Stephan Tillmann

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

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)

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

- 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)

- The University of Sydney
- • TBA with Hazel Browne as mentor:
Science Dalyell Showcase (SCDL1991):
*Renewal in Fractals and Random Walks*(2018) - • Richie Lim, Jonathan Mui, Michael Zhao, Summer Vacation Research Project:
*Solv manifolds*(2017/18) - • 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)

- •
*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 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
- • Hazel Browne,
*Lie Groups and Lie Algebras*, SCTP3753 TSP Project (Semester 1, 2018) - • Shane Arora and Hazel Browne,
*Naive Lie Theory*, SCTP2649 TSP Project (Semester 1, 2017) - • 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)

- 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)

- 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)

- 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*

- 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

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

- 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