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Professor
Biography
Prof. Chiang attended several primary and secondary schools in Hong Kong before he received both his undergraduate (1984) and postgraduate (1991) qualification from University College London. His PhD was directed under the late Professor J. Milne Anderson on topics related to Schwarzian derivatives and linear differential equations. Although special functions are almost as old as calculus, many of the centuries old special functions that appear frequently in applications are still far from being understood. His current interests lie in application of Nevanlinna theory, algebraic and geometric methods to better understand these special functions.Research Interests
Complex function theory; ordinary differential equations in the complex plane; orthogonal polynomials; difference equationsTeaching
 MATH1014 Calculus II
Selected Publications
Article

WimanValiron theory of a polynomial series based on AskeyWilson divided difference operator
 Author(s): Cheng, Kam Hang; Chiang, Yik Man
 Source: Constructive Approximation, 12 March 2021
 Year: 2021

Resolving Singularities and Monodromy Reduction of Fuchsian Connections
 Author(s): Chiang, Yik Man; Ching, Avery; Tsang, ChinYin
 Source: Annales Henri Poincaré, 27 April 2021
 Year: 2021

Galoisian approach to complex oscillation theory of some Hill equations
 Author(s): Chiang, Yik Man ; Yu, GUOFU
 Source: Mathematica Scandinavica, v. 124, (1), January 2019, p. 102131
 Year: 2019

Symmetry of the Darboux equation
 Author(s): Chiang, Yik Man ; Tsang, Chiu Yin ; Ching, Avery
 Source: Kumamoto Journal of Mathematics. , v. 31, January 2018, p. 1548
 Year: 2018

Nevanlinna Theory of the Askey–wilson Divided Difference Operator
 Author(s): Chiang, Yik Man ; Feng, shaoji
 Source: Advances in Mathematics. , v. 329, April 2018, p. 217272
 Year: 2018

Difference Nevanlinna Theories With Vanishing and Infinite Periods
 Author(s): Chiang, Yik Man; Luo, Xudan
 Source: Michigan Mathematical Journal. , v. 66, (3), 2017, p. 451480
 Year: 2017

Nevanlinna Theory of the Wilson Divideddifference Operator
 Author(s): Cheng, Kam Hang; Chiang, YikMan
 Source: Annales Academiae Scientiarum Fennicae Mathematica. , v. 42, (1), 2017, p. 175209
 Year: 2017

On the Growth of Logarithmic Difference of Meromorphic Functions and a Wiman–Valiron Estimate
 Author(s): Chiang, Yik Man; Feng, ShaoJi
 Source: Constructive Approximation. , v. 44, (3), December 2016, p. 313326
 Year: 2016

On complex oscillation, functiontheoretic quantization of nonhomogeneous periodic ordinary differential equations and special functions
 Author(s): Chiang, Yik Man ; Yu, Kit Wing
 Source: Proceedings of the Royal Society of Edinburgh Section A: Mathematics. , v. 142A, (3), June 2012, p. 449477
 Year: 2012

Subnormal solutions of nonhomogeneous periodic ODEs, special functions and related polynomials
 Author(s): Chiang, YikMan; Yu, KitWing
 Source: Journal für die reine und angewandte Mathematik. , v. 651, February 2011, p. 127164
 Year: 2011

On the Growth of Logarithmic Differences, Difference Quotients and Logarithmic Derivatives of Meromorphic Functions
 Author(s): Chiang, YikMan; Feng, ShaoJi
 Source: Transactions of the American Mathematical Society. , v. 361, (7), 2009, JUL, p. 37673791
 Year: 2009

On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane
 Author(s): Chiang, YikMan; Feng, ShaoJi
 Source: The Ramanujan Journal. , v.16, (1), 2008, MAY, p. 105129
 Year: 2008

Difference independence of the Riemann zeta function
 Author(s): Chiang, YikMan; Feng, ShaoJi
 Source: Acta Arithmetica. , v. 125, (4), 2006, p. 317329
 Year: 2006

On value distribution theory of second order periodic ODEs, special functions and orthogonal polynomials
 Author(s): Chiang, YikMan; Ismail, Mourad E.H.
 Source: CANADIAN journal OF mathematicsjournal canadien DE Mathematiques. , v. 58, (4), 2006, AUG, p. 726767
 Year: 2006

On the nevanlinna order of meromorphic solutions to linear analytic difference equations
 Author(s): Chiang, YM; Ruijsenaars, SNM
 Source: Studies in applied mathematics. , v. 116, (3), 2006, APR, p. 257287
 Year: 2006

Estimates on the growth of meromorphic solutions of linear differential equations
 Author(s): Chiang, YM; Hayman, WK
 Source: Commentarii mathematici Helvetici. , v. 79, (3), 2004, SEP, p. 451470
 Year: 2004

On the meromorphic solutions of an equation of Hayman
 Author(s): Chiang, YM; Halburd, RG
 Source: Journal of mathematical analysis and applications. , v. 281, (2), 2003, MAY 15, p. 663677
 Year: 2003

On a problem in complex oscillation theory of periodic second order linear differential equations and some related perturbation results
 Author(s): Chiang, YM; Gao, SA
 Source: ANNALES Academiae scientiarum fennicaemathematica. , v. 27, (2), 2002, p. 273290
 Year: 2002

Complex oscillation theory and special functions
 Author(s): Chiang, YikMan; Ismail, M.E.H.
 Source: Mathematical Reports of the Academy of Science of Canada. , Vol. 24, pp. 117123
 Year: 2002

On the zerofree solutions of linear periodic differential equations in the complex plane
 Author(s): Chiang, Yik Man
 Source: Results in Mathematics. , v. 38, (34), November 2000, p. 213225
 Year: 2000

Some oscillation results for linear differential equations in the complex plane
 Author(s): Chiang, Yik Man ; Laine, Ilpo
 Source: Japanese Journal of Mathematics. , v. 24, (2), 1998, p. 367402
 Year: 1998

Oscillation results of certain higher order linear differential equations with periodic coefficients in the complex plane
 Author(s): Chiang, YM; Wang, SP
 Source: Journal of mathematical analysis and applications. , v. 215, (2), 1997, NOV 15, p. 560576
 Year: 1997

Oscillation results on y″ + Ay = 0 in the complex domain with transcendental entire coefficients which have extremal deficiencies
 Author(s): Chiang, Yik Man
 Source: Proceedings of the Edinburgh Mathematical Society, v. 38, (1), February 1995, p. 1334
 Year: 1995

On the complex oscillation of y′′ + (ez − K)y = 0 and a result of Bank
 Author(s): Chiang, Y.M.
 Source: Laine and Langley, Proc. Comput. Methods and Function Theory, Series in Approximations and Decompositions. , v. 5, 1995, p. 125134
 Year: 1995

Oscillation results for some linear differential equations
 Author(s): Chiang, YM; Laine, I.; Wang, SP
 Source: Mathematica Scandinavica. , v. 77, (2), 1995, p. 209224
 Year: 1995

Oscillation results on y "+ Ay= 0 in the complex domain with transcendental entire coefficients which have extremal deficiencies
 Author(s): Chiang, YM
 Source: Proceedings of the Edinburgh Mathematical Society. , v. 38, (1), p. 1334
 Year: 1995

Some properties of analytic functions with small schwarzian
 Author(s): Chiang, Y.M.
 Source: Complex Variables Theory and Application. , . 25, 1994, p. 107118
 Year: 1994

Some remarks on Lehto's domain constant
 Author(s): Chiang, Y.M.
 Source: Annales Academiae Scientiarum Fennicae. Series A I. Mathematica. , . 17, 1992, p. 285293
 Year: 1992

On a subclass of strongly gammastarlike functions and quasiconformal extensions
 Author(s): Chiang, Y.M.
 Source: Annales Universitatis Mariae CurieSklodowska.Sectio A. Mathematica. , . 45, 1991, p. 2127
 Year: 1991
Conference paper

Galoisian Approach to Complex Oscillation Theory
 Author(s): Chiang, Yik Man; Yu, Guofu
 Year: 2016

When Does a Formal Finitedifference Expansion Become Real?
 Author(s): Feng, Shaoji; Chiang, Yik Man
 Year: 2016

Galoisian Approach to Complex Oscillation of Hill's Eqauations
 Author(s): Yu, Guofu; Chiang, Yik Man
 Year: 2016

A Galoisian Approach to Complex Oscillation Theory
 Author(s): Chiang, Yik Man; Yu, Guofu
 Year: 2016

Complex Oscillation Theory and Semifinite Gap Problems
 Author(s): Luo, Xudan; Chiang, Yik Man
 Year: 2016

Estimates on the growth of meromorphic solutions of linear differential equations with density conditions
 Author(s): Chiang, Yik Man
 Source: Reports and Studies in Forestry and Natural Sciences. , v. 14, p. 4555
 Year: 2014

Eigensolutions of Biconfluent Heun equation with respect to a complex weight
 Author(s): Chiang, Yik Man
 Source: Colloquium on Jordan Theory and Analysis. , 812 April 2010
 Year: 2010

A qdeformation of Nevanlinna Theory
 Author(s): Chiang, Yik Man
 Source: Conference on Value Distribution Theory and Complex Geometry. , 2730 July 2009
 Year: 2009

A qdeformation of classical Nevanlinna theory
 Author(s): Chiang, Yik Man
 Source: International Conference on Complex Analysis and Related Topics. , 2023 August 2009, Beijing
 Year: 2009

Malmquisttype theorems for secondorder ODEs
 Author(s): Chiang, YikMan
 Source: International Conference on Nonlinear Waves: Theory and Applications, Beijing, China, organised by M. Ablowitz, DY. Hsieh and J. Yang. , 912 June 2008
 Year: 2008

On The Nevanlinna Order Of Lommel And Struve Functions And Complex Differential Equations
 Author(s): Chiang, YikMan
 Source: The 9th International Conference on Special Functions, Orthogonal Polynomials and their Applications, Marseille, France, organized by G. Valent. , 26 July 2007 (30 minutes talk)
 Year: 2007

On the Nevanlinna Order of Lommel, Struve Functions and Complex Differential Equations
 Author(s): Chiang, YikMan
 Source: 1st Joint Meeting of American and the Newzealand Mathematical Societies, Special session on Special Functions and Orthogonal Polynomials, Victoria Univ. of Wellington, organized by D. Dominici, O. Warnaar, S. Cooper. , 1215 December 2007 (25 minutes invi
 Year: 2007

Estimates of difference operators in the complex plane
 Author(s): Chiang, YikMan
 Source: The Painleve Equations and Monodromy Problems: Recent Developments, Newton Institute, Cambridge September 2006.
 Year: 2006

Structural results of orthogonal polynomials that generalize Lommel's polynomials
 Author(s): Chiang, YikMan
 Source: ICM06 satelite meeting: 'Recent Trends in Constructive Approximation Theory', Univ. Carlos III de Madrid.
 Year: 2006

Some Nevanlinnatype estimates related to discrete equations
 Author(s): Chiang, YikMan; Feng, S.J.
 Source: International Conference on Nonlinear Waves, Integrable Systems, and their Applications, in honor of Mark Ablowitz's sixtieth birthday, University of Colorado Spring, , organized by M. Kruskal, T. Fokas, S. Chakravarty and R. Cascaval. , 48th June 2005
 Year: 2005

On the growth of entire solutions to some difference equations
 Author(s): Chiang, YikMan; Feng, S.J.
 Source: Computational Methods and Function Theory 2005, University of Joensuu, Finland, organized by St. Ruscheweyh, E. B. Saff, O. Martio and I. Laine.. , 1317th June 2005,
 Year: 2005

On The Location of Complex Zeros of Bessel Functions and Complex Oscillation Theory
 Author(s): Chiang, YikMan; Ismail, Mourad E.M.
 Source: American Mathematics Society, Joint Mathematics Meetings, Phoenix, AZ. Special Session in 'Value Distribution Theory in Classical and padic Function Theory', organized by A. Escassut, I. Laine and C. C. Yang.. , January 710
 Year: 2004

On Value Distribution Theory, Complex Oscillation of Differential Equations and Special Functions
 Author(s): Chiang, YikMan
 Source: Summer School in Complex Difference Equations, August, University of Joensuu (Mekrijarvi Research Station).
 Year: 2001

On Value Distribution Theory, Complex Oscillation of Differential Equations and Bessel polynomials
 Author(s): Chiang, YikMan
 Source: Summer School/Seminar in Applied Analysis, July, City University of Hong Kong.
 Year: 2001

Efficient Software Multicast in WormholeRouted Unidirectional Multistage Networks
 Author(s): Chiang, ChiMing; Ni, Lionel MingShuan
 Source: Proceedings of the Seventh IEEE Symposium on Parallel and Distributed Processing, Los Alamitos, CA : IEEE Computer Society Press, 1995, p. 106113
 Year: 1995
Preprint

Two integrable differentialdifference equations derived from NLStype equation
 Author(s): Xu, ZongWei; Yu, GuoFu; Chiang, YikMan
 Source: arXiv, Mar 2015, Article number 1503.09073
 Year: 2015

Nevanlinna theory of the AskeyWilson divided difference operator
 Author(s): Chiang, YikMan; Feng, Shaoji
 Source: arXiv, Feb 2015, Article number 1502.02238
 Year: 2015