP1832 TSP Project (Semester 2, 2013)
• Joshua Ciappara, Discrete Groups of Isometries, SCTP2649 TSP Project (Semester 2, 2013)
• Montek Gill, Geometry after Klein, SCTP2831 TSP Project (Semester 2, 2012)
The University of Queensland
• Nirav Shah, Invariants of knots, SCIE3012 (Semester 2, 2010)

undergraduate working seminars

The University of Sydney
Surfaces: A Junction of Geometry, Topology and Analysis, SCTP3753 TSP Mathematics Activity A Snr (Semester 1, 2014)
Working Seminar B (Special Studies Program), MATH2917 (Semester 2, 2012)
The University of Queensland
Topology & Groups, MATH6006 Proseminar (Semester 1, 2011)

lecture courses

The University of Sydney, 2012–present
Basic Pharmaceutical Sciences, PHAR1812 (Semester 1, 2017 and 2016)
Topology and Geometry of Three Dimensional Manifolds, PMH6 (Semester 2, 2016)
Algebra (Advanced), MATH2968 (Semester 2, 2016, 2015, 2014, 2013 and 2012)
Discrete Mathematics, MATH1004 (Semester 2, 2015)
Linear Algebra (Advanced), Weeks 1–6 of MATH1902 (Semester 1, 2015)
Differential Geometry (Advanced), Weeks 7–13 of MATH3968 (Semester 2, 2014)
Linear Mathematics, Weeks 1–6 of MATH2061 (Semester 1, 2014, 2013 and 2012)
Fields and Galois Theory (Advanced), Weeks 7–13 of MATH3962 (Semester 1, 2013)
The University of Queensland, 2009–2011
Functional Analysis III/IVH, MATH4404 (Semester 2, 2011 and 2009)
Differential Geometry, MATH3405 (Semester 2, 2011)
Functional Analysis, MATH3402 (Semester 1, 2011)
Discrete Mathematics, MATH1061 (Semester 2, 2010)
Measure Theory, MATH4405 (Semester 2, 2010)
The University of Melbourne, 2007–2008
Linear Algebra, 620-156, The University of Melbourne (Semester 2, 2008)
Complex Analysis, 620-413, The University of Melbourne (Semester 2, 2007)
UQAM, 2004–2006
Algèbre linéaire I, UQAM (Hiver 2004, 2005 et 2006)
McGill University 2004–2005
Advanced Calculus, MATH 264, McGill University (Fall 2005)
Vectors, Matrices and Geometry, MATH 133, McGill University (Fall 2004)

undergraduate tutorial teaching / recitation classes

The University of Sydney, 2012–present
Discrete Mathematics, MATH1004 (Semester 2, 2015)
Algebra (advanced), MATH2968, Tutorial (Semester 2, 2012 and 2013) and Practice class (Semester 2, 2012, 2013, 2014, 2015 and 2016)
Rings, Fields and Galois Theory (Advanced), MATH3962 (Semester 1, 2013)
• Two tutorial groups of Linear Mathematics and Vector Calculus, Weeks 2–7 of MATH2061 (Semester 1, 2012)
The University of Queensland, 2009–2011
Functional Analysis III/IVH, MATH4404 (Semester 2, 2011)
Measure Theory, MATH4405 (Semester 2, 2010)
Functional Analysis III/IVH, MATH4404 (Semester 2, 2009)
The University of Melbourne, 2008
Complex Analysis, 620-252 (Semester 2, 2008)
Technische Universität Berlin, 2002
Linear Algebra and Linear Differential Equations for Engineers
Trinity College at The University of Melbourne, 2000–2003
Courses include Mathematical Methods, Linear Algebra, Abstract Algebra
The University of Melbourne, 1999–2003
Courses include Real and Complex Analysis, Vector Analysis, Linear Algebra, Abstract Algebra, Differential Equations

expository lectures

23 April 2015
Scissors congruence and Hilbert's third problem, SUMS Seminar, The University of Sydney
11 September 2014
Three angles on tropical geometry, SUMS Seminar, The University of Sydney
16 August 2010
Circle packing and Ricci flow, GI/LA Seminar, The University of Queensland
26 November 2009
Kneser's Lemma and Decompositions of 3-Manifolds, PhD Journal Club, The University of Queensland
29 October 2009
Introduction to geometric group theory, III (with Murray Elder), PhD Journal Club, The University of Queensland
22 October 2009
Introduction to geometric group theory, II (with Murray Elder), PhD Journal Club, The University of Queensland
15 October 2009
Introduction to geometric group theory, I (with Murray Elder), PhD Journal Club, The University of Queensland
25 June 2007
Two lectures on the A-polynomial, CMS, Zhejiang University, Hangzhou, China
3 November 2005
All about the A-polynomial, Séminaire CIRGET Junior, Montréal, Canada
2 December 2003
Circle packing and Ricci flow, ISM Graduate Students Seminar, Montréal, Canada
27 November 2003
Kneser's lemma and decompositions for 3-manifolds, Séminaire CIRGET Junior, Montréal, Canada

(outreach) high schools

2013–
"Mathematicians in Schools" partnership with Randwick Public School

outreach (lectures and activities for high school and early undergraduate students)

13 June 2017
The shape of space, lecture at MANSW "MX1&2 Day," The University of Sydney, Australia
7 June 2016
The shape of space, lecture at MANSW "MX1&2 Day," The University of Sydney, Australia
14 August 2014
The shape of space, lecture and activity for year 8 students of Scots College, Bellevue Hill, at The University of Sydney, Australia
19 June 2014
The shape of space, lecture at MANSW "Talented Students Day," UNSW, Australia
1 April 2010
Knots, "Advanced Study Program in Science" seminar, The University of Queensland, Australia
19-21 January 2010
The shape of space, a hands-on workshop for "The Science Experience," The University of Queensland, Australia
4 September 2009
Minimal surfaces, a bubbly activity for Year 10 physics classes from Forest Lake College and Alexander State High School as part of the SMP Activities Day, The University of Queensland, Australia
15 February 2008
The shape of space, lecture and activity for K12 Students of Kyneton Secondary College at The University of Melbourne, Australia
7 February 2007
The shape of space, lecture and activity for K12 Students of Kyneton Secondary College at The University of Melbourne, Australia
2 May 2006
Living in hyperbolic space, Marianopolis College, Montréal, Canada
5 April 2006
Living in hyperbolic space, Heritage College, Hull, Canada