A/ Prof. Daniel Chan

Head of Pure Mathematics
School of Mathematics and Statistics
UNSW, Sydney, Australia

E-mail: danielc followed by shift two unsw period edu period au
Office: Red Centre (East Wing) 4104
Consultation Times: TBA

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My YouTube Channel: Adventures in Pure Mathematics

If you know the basic language of pure mathematics (i.e. what's a group, ring, topological space), then you may be interested my Youtube channel videos which give snapshots of more advanced pure mathematics. These adventures in pure mathematics are mostly 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.

Research Papers and articles

Publications

  1. Twisted Multi-Homogeneous Coordinate Rings in Journal of Algebra vol. 223 (2000).
  2. Noncommutative Rational Double Points in Journal of Algebra vol. 232 (2000).
  3. Morita Dualities and Dualizing Complexes [PDF] with Q.S. Wu and J. Zhang. In Israel Journal of Maths vol. 132 (2002).
  4. Del Pezzo Orders with Rajesh Kulkarni in Advances in Math. vol. 173 (2003).
  5. Noncommutative Coordinate Rings and Stacks [PDF] with Colin Ingalls, in Proc. of the LMS vol. 88 (2004).
  6. Splitting Bundles over Hereditary Orders Comm in Algebra vol. 333(7) (2005) p.2193-9.
  7. The minimal model program for orders over surfaces [PDF] with Colin Ingalls. Inventiones Math. vol. 161 (2005)
  8. Numerically Calabi-Yau orders on surfaces with Rajesh Kulkarni, Journal of the LMS vol. 72 (2005).
  9. Noncommutative cyclic covers and maximal orders on surfaces [PDF] in Mike Artin's 70th birthday issue of Advances in Math. vol. 198(2) (2005)
  10. Canonical Singularities of Orders over Surfaces with Colin Ingalls and Paul Hacking, Proc. of the LMS vol. 98 p. 83-115 (Jan, 2009)
  11. McKay correspondence for canonical orders. Trans. AMS vol. 362 (2010), p. 1765-95
  12. Hilbert schemes for quantum planes are projective. Algebras & Repr. Theory vol. 13 (2010), p. 119-26
  13. Moduli of bundles on exotic del Pezzo orders with Rajesh Kulkarni, American Journal of Math. vol. 133, no. 1, (Feb. 2011) p.273-93
  14. Conic bundles and Clifford algebras with Colin Ingalls. Contemp. Math. vol. 562 (2012) p.53-75
  15. Twisted rings and moduli stacks of "fat" point modules in non-commutative projective geometry Advances in Mathematics vol. vol. 229 (2012) p.2184-209
  16. Noncommutative Mori contractions and P1-bundles with Adam Nyman, Advances in Mathematics vol. 245 (2013) p.327-81
  17. Rational curves and ruled orders on surfaces with Kenneth Chan. Journal of Algebra vol. 435 (2015) 52-87
  18. Species and non-commutative P1's over non-algebraic bimodules.with Adam Nyman. Journal of Algebra vol. 460 (2016) 143-80
  19. 2-hereditary algebras and almost Fano weighted surfaces. Journal of Algebra vol. 478 (2017) 92-13
  20. Moduli stacks of Serre stable representations in tilting theory with Boris Lerner. Advances in Math. vol. 312 (2017) 588-635
  21. A representation theoretic study of noncommutative symmetric algebras with Adam Nyman. Proc. Edinburgh Mathematical Society vol. 62 (2019) 875-887
  22. Low dimensional orders of finite representation type with Colin Ingalls. accepted, Math. Z.

Here are some preprints.

In 2010, I gave a series of lectures on the theory of orders. The main purpose was to provide details on ramification theory so that one can read papers on recent work on concerning orders on surfaces. These LECTURES ON ORDERS have been typed up by Boris Lerner and should be appropriate for graduate students.

Honours, Masters and PhD students

If you are interested in doing an honours project in algebra, geometry or number theory, 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. You can also check out my past students below and their theses.

Past Honours/Masters Students

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

Current Honours/Masters Students

Postgraduate Students

  1. Kenneth Chan (2010) wrote a thesis entitled Resolving singularities of orders on surfaces. He had postdocs at the University of Washington and the Mathematical Sciences Research Institute, Berkeley.
  2. Hugo Bowne-Anderson (2011) wrote a thesis entitled Explicit construction of orders on surfaces. He had postdocs at Max Planck Institute, Dresden and Yale University.
  3. Boris Lerner (2012) wrote a thesis entitled Line bundles and curves on a del Pezzo order. He did a postdoc at Nagoya University and with me at UNSW and is now at Amazon.
  4. Sean Lynch is studying zeta functions in noncommutative algebra.

Postdocs

Teaching materials for current courses

See Extra Material for teaching materials related to past years.

MATH3701/5700 Higher Topology and Differential Geometry/Modern Geometry (2020)

Here are the lecture notes. An error means I haven't uploaded it yet.

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

MATH1141 Higher Mathematics 1A (Algebra) (2020)

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.

Extra material