A/Prof Daniel Chan

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

Office: Red Centre Room 4104
Phone No: 9385 7084

Consultation Times: Thursday 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.


Publications

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)



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. 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.
Current Honours/Masters Students


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.



MATH1231 Higher Mathematics 1B (Algebra) (2016)
TO BE UPDATED

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



MATH5665 Algebraic Topology(2015)

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

Assignment 1 is due in the wednesday lecture of week 5. Assignment 2 is due in the wednesday lecture of week 10.



MATH1141 Higher Mathematics 1A (Algebra) (2016)

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.



MATH5735 Modules and Representation Theory (2014)

Here's the course handout

Joel Beeren took the course in 2012 and typed up notes which he has kindly agreed to let me post.

Here's Problem Set 0 Problem Set 1 Problem Set 2 Problem Set 3 Problem Set 4 Problem Set 5

Here is the 2012 exam . 2013 exam.


SCIF1121 Professional perspective and practice(2014)

Here's the course handout

Lecture 1 Lecture 2 Lecture 3 Lecture 4 Lecture 5


MATH2601 Higher linear algebra (2013)

Here's the course outlines

Here are the lecture slides. If you get an error message, that means the slides have not yet been updated for this year.

Lecture 0 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
Lecture 19 Lecture 20 Lecture 21 Lecture 22 Lecture 23 Lecture 24 Lecture 25 Lecture 26 Lecture 27
Lecture 28 Lecture 29 Lecture 30 Lecture 31 Lecture 32 Lecture 33 Lecture 34 Lecture 35 Lecture 36
Lecture 37 Lecture 38 Lecture 39 Lecture 40 Lecture 41 Lecture 42 Lecture 43 Lecture 44

Here are the problem sets. Problem Set 1 Problem Set 2 Problem Set 3 Problem Set 4 Problem Set 5
Problem Set 6 Problem Set 7 Problem Set 8 Problem Set 9 Problem Set 10

Honours info meeting

You will find the class tests will cover fairly standard material and is very similar to the problem sets. Here are last year's test 1 and test 2

Here is this year's test 1 and solutions.

Here is the 2012 exam and an exam check list.



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


  • Miscellaneous teaching

    Here are your MATH1081 test 4 and some partial solutions.


    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.