Associate Professor Daniel Chan
Associate Professor

Associate Professor Daniel Chan

PhD 1999, Massachusetts Institute of Technology.

BE in Electrical Engineering 1994, UNSW

BA (Hons) in Mathematics 1994, UNSW

Science
School of Mathematics & Statistics

INTRODUCTION

A/Prof. Daniel Chan is an associate professor and Head of the Department of Pure Mathematics.

 

RESEARCH INTERESTS

He works in the area of non-commutative algebraic geometry, an exciting new field where sophisticated techniques from algebraic geometry have been imported to study non-commutative algebras. Much of his work has focussed on studying orders on projective surfaces which can be studied via a non-commutative adaptation of Mori's minimal model program. Other interests include finite dimensional algebras, non-commutative surfaces, moduli spaces in non-commutative algebra, the McKay correspondence and non-commutative rings arising from projective geometry such as the twisted homogeneous co-ordinate ring.

He is part of the Geometry group and the Algebra and Number Theory group.

 

ADMINISTRATIVE DUTIES

He is also an associate editor for the Journal of the Australian Mathematical Society. 

 

Phone
9385 7084
Location
School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room 4104
  • Journal articles | 2021
    Chan D; Ingalls C, 2021, 'Low dimensional orders of finite representation type', Mathematische Zeitschrift, vol. 297, pp. 1161 - 1190, http://dx.doi.org/10.1007/s00209-020-02552-2
    Journal articles | 2021
    Chan D; Ingalls C, 2021, 'The minimal model program for arithmetic surfaces enriched by a Brauer class', , http://arxiv.org/abs/2108.03105v1
    Journal articles | 2021
    Chan D; Nyman A, 2021, 'Morphisms to noncommutative projective lines', Proceedings of the American Mathematical Society, vol. 149, pp. 2789 - 2803, http://dx.doi.org/10.1090/proc/15386
    Journal articles | 2019
    Abdelgadir T; Chan D, 2019, 'Tensor stable moduli stacks and refined representations of quivers', , http://arxiv.org/abs/1907.07070v1
    Journal articles | 2019
    Chan D; Nyman A, 2019, 'A Representation Theoretic Study of Non-Commutative Symmetric Algebras', Proceedings of the Edinburgh Mathematical Society, vol. 62, pp. 875 - 887, http://dx.doi.org/10.1017/S0013091518000871
    Journal articles | 2017
    Chan D; Chan K; Völcsey LDTD; Ingalls C; Jabbusch K; Kovács SJ; Kulkarni R; Lerner B; Nanayakkara B; Okawa S; Bergh MVD, 2017, 'The minimal model program for b-log canonical divisors and applications', The minimal model program for b-log canonical divisors and applications, http://arxiv.org/abs/1707.00834v2
    Journal articles | 2017
    Chan D; Lerner B, 2017, 'Moduli stacks of Serre stable representations in tilting theory', Advances in Mathematics, vol. 312, pp. 588 - 635, http://dx.doi.org/10.1016/j.aim.2017.03.027
    Journal articles | 2016
    Chan D; Nyman A, 2016, 'Species and non-commutative P1's over non-algebraic bimodules', Journal of Algebra, vol. 460, pp. 143 - 180, http://dx.doi.org/10.1016/j.jalgebra.2016.03.048
    Journal articles | 2015
    Chan D; Chan K, 2015, 'Rational curves and ruled orders on surfaces', Journal of Algebra, vol. 435, pp. 52 - 87, http://dx.doi.org/10.1016/j.jalgebra.2015.03.018
    Journal articles | 2013
    Chan DS; Nyman A, 2013, 'Non-commutative Mori contractions and P{double-struck}1-bundles', Advances in Mathematics, vol. 245, pp. 327 - 381, http://dx.doi.org/10.1016/j.aim.2013.06.018
    Journal articles | 2012
    Chan DS, 2012, 'Twisted rings and moduli stacks of "fat" point modules in non-commutative projective geometry', Advances in Mathematics, vol. 229, pp. 2184 - 2209, http://dx.doi.org/10.1016/j.aim.2011.12.006
    Journal articles | 2011
    Chan DS; Kulkarni RS, 2011, 'Moduli of bundles on exotic del pezzo orders', American Journal of Mathematics, vol. 133, pp. 273 - 293, http://dx.doi.org/10.1353/ajm.2011.0002
    Journal articles | 2010
    Chan DS, 2010, 'Hilbert schemes for quantum planes are projective', Algebras and Representation Theory, vol. 13, pp. 119 - 126, http://dx.doi.org/10.1007/s10468-008-9111-8
    Journal articles | 2010
    Chan DS, 2010, 'McKay correspondence for canonical orders', Transactions of the American Mathematical Society, vol. 362, pp. 1765 - 1795, http://dx.doi.org/10.1090/S0002-9947-09-05010-7
    Journal articles | 2009
    Chan DS; Hacking P; Ingalls C, 2009, 'Canonical singularities of orders over surfaces', Proceedings of the London Mathematical Society, 3rd Series, vol. 98, pp. 83 - 115, http://dx.doi.org/10.1112/plms/pdn025
    Journal articles | 2005
    Chan DS, 2005, 'Noncommutative cyclic covers and maximal orders on surfaces', Advances in Mathematics, vol. 198, pp. 654 - 683, http://dx.doi.org/10.1016/j.aim.2005.06.012
    Journal articles | 2005
    Chan DS, 2005, 'Splitting bundles over hereditary orders', Communications in Algebra, vol. 33, pp. 2193 - 2199, http://dx.doi.org/10.1081/AGB-200063537
    Journal articles | 2005
    Chan DS; Ingalls C, 2005, 'The minimal model program for orders over surfaces', Inventiones Mathematicae, vol. 161, pp. 427 - 452, http://dx.doi.org/10.1007/s00222-005-0438-z
    Journal articles | 2005
    Chan DS; Kulkarni RS, 2005, 'Numerically Calabi-Yau orders on surfaces', Journal of the London Mathematical Society - Second Series, vol. 72, pp. 571 - 584, http://dx.doi.org/10.1112/S0024610705006976
    Journal articles | 2004
    Chan DS; Ingalls C, 2004, 'Non-commutative coordinate rings and stacks', Proceedings of the London Mathematical Society, 3rd Series, vol. 88, pp. 63 - 88, http://dx.doi.org/10.1112/S0024611503014278
    Journal articles | 2003
    Chan DS; Kulkarni RS, 2003, 'Del Pezzo orders on projective surfaces', Advances in Mathematics, vol. 173, pp. 144 - 177, http://dx.doi.org/10.1016/S0001-8708(02)00020-8
    Journal articles | 2002
    Chan DS, 2002, 'Pre-balanced dualizing complexes', Israel Journal of Mathematics, vol. 132, pp. 285 - 314
    Journal articles | 2000
    Chan DS, 2000, 'Noncommutative Rational Double Points', Journal of Algebra, vol. 232, pp. 725 - 766, http://dx.doi.org/10.1006/jabr.2000.8419
    Journal articles | 2000
    Chan DS, 2000, 'Twisted multi-homogeneous coordinate rings', Journal of Algebra, vol. 223, pp. 438 - 456, http://dx.doi.org/10.1006/jabr.1999.7938
    Journal articles | 1996
    Corkish R; Chan DS; Green MA, 1996, 'Excitons in silicon diodes and solar cells: A three-particle theory', Journal of Applied Physics, vol. 79, pp. 195 - 203
  • Working Papers | 2017
    Chan D, 2017, 2-Hereditary algebras and almost Fano weighted surfaces, http://dx.doi.org10.1016/j.jalgebra.2016.11.037
  • Conference Papers | 2010
    Chan DS; Ingalls C, 2010, 'Conic bundles and Clifford algebras', in Ara P; Brown KA; Lenagan TH; Letzter ES; Stafford JT; Zhang JJ (eds.), Contemporary Mathematics, Vol 562, American Mathematical Society, USA, pp. 53 - 75, presented at New Trends in Noncommutative Algebra, University of Washington, Seattle, 09 August 2010 - 14 August 2010, http://dx.doi.org/10.1090/conm/562/11130