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Professor Daniel Chan

Professor Daniel Chan

Professor

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.

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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.

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ADMINISTRATIVE DUTIES

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

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Phone
9385 7084
Location
School of Mathematics and Statistics University of New South Wales Sydney NSW 2052 The Red Centre Room 4104
  • Journal articles | 2024
    Chan D; Ingalls C, 2024, 'Terminal orders on arithmetic surfaces', Algebra and Number Theory, 18, pp. 2027 - 2046,
    Journal articles | 2024
    Chan D; Nyman A, 2024, 'NONCOMMUTATIVE LINEAR SYSTEMS AND NONCOMMUTATIVE ELLIPTIC CURVES', Transactions of the American Mathematical Society, 377, pp. 1957 - 1987,
    Journal articles | 2023
    Abdelgadir T; Chan D, 2023, 'Tensor stable moduli stacks and refined representations of quivers', Journal of the London Mathematical Society, 108, pp. 2085 - 2114,
    Journal articles | 2023
    Chan D; Chan K; de Thanhoffer de Völcsey L; Ingalls C; Jabbusch K; Kovács SJ; Kulkarni R; Lerner B; Nanayakkara B; Okawa S; Van den Bergh M, 2023, 'The minimal model program for b-log canonical divisors and applications', Mathematische Zeitschrift, 303,
    Journal articles | 2021
    Chan D; Ingalls C, 2021, 'Low dimensional orders of finite representation type', Mathematische Zeitschrift, 297, pp. 1161 - 1190,
    Journal articles | 2021
    Chan D; Ingalls C, 2021, 'The minimal model program for arithmetic surfaces enriched by a Brauer class', ,
    Journal articles | 2021
    Chan D; Nyman A, 2021, 'Morphisms to noncommutative projective lines', Proceedings of the American Mathematical Society, 149, pp. 2789 - 2803,
    Journal articles | 2019
    Abdelgadir T; Chan D, 2019, 'Tensor stable moduli stacks and refined representations of quivers', Journal of the LMS 108 (2023), 2085-2114,
    Journal articles | 2019
    Chan D; Nyman A, 2019, 'A Representation Theoretic Study of Non-Commutative Symmetric Algebras', Proceedings of the Edinburgh Mathematical Society, 62, pp. 875 - 887,
    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,
    Journal articles | 2017
    Chan D; Lerner B, 2017, 'Moduli stacks of Serre stable representations in tilting theory', Advances in Mathematics, 312, pp. 588 - 635,
    Journal articles | 2016
    Chan D; Nyman A, 2016, 'Species and non-commutative P1's over non-algebraic bimodules', Journal of Algebra, 460, pp. 143 - 180,
    Journal articles | 2015
    Chan D; Chan K, 2015, 'Rational curves and ruled orders on surfaces', Journal of Algebra, 435, pp. 52 - 87,
    Journal articles | 2013
    Chan DS; Nyman A, 2013, 'Non-commutative Mori contractions and P{double-struck}1-bundles', Advances in Mathematics, 245, pp. 327 - 381,
    Journal articles | 2012
    Chan DS, 2012, 'Twisted rings and moduli stacks of "fat" point modules in non-commutative projective geometry', Advances in Mathematics, 229, pp. 2184 - 2209,
    Journal articles | 2011
    Chan DS; Kulkarni RS, 2011, 'Moduli of bundles on exotic del pezzo orders', American Journal of Mathematics, 133, pp. 273 - 293,
    Journal articles | 2010
    Chan DS, 2010, 'Hilbert schemes for quantum planes are projective', Algebras and Representation Theory, 13, pp. 119 - 126,
    Journal articles | 2010
    Chan DS, 2010, 'McKay correspondence for canonical orders', Transactions of the American Mathematical Society, 362, pp. 1765 - 1795
    Journal articles | 2009
    Chan DS; Hacking P; Ingalls C, 2009, 'Canonical singularities of orders over surfaces', Proceedings of the London Mathematical Society, 3rd Series, 98, pp. 83 - 115
    Journal articles | 2005
    Chan DS; Ingalls C, 2005, 'The minimal model program for orders over surfaces', Inventiones Mathematicae, 161, pp. 427 - 452
    Journal articles | 2005
    Chan DS; Kulkarni RS, 2005, 'Numerically Calabi-Yau orders on surfaces', Journal of the London Mathematical Society - Second Series, 72, pp. 571 - 584
    Journal articles | 2005
    Chan DS, 2005, 'Noncommutative cyclic covers and maximal orders on surfaces', Advances in Mathematics, 198, pp. 654 - 683,
    Journal articles | 2005
    Chan DS, 2005, 'Splitting bundles over hereditary orders', Communications in Algebra, 33, pp. 2193 - 2199
    Journal articles | 2004
    Chan DS; Ingalls C, 2004, 'Non-commutative coordinate rings and stacks', Proceedings of the London Mathematical Society, 3rd Series, 88, pp. 63 - 88
    Journal articles | 2003
    Chan DS; Kulkarni RS, 2003, 'Del Pezzo orders on projective surfaces', Advances in Mathematics, 173, pp. 144 - 177
    Journal articles | 2002
    Chan DS, 2002, 'Pre-balanced dualizing complexes', Israel Journal of Mathematics, 132, pp. 285 - 314
    Journal articles | 2000
    Chan DS, 2000, 'Noncommutative Rational Double Points', Journal of Algebra, 232, pp. 725 - 766,
    Journal articles | 2000
    Chan DS, 2000, 'Twisted multi-homogeneous coordinate rings', Journal of Algebra, 223, pp. 438 - 456,
    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, 79, pp. 195 - 203
  • Working Papers | 2017
    Chan D, 2017, 2-Hereditary algebras and almost Fano weighted surfaces,
  • Preprints | 2024
    Abdelgadir T; Chan D; Okawa S; Ueda K, 2024, A compact moduli of orbifold projective curves, ,
    Preprints | 2024
    Abdelgadir T; Chan D; Okawa S; Ueda K, 2024, Degenerations of orbifold curves as noncommutative varieties, ,
    Preprints | 2022
    Chan D; Ingalls C, 2022, Terminal orders on arithmetic surfaces,
    Preprints | 2022
    Chan D; Nyman A, 2022, Noncommutative linear systems and noncommutative elliptic curves, ,
    Conference Papers | 2010
    Chan DS; Ingalls C, 2010, 'Conic bundles and Clifford algebras', in 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