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
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
- Twisted Multi-Homogeneous Coordinate Rings
in Journal of Algebra vol. 223 (2000).
- Noncommutative Rational Double Points
in Journal of Algebra vol. 232 (2000).
- Morita Dualities and Dualizing Complexes
with Q.S. Wu and J. Zhang. In Israel Journal of Maths vol. 132 (2002).
- Del Pezzo Orders with
in Advances in Math. vol. 173 (2003).
- Noncommutative Coordinate Rings and Stacks
with Colin Ingalls, in Proc. of the LMS vol. 88 (2004).
- Splitting Bundles over Hereditary Orders
Comm in Algebra vol. 333(7) (2005) p.2193-9.
- The minimal model program for orders over
Inventiones Math. vol. 161 (2005)
- Numerically Calabi-Yau orders on surfaces with
Rajesh Kulkarni, Journal of the LMS vol. 72 (2005).
- Noncommutative cyclic covers and maximal orders
[PDF] in Mike Artin's 70th birthday
issue of Advances in Math. vol. 198(2) (2005)
- Canonical Singularities of Orders over
Surfaces with Colin Ingalls and
Proc. of the LMS vol. 98 p. 83-115 (Jan, 2009)
- McKay correspondence for canonical orders.
Trans. AMS vol. 362 (2010), p. 1765-95
- Hilbert schemes for quantum planes are
projective. Algebras & Repr. Theory vol. 13 (2010), p. 119-26
- Moduli of bundles on exotic del Pezzo
orders with Rajesh Kulkarni, American Journal of Math. vol. 133, no. 1,
(Feb. 2011) p.273-93
- Conic bundles and Clifford algebras with
Colin Ingalls. Contemp. Math. vol. 562 (2012) p.53-75
- Twisted rings and moduli stacks of "fat"
point modules in non-commutative projective geometry
Advances in Mathematics vol. vol. 229 (2012) p.2184-209
- Noncommutative Mori contractions and P1-bundles
with Adam Nyman, Advances in Mathematics vol. 245 (2013) p.327-81
- Rational curves and ruled
orders on surfaces with Kenneth Chan. Journal of Algebra vol. 435 (2015)
- Species and non-commutative P1's over
non-algebraic bimodules.with Adam Nyman. Journal of Algebra vol. 460
- 2-hereditary algebras and almost Fano weighted
surfaces. Journal of Algebra vol. 478 (2017) 92-13
- Moduli stacks of Serre stable
representations in tilting theory with Boris Lerner. Advances
in Math. vol. 312 (2017) 588-635
- A representation theoretic study of
noncommutative symmetric algebras with Adam Nyman. Proc. Edinburgh Mathematical Society vol. 62 (2019) 875-887
- Low dimensional orders of finite representation type with Colin Ingalls.
vol. 297 (2021) Math. Z. 1161-1190
- Morphisms to noncommutative projective lines
with Adam Nyman. vol. 149 (2021) Proc. AMS 2789-2803
- The minimal model program for
b-log canonical divisors and applications with Kenneth Chan,
Louis de Thanhoffer de Volcsey, Colin Ingalls, Kelly Jabbusch,Sandor Kovacs,
Rajesh Kulkarni, Boris Lerner, Basil Nanayakkara, Shinnosuke Okawa and
Michel Van den Bergh.
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.
Conference and seminar talks (videos and beamer slides).
here for old lecture notes, problem sets etc
concerning the following courses: Higher Algebra: Group and Ring Theory,
Group theory, Homology and homological algebra, Algebraic Topology, Galois theory,
MATH1241: algebra, Algebraic geometry, Commutative algebra,
SCIF1121: Elementary mathematical modelling, MATH2601: Higher linear algebra,
MATH5735: Modules and representation theory
- 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