A/Prof Daniel Chan

Associate Professor
Head of Pure Mathematics
School of Mathematics and Statistics
University of New South Wales
Sydney, 2052, NSW
danielc "shift-2" unsw.edu.au

Office: Red Centre Room 4104
Phone No: 9385 7084

Consultation Times: Tuesday 9-10

To find out a little about me, look at mon autobiographie. [PDF]

Unique Cinematic Experience

Watch the movie Noncommutative Polarisations starring Daniel Chan. Filmed on location at MSRI, Berkeley.

The long awaited sequel is here. Watch Singularities in the Mori program for orders starring Daniel Chan. Filmed on location at the Simons Center for Geometry and Physics, Stony Brook.

Another thrilling episode. Watch Algebraic stacks in the representation theory of finite dimensional algebras. Filmed on location at Casa Matematica Oaxaca, Mexico. Slides below.

Adventures in Pure Mathematics: Youtube videos

If you know the basic language of pure mathematics (i.e. what's a group, ring, topological space), then you may be interested in the following videos which give snapshots of more advanced pure mathematics. They are aimed at honours students, and more generally, anyone who has completed MATH3711 and MATH3611. The goal is to present important ideas and results in mathematics without the burden of going through heavy duty proofs. For the latter, you just need to do the hard work.

DanielChanMaths Youtube channel. The only videos there at the moment are in the Adventures in Pure Mathematics series.

ARC Discovery Project grants

2005-07 Noncommutative algebraic geometry
2008-10 Towards Mike Artin's Conjecture
2013- Interactions between noncommutative algebra and algebraic geometry


Here are some preprints.

Seminar talks

A non-commutative Mori contraction [handout] (Banff 2008) Macaulay assumption is missing from definition of non-commutative smooth projective d-fold
Non-commutative projective geometry (University of Melbourne 2009)
Non-commutative Mori contractions (RIMS 2009)
Singularities in the Mori program for orders [handout] (Simons Center for Geometry and Physics 2011)
Algebraic stacks in the representation theory of finite dimensional algebras (Casa Matematica Oaxaca 2015)
Bimodule species and non-commutative projective lines (Victorian Algebra Conference, UWS 2015)
Moduli stacks of Serre stable representations, ANU 2016)
Axioms for noncommutative smooth proper surfaces , (Clay Mathematics Institute, Oxford 2016)

Lectures on orders (2010) I will be giving a series of lectures on the theory of orders. The main purpose will be to provide details on ramification theory so that one can read papers on recent work on concerning orders on surfaces. The lectures have been typed up by Boris Lerner and should be appropriate for graduate students. They will be updated roughly every week and the final version will be put up on arXiv.

Interested in doing Honours?
If you are interested in doing an honours project in algebra or geometry, feel free to pop in to my office at any time or browse my Adventures in Pure Mathematics: Youtube videos above. Some suggestions for thesis topics.

Past Honours/Masters Students
Antony Orton (2003) wrote an excellent thesis on Algebraic Geometry and the Generalisation of Bezout's Theorem.
Kenneth Chan (2004) wrote a thesis on Riemann surfaces and the Jacobian variety On a proof of Torelli's theorem.
Dave Cock (2004) wrote a thesis on The Weyl algebras.
Piotr Horodynski wrote a thesis on Grobner Bases.
Maiyuran Arumugam (2005) wrote a thesis on A theorem of homological algebra: the Hilbert-Burch theorem.
James Maclaurin (2006) wrote a thesis on The resolution of toric singularities.
Boris Lerner (2007) wrote his thesis on The Brauer-Manin obstruction to the Hasse principle.
Koushik Panda (2007) wrote his thesis on Twisted rings of differential operators on the projective line and the Beilinson-Bernstein theorem.
Nathan Menzies (2007) wrote a thesis entitled An introduction to A-infinity algebras.
Steve Ozvatic (2009) wrote a thesis on Factorisation theory in a non-commutative algebra.
Daniel Smyth (2010) wrote a thesis on Finitely generated powerful pro-p groups.
Anthony Christie (2011) wrote a thesis on Classification of simple plane curve singularities and their Auslander-Reiten quiver.
Matthew Brassil (2012) wrote his thesis on Geometric invariant theory.
Hanning Zhang (2013) wrote a wonderful thesis on homotopical algebra.
Steve Siu (2013) wrote a thesis on K-theory and the Adams operation.
Dorothy Cheung (2015) wrote a thesis on Classification of quadratic forms with Clifford algebras.
Timothy Chan (2016) wrote a thesis on Dimer models and their characteristic polygons.
Adrian Miranda (2017) wrote a masters thesis on Bicategories and higher categories.
Current Honours/Masters Students
Matthew Evat is looking at generating functions associated to polynomial invariants.
Zac Murphy is looking at the theory of quotient categories and applications to geometry.

Postgraduate Students

Kenneth Chan (2010) wrote a thesis entitled Resolving singularities of orders on surfaces. He is currently a postdoc at the University of Washington.
Hugo Bowne-Anderson (2011) wrote a thesis entitled Explicit construction of orders on surfaces. He is currently at Yale University.
Boris Lerner (2012) wrote a thesis entitled Line bundles and curves on a del Pezzo order. He did a postdoc at Nagoya University and is now doing a postdoc with me.


Boris Lerner (see above)
Tarig Abdelgadir

MATH1231 Mathematics 1B (Algebra) (2017)

Some housekeeping for lecture 1.

You can print off the lecture notes here: Chapter 6 Chapter 7 Chapter 8 Chapter 9

I will use Chapter 6 Chapter 7 Chapter 8 Chapter 9 We will also need the standard normal table.

Last year's exam.

MATH5725 Galois theory (2016)

Here are the course outlines.

You can print off the lecture notes here: Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5 Lecture 6 Lecture 7 Lecture 8 Lecture 9 Lecture 10 Lecture 11 Lecture 12 Lecture 13 Lecture 14 Lecture 15 Lecture 16 Lecture 17 Lecture 18 Graphs 1 Graphs 2 Graphs 3 Infinite 1 Infinite 2 Infinite 3 Galois Cohomology 1 Galois Cohomology 2 Galois Cohomology 3 Galois Cohomology 4 Ramification 1 Ramification 2

MATH5665 Algebraic Topology(2017)

Here's the course handout

Here's an incomplete version of the lecture notes which will be updated throughout the semester.

Here's Problem Set 1 Problem Set 2 Problem Set 3 Problem Set 4 Problem Set 5 Problem Set 6

MATH1141 Higher Mathematics 1A (Algebra) (2017)

Some housekeeping for lecture 1.

You can print off the lecture notes here: Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5

Some MAPLE outputs/files: vectors[PDF]

I will use Chapter 1 Chapter 2 Chapter 3 Chapter 4 Chapter 5

Some past exams. A quick checklist.

Here is the 2012 exam . 2013 exam.

Material for courses taught in the past

Click here for old lecture notes, problem sets etc concerning the following courses:

  • Higher Algebra: Group and Ring Theory
  • Group theory
  • Homology and homological algebra
  • MATH1141: algebra
  • MATH1241: algebra
  • Algebraic geometry
  • Commutative algebra
  • SCIR1121: Elementary mathematical modelling
  • MATH2601: Higher linear algebra
  • MATH5735: Modules and represenation theory

  • Miscellaneous teaching

    For talented first year students
    Here's a short parabola article I wrote on quaternions and their role in rotating objects in computer animation. It is aimed at high school students but should have some interesting tidbits for talented MATH1241 students.
    MathWorld has lots of general information about maths.
    Pi in the Sky is a magazine for high school maths enthusiasts and is published by the Pacific Institute for Mathematical Sciences.
    Interactive Mathematics Activities contains lots of interesting tidbits about mathematics from fractals to groups to classical geometry.
    History Topics Index contains fairly comprehensive information about the history of maths.
    Famous Curves Index.

    Return to University of New South Wales School of Mathematics and Statistics.