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Stephen Gardiner

Full Professor of Mathematics

School Of Mathematics & Statistics
Science Centre - North
Belfield
Dublin 4

Tel: +353 1 7162574
Email: stephen.gardiner@ucd.ie

Biography

Stephen J. Gardiner is Professor of Mathematics at UCD, the eighth holder of this chair since the foundation of the university in 1854. In 1995 he was awarded the degree of Doctor of Science by Queen's University on the basis of published research, and in 2000 he was elected a Member of the Royal Irish Academy. He has served as Associate Dean in the Faculty of Arts (1996-2002) and as Head of the Department of Mathematics (2002-2005). Since 2007 he has been School Head of Finance and Staffing.

Professional

Honours and Awards

Year: 2008.
Title: External Examiner in Pure Mathematics, Queen's University Belfast (2008-2012)
Year: 2006.
Title: Erskine Fellowship, University of Canterbury, New Zealand
Year: 2006.
Title: Editorial Board, Potential Analysis
Year: 2005.
Title: UCD President's Research Fellowship
Year: 2001.
Title: London Mathematical Society Editorial Advisory Board (2001-2010)
Year: 2000.
Title: Member of the Royal Irish Academy

Associations

Association: London Mathematical Society, Function/Role:
Association: Irish Mathematical Society, Function/Role:
Association: American Mathematical Society, Function/Role:
     

Conference Contributions

Gardiner, S. (2015) Potential theoretic aspects of universal Taylor series. [Invited Lecture], Universal Functions 2015, Crete , 18-MAY-15 - 22-MAY-15.
Gardiner, S. (2014) Universal Taylor Series and Potential Theory. [Invited Lecture], Function Theory Meeting, London Mathematical Society , 01-SEP-14 - 01-SEP-14.
Gardiner, S. (2014) Universal Taylor series and potential theory. [Invited Lecture], Harmonic Meeting, Charles Univeristy, Prague , 26-JUN-14 - 26-JUN-14.
Gardiner, S. (2014) Potatoes and Potentials. [Invited Lecture], Second Joint international meeting of the Israel Mathematical Union and the American Mathematical Society, Tel Aviv , 16-JUN-14 - 19-JUN-14.
Gardiner, S. (2014) Universal Taylor series and potential theory. [Invited Lecture], International Conference on Complex Analysis and Related Topics, St Petersburg, Russia , 14-APR-14 - 18-APR-14.
Gardiner, S. (2013) Universal Taylor series and potential theory. [Invited Lecture], 26th Nordic Congress of Marthematicians, Lund University , 10-JUN-13 - 13-JUN-13.
Gardiner, S. (2012) Universal Taylor Series and Potential Theory. [Invited Lecture], Workshop on Potential Theory and Applications, Szeged, Hungary , 28-MAY-12 - 31-MAY-12.
Gardiner, S. (2012) Universal Taylor Series on Multiply Connected Domains. [Invited Lecture], HCAA 2012, Tenerife , 05-MAR-12 - 09-MAR-12.
Gardiner, S.; (2011) Existence of universal Taylor series for non-simply connected domains. [Invited Lecture], Universal functions and hypercyclic operators, University of Crete , 04-JUL-11 - 08-JUL-11.
Gardiner, S.; (2011) Two-phase quadrature domains. [Plenary Lecture], Complex Analysis and Potential Theory, Centre de Recherches Mathematiques, Universite de Montreal , 20-JUN-11 - 23-JUN-11.
Gardiner, S.; (2011) Two-phase quadrature domains. [Invited Lecture], Free boundary problems, theory and applications, Mathematical Sciences Research Institute, Berkeley, CA , 07-MAR-11 - 11-MAR-11.
Gardiner, S.; (2010) Sets of determination for the Nevanlinna class. [Plenary Lecture], One Day Function Theory Meeting, University College London , 06-SEP-10 - 06-SEP-10.
Gardiner, S.; (2009) Sets of determination. [Invited Lecture], International Workshop on Complex Analysis, University of Bergen , 30-NOV-09 - 02-DEC-09.
Gardiner, S.; (2009) Quadrature domains, partial balayage, and the inverse problem of potential theory (course of lectures). [Invited Lecture], 8th Summer School on Potential Theory, Renyi Institute of Mathematics, Hungarian Academy of Sciences , 06-JUL-09 - 12-JUL-09.
Gardiner, S.; (2009) Finely continuously differentiable functions. [Plenary Lecture], Summer School on Conformal geometry, potential theory, and applications, NUI Maynooth , 23-JUN-09 - 27-JUN-09.
Gardiner, S.; (2009) Harmonic functions outside a cylinder. [Invited Lecture], British Mathematical Colloquium, Special Session on Analysis, NUI Galway , 06-APR-09 - 09-APR-09.
Gardiner, S.; (2008) Lipschitz continuity of the Green function in Denjoy domains. [Invited Lecture], One Day Function Theory Conference, Open University , 08-SEP-08 - 08-SEP-08.
Gardiner, S.; (2007) Potential theory of the farthest point distance function. [Invited Lecture], Potential theory and applications, KTH, Stockholm , 25-OCT-07 - 27-OCT-07.
Gardiner, S.; (2007) Recent progress on problems of gravi-equivalence. [Invited Lecture], Potential theory and stochastics, Albac, Romania , 04-SEP-07 - 08-SEP-07.
Gardiner, S.; (2007) Positive harmonic functions associated with an irregular boundary point. [Invited Lecture], New trends in complex and harmonic analysis, Voss, Norway , 07-MAY-07 - 12-MAY-07.
Gardiner, S.; (2005) Pointwise convergence and radial limits of harmonic functions. [Invited Lecture], International Conference on Multivariate Approximation, Haus Bommerholz, University of Dortmund, Germany , 25-SEP-05 - 30-SEP-05.
Gardiner, S.; (2006) Potential theory of the farthest point distance function. [Invited Lecture], Complex and harmonic analysis, an international conference, University of Thessaloniki, Greece , 25-MAY-06 - 27-MAY-06.
Gardiner, S.; (2006) The Riesz decomposition of finely superharmonic functions. [Invited Lecture], Colloque sur la theorie du potentiel et d'analyse complexe, McGill University, Montreal , 15-MAY-06 - 19-MAY-06.
   

Education

Year 1995 Institution: Queen's University of Belfast, UK
Qualification: DSc Subject:
Year 1982 Institution: Queen's University of Belfast, UK
Qualification: PhD Subject:
         

Publications

Books

Armitage, David, H; Gardiner, Stephen J.; (2001) Classical potential theory. : Springer-Verlag. [Details]
Gardiner, Stephen J.; (1995) Harmonic Approximation. : Cambridge University Press. [Details]

Book Chapters

Gardiner, Stephen J.; Sjödin, Tomas (2014) 'Quadrature domains and their two-phase counterparts' In: A. Vasil'ev (eds). Harmonic and Complex Analysis and its Applications. Switzerland: Springer International Publishing. , pp.261-285 Available Online [DOI] [Details]
Gardiner, Stephen J.; (2001) 'Harmonic Approximation and its Applications' In: N. Arakelian, P. M. Gauthier (eds). Approximation, Complex Analysis and Potential Theory. Dordrecht: Kluwer. , pp.191-219 [Details]
 

Peer Reviewed Journals

Gardiner, Stephen J.; Manolaki, Myrto (2016) 'Boundary behaviour of Dirichlet series with applications to universal series'. Bulletin of the London Mathematical Society, 48 (5):735-744. [DOI] Link to full text [Details]
Gardiner, Stephen J.; Render, Hermann (2016) 'A reflection result for harmonic functions which vanish on a cylindrical surface'. Journal of Mathematical Analysis and Applications, 443 (1):81-91. [DOI] Link to full text [Details]
Gardiner, Stephen J.; Manolaki, Myrto (2016) 'A convergence theorem for harmonic measures with applications to Taylor series'. Proceedings of the American Mathematical Society, 144 (3):1109-1117. [DOI] Link to full text [Details]
Gardiner, Stephen J.; Render, Hermann (2016) 'Harmonic functions which vanish on a cylindrical surface'. Journal of Mathematical Analysis and Applications, 433 (2):1870-1882. [DOI] Link to full text [Details]
Gardiner, Stephen J.; Manolaki, Myrto (2014) 'Boundary behaviour of universal Taylor series on multiply connected domains'. Constructive Approximation, 40 (2):259-279. [DOI] Link to full text [Details]
Gardiner, Stephen J.; Sjödin, Tomas (2014) 'Stationary Boundary Points for a Laplacian Growth Problem in Higher Dimensions'. Archive for Rational Mechanics and Analysis, 213 (2):503-526. Available Online [DOI] Link to full text [Details]
Gardiner, Stephen J.; Khavinson, Dmitry (2014) 'Boundary behaviour of universal Taylor series'. Comptes Rendus Mathématique. Académie des Sciences. Paris, 352 (2):99-103. Available Online [DOI] Link to full text [Details]
Gardiner, Stephen J. (2014) 'Universal Taylor series, conformal mappings and boundary behaviour'. Annales De L'Institit Fourier, 64 (1):327-339. Available Online [DOI] Link to full text [Details]
Gardiner, Stephen J. (2013) 'Boundary behaviour of functions which possess universal Taylor series'. Bulletin of the London Mathematical Society, 45 (1):191-199. Link to full text [Details]
Gardiner, Stephen J. (2012) 'Existence of universal Taylor series for non-simply connected domains'. Constructive Approximation, 35 :245-257. Link to full text [Details]
Gardiner, Stephen J.; Sjödin, Tomas (2012) 'Two-phase quadrature domains'. Journal D`Analyse Mathématique, 116 :335-354. Link to full text [Details]
Gardiner, Stephen J.; (2011) 'Coincidence of harmonic and finely harmonic functions'. Potential Analysis, 34 (1):81-88. [Details]
Gardiner, Stephen J. (2010) 'Potential theory in the exterior of a cylindrical set'. Indiana University Mathematics Journal, 59 (5):1777-1792. [Details]
Gardiner, Stephen J.; (2010) 'Sets of determination for the Nevanlinna class'. Bulletin of the London Mathematical Society, 42 (6):1115-1120. [Details]
Gardiner, Stephen J.; (2010) 'Finely continuously differentiable functions'. Mathematische Zeitschrift, 266 (4):851-861. [Details]
Gardiner, S. J. and Tsirivas, N.; (2010) 'Universal Taylor series for non-simply connected domains'. Comptes Rendus Mathématique. Académie des Sciences. Paris, 348 (9-10):521-524. [Details]
Gardiner, S.J. and Ghergu, M.; (2010) 'Champagne subregions of the unit ball with unavoidable bubbles'. Annales Academiæ Scientiarum Fennicæ Mathematica, 35 :321-329. [DOI] [Details]
Gardiner, Stephen J.; Carroll, Tom; (2008) 'Lipschitz continuity of the Green function in Denjoy domains'. Arkiv for Matematik, 46 :271-283. [Details]
Gardiner, Stephen J.; Sjödin, Tomas; (2008) 'Convexity and the exterior inverse problem of potential theory'. Proceedings of the American Mathematical Society, 136 :1699-1703. [Details]
Gardiner, Stephen J.; (2008) 'Asymptotic maximum principles for subharmonic functions'. Computational Methods and Function Theory, 8 (1):167-172. [Details]
Gardiner, Stephen J.; Hansen, Wolfhard; (2007) 'The Riesz decomposition for finely superharmonic functions'. Advances in Mathematics, 214 :417-436. [Details]
Gardiner, Stephen J.; Sjödin, Tomas; (2007) 'Quadrature domains for harmonic functions'. Bulletin of the London Mathematics Society, 39 :586-590. [Details]
Gardiner, Stephen J.; Netuka, Ivan; (2007) 'Potential theory of the farthest point distance function'. Journal d`Analyse Mathématique, 101 :163-177. [Details]
Gardiner, Stephen J.; (2005) 'Radial limits of harmonic functions on the unit disc'. Proceedings of the American Mathematical Society, 133 (5):1387-1389. [Details]
Gardiner, Stephen J.; Gustafsson, Anders; (2005) 'Pointwise convergence and radial limits of harmonic functions'. Israel Journal of Mathematics, 145 :243-256. [Details]
Gardiner, Stephen J.; Gustafsson, Anders; (2004) 'Smooth potentials with prescribed boundary behaviour'. Publicacions Matemàtiques, 48 :241-249. [Details]
Gardiner, Stephen J.; (2004) 'Sets of harmonicity for finely harmonic functions'. Potential Analysis, 21 (1):1-6. [Details]
Gardiner, Stephen J.; (2004) 'Completeness of spaces of harmonic functions under restricted supremum norms'. Computational Methods and Function Theory, 4 (1):43-45. [Details]
Gardiner, Stephen J; Hanley, Mary; (2003) 'Farrell sets for harmonic functions'. Proceedings of the American Mathematical Society, 131 (3):773-779. [Details]
Gardiner, Stephen J.; (2003) 'Carleman approximation for superharmonic functions'. Bulletin of the London Mathematical Society, 35 (1):92-96. [Details]
Gardiner, Stephen J.;Pau, Jordi; (2003) 'Approximation on the boundary and sets of determination for harmonic functions'. Illinois Journal of Mathematics, 47 :1115-1136. [Details]
Gardiner, Stephen J.; (2002) 'An equilibrium measure characterization of circles'. Forum Mathematicum, 14 (6):953-954. [Details]
Gardiner, Stephen J.; Hansen, Wolfhard; (2002) 'Boundary sets where harmonic functions may become infinite'. Mathematische Annalen, 323 (1):41-54. [Details]
Gardiner, Stephen J.; Pommerenke, Christian; (2002) 'Balayage properties related to rational interpolation'. Constructive Approximation, 18 (3):417-426. [Details]
Gardiner, Stephen J. ; (2001) 'Non-tangential limits, fine limits and the Dirichlet integral'. Proceedings of the American Mathematical Society, 129 :3379-3387. [Details]
Gardiner, Stephen J.; (2001) 'Convergence of rational interpolants with preassigned poles'. Constructive Approximation, 17 (1):139-146. [Details]
Gardiner, Stephen J.; (2000) 'Growth properties of superharmonic functions along rays'. Proceedings of the American Mathematical Society, 128 (7):1963-1970. [Details]
Armitage, David H.; Gardiner, Stephen J.; Haussmann, W.; Rogge, Lothar; (2000) 'Incomplete lattice sets that control the bahaviour of entire harmonic functions'. Mathematical Proceedings of the Cambridge Philosophical, 129 :549-563. [Details]
Aikawa, H; Gardiner, SJ; ; (2000) 'Evaluation of superharmonic functions using limits along lines'. Bulletin of the London Mathematical Society, 32 (NA):209-213. [Details]
Armitage, DH; Gardiner, SJ; Haussmann, W; Rogge, L; ; (2000) 'Incomplete lattice sets that control the behaviour of entire harmonic functions'. Mathematical Proceedings of the Cambridge Philosophical, 129 (NA):549-563. [Details]
Essen, Matts R.; Gardiner, Stephen J.; (1999) 'Limits along parallel lines and the classical fine topology'. Journal of the London Mathematical Society, 59 (3):881-894. [Details]
Gardiner, Stephen J.; (1999) 'Boundary Growth theorems for superharmonic functions using limits along lines'. Arkiv Fur Mathematik, 37 (2):255-273. [Details]
Essen, MR; Gardiner, SJ; ; (1999) 'Limits along parallel lines and the classical fine topology'. Journal of the London Mathematical Society-Second Series, 59 (NA):881-894. [Details]
Armitage, DH; Gardiner, SJ; ; (1999) 'Best harmonic and superharmonic L-1-approximants in strips'. Journal of Approximation Theory, 100 (2):266-283. [Details]
Gardiner, Stephen J. ; (1998) 'Asympototic values and minimal fine limits of subharmonic functions of slow growth'. Journal of the London Mathematical Society, 57 (3):668-676. [Details]
Gardiner, Stephen J. ; (1998) 'Mergelyan pairs for harmonic functions'. Proceedings of the American Mathematical Society, 126 (9):2699-2703. [Details]
Armitage, D.H.; Gardiner, S. J.; Haussmann, W; Rogge, L.; (1998) 'Best one-sided L^1-approximation by harmonic functions'. Manuscripta Mathematica, 96 (2):181-194. [Details]
Gardiner, Stephen J.; (1997) 'Decomposition of approximable harmonic functions'. Mathematische Annalen, 308 (1):175-185. [Details]
Gardiner, Stephen J.; (1997) 'Cluster sets of harmonic functions at the boundary of a half-space'. Bulletin of the London Mathematical Society, 29 (2):191-194. [Details]
Armitage, David H.; Gardiner, Stephen J.; Haussmann, Werner; Rogge, Lothar; (1996) 'Characterization of best harmonic and superharmonic L^1-approximants'. Journal Fur Die Reine Und Angewandte Mathematik, 478 :1-15. [Details]
Gardiner, Stephen J.; (1996) 'Uniform harmonic approximation of bonded functions'. Transactions of the American Mathematical Society, 348 (1):251-265. [Details]
Gardiner, Stephen J.; (1996) 'Representation of continous functions as sum of Green Functions'. Proceedings of the American Mathematical Society, 124 (4):1149-1157. [Details]
Gardiner, Stephen J.; (1996) 'The Lusin-Privalov theorum for subharmonic functions'. Proceedings of the American Mathematical Society, 124 (12):3721-3727. [Details]
Gardiner, Stephen J.; (1996) 'Uniform harmonic approximation with continuous extension to the boundary'. Journal d'Analyse Mathematique, 68 :95-106. [Details]
Gardiner, Stephen J.; (1995) 'Superharmonic extension from the boundary of a domain'. Bulletin of the London Mathematical Society, 27 (4):347-352. [Details]
Gardiner, Stephen J.; (1995) 'Tangential harmonic approximation on relatively closed sets'. Illinois Journal of Mathematics, 39 (1):143-157. [Details]
Gardiner, Stephen J.; Goldstein, Myron; (1995) 'Carleman approximation by harmonic functions'. American Journal of Mathematics, 117 (1):245-255. [Details]
Gardiner, Stephen J.; (1994) 'Superharmonic extension and harmonic approximation'. Annales de l'Institut Fourier, 44 :65-91. [Details]
Gardiner, Stephen J.; Goldstein, Myron; GowriSnkaran, Kohur; (1994) 'Global approximation in harmonic spaces'. Proceedings of the American Mathematical Society, 122 (1):213-221. [Details]
Gardiner, Stephen J.; Goldstein, M.; GowriSankaran, K.; (1994) 'Tangential approximation in harmonic spaces'. Indiana University Mathematics Journal, 43 (3):1003-1012. [Details]
Gardiner, Stephen J.; (1993) 'Conditions for separately subharmonic functions to be subharmonic'. Potential Analysis, 2 (3):255-261. [Details]
Gardiner, Stephen J.; (1993) 'Sets of determination for harmonic functions'. Transactions of the American Mathematical Society, 338 (1):233-243. [Details]
Gardiner, Stephen J.; (1993) 'Positive harmonic majorization of the real part of a holomorphic function'. Proceedings of the American Mathematical Society, 117 (3):767-770. [Details]
Gardiner, Stephen J.; (1993) 'The Dirichlet problem with noncompact boundary'. Mathematische Zeitschrift, 213 (1):163-170. [Details]
Gardiner, Stephen J.; (1993) 'Uniqueness and extension theorums for subharmonic functions'. Journal of the London Mathematical Society, 48 (3):515-525. [Details]
Armitage, David H.; Gardiner, Stephen J.; Netuka, I.; (1993) 'Separation of points by classes of harmonic functions'. Mathematical Proceedings of the Cambridge Philosophical, 113 :561-571. [Details]
 

Conference Publications

Gardiner, Stephen J. (2012) Recent progress on fine differentiability and fine harmonicity . In: André Boivin and Javad Mashreghi eds. Complex Analysis and Potential Theory Montreal, , 20-JUN-11 - 23-JUN-11 , pp.283-291 Link to full text [Details]
Gardiner, S. J. and Sjödin, T.; (2009) Potential theory in Denjoy domains Analysis and Mathematical Physics , pp.143-166 [Details]
Gardiner, S. J. and Sjödin, T.; (2009) Partial balayage and the exterior inverse problem of potential theory Potential theory and stochastics in Albac , pp.111-123 [Details]
Gardiner, Stephen J.; Netuka, Ivan; (2007) The farthest point distance function . In: A. Carbery et al eds. Complex and Harmonic Analysis , pp.35-43 [Details]
Gardiner, Stephen J.; (2006) Radial limits of harmonic functions . In: H. Aikawa eds. Potential theory in Matsue Tokyo, , pp.43-51 [Details]
Armitage, David H., Gardiner, Stephen J.; (1998) Best one-sided L^1-approximation by harmonic and subharmonic functions Advances in Multivariate Approximation Haus Bommerholz, University of Dortmund, , 27-SEP-98 - 02-OCT-98 , pp.43-56 [Details]
                                                                                                                                       

Research

Research Interests

Stephen J. Gardiner is Professor of Mathematics at UCD. His research interests are in potential theory, function theory and approximation by harmonic functions.

He is author of about 100 scientific publications in leading journals and books and has written the research monograph Harmonic Approximation (Cambridge University Press, 1995). His second book, Classical Potential Theory, written jointly with Professor David Armitage, is in the Springer Monographs in Mathematics Series (352pp., Springer, London, 2001). In 1995 he was awarded the degree of Doctor of Science by Queen's University on the basis of published research. In 2000 he was elected a Member of the Royal Irish Academy, the highest academic honour in Ireland.

He spent the year 1992 on sabbatical leave at McGill University, Montreal, and visited Charles University, Prague for the autumn term in 2005. Other assignments outside the university include lecture series in Sweden (1996), Japan (1997), the Czech Republic (1998), Canada (2000), Russia (2001) and Hungary (2009), and collaborative research projects at the Oberwolfach Mathematical Research Institute (1995, 1997, 1999) and the Mittag-Leffler Institute (1999). Other awards include a UCD President's Research Fellowship (2005/06), and an Erskine Fellowship at the University of Canterbury, New Zealand (2006).

He served as the Irish co-ordinator of the European Union Research Training Network 'Classical Analysis, Operator Theory, Geometry of Banach Spaces, their Interplay and Applications' (2000-2004) and as a member of the Steering Committee of the European Science Foundation Research Network 'Harmonic and Complex Analysis and its Applications' (2007-2012). He was Principal Investigator of the Science Foundation Ireland Research Frontiers projects 'Potential theory and quadrature domains' (2006-2010) and 'Universality, approximation and potential theory' (2009-2013). He served from 2001-2010 as an Editorial Adviser for the Proceedings, Journal and Bulletin of the London Mathematical Society and is at present on the Editorial Board of the Springer journal Potential Analysis.


Research Projects

Sponsor : Irish Research Council (IRC)
Title : Universal series and potential theory
Start Date / End Date : 01-OCT-17 / 30-SEP-19
Sponsor : Science Foundation Ireland (SFI)
Title : Universality, approximation and potential theory
Start Date / End Date : 01-SEP-09 / 31-AUG-13
Sponsor : Science Foundation Ireland (SFI)
Title : Potential Theory of the Farthest Point Distance Function
Start Date / End Date : 03-JUN-08 / 28-JUL-08
Sponsor : Science Foundation Ireland (SFI)
Title : Potential theory and quadrature domains
Start Date / End Date : 01-SEP-06 / 28-FEB-10
Sponsor : European Commission FP5
Title : Classical, Analysis, Operator Theory, Geometry of Banach spaces, their interplay and their applications
Start Date / End Date : 01-MAY-00 / 30-APR-04