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Researchers at UCD

researcher

Richard Smith

Lecturer

School of Mathematics & Statistics
Room S1.71
First Floor, Science Centre South
University College Dublin
Belfield, Dublin 4

Tel: +353 1 7162570
Email: richard.smith@ucd.ie

Professional

Honours and Awards

Year: 2011.
Title: Research Frontiers Programme Grant

Associations

Association: American Mathematical Society, Function/Role: MR Reviewer
     

Conference Contributions

Smith, R. J. (2015) Applying topology to problems in the geometry of Banach spaces. [Plenary Lecture], 30th Summer Conference on Topology and Applications, NUI Galway , 23-JUN-15 - 26-JUN-15.
Smith, R. J. (2015) Weak compactness in Banach spaces. [Invited Lecture], 18th Galway Topology Colloquium, NUI Galway , 22-JUN-15 - 22-JUN-15.
Smith, R. J. (2015) Lipschitz-free spaces and the metric approximation property. [Invited Lecture], Spring School (Mathematics and Statistics, University of Tartu), Otepää, Estonia , 22-MAY-15 - 22-MAY-15.
Smith, R. J. (2015) Lipschitz-free spaces and the metric approximation property. [Invited Oral Presentation], Infinite Dimensional Function Theory, University College Dublin, Ireland , 08-JAN-15 - 09-JAN-15.
Smith, R. J. (2014) Boundaries, polyhedrality and LFC norms. [Invited Lecture], First Brazilian Workshop in Geometry of Banach Spaces, Maresias, Brazil , 25-AUG-14 - 29-AUG-14.
Smith, R. J. (2014) Isomorphisms to improve the norm. [Plenary Lecture], Geometry of Banach Spaces, Albacete, Spain , 10-JUN-14 - 13-JUN-14.
Smith, R. J. (2014) Visualisation of three-dimensional concepts in mathematics and science using touch screens. [Oral Presentation], 15th Educational Technology Conference of the ILTA, UCD , 29-MAY-14 - 30-MAY-14.
Smith, R.J. (2013) Topology, polyhedrality and smoothness in Banach spaces. [Invited Lecture], Interactions between Logic, Topological structures and Banach spaces theory, Eilat, Israel , 19-MAY-13 - 24-MAY-13.
Smith, R.J. (2013) Topological properties associated with strict convexity. [Plenary Lecture], QOP Network Meeting, Lancaster University, UK , 29-APR-13 - 30-APR-13.
Smith, R.J. (2013) Topological properties associated with strict convexity. [Plenary Lecture], Workshop on set theoretic methods in compact spaces and Banach spaces, Warsaw, Poland , 17-APR-13 - 21-APR-13.
Smith, R.J. (2013) Strictly convex norms and topology. [Plenary Lecture], 41st Winter School in Analysis, Kacov, Czech Republic , 12-JAN-13 - 19-JAN-13.
Fonf, V.P., Pallares, A.J., Smith, R.J. and Troyanski, S (2012) Recent advances in the theory of isomorphic polyhedrality. [Invited Lecture], Geometry of Banach Spaces Workshop, CIRM, Luminy, Marseille , 27-AUG-12 - 31-AUG-12.
Smith, R.J.; (2011) Strictly convex norms and topology. [Oral Presentation], General Topology and its Applications, New York City , 25-JUL-11 - 29-JUL-11.
Orihuela, J., Smith, R.J. and Troyanski, S.; (2010) Scattered spaces and strictly convex dual norms. [Invited Lecture], Functional Analysis Valencia, Valencia, Spain , 07-JUN-10 - 11-JUN-10.
Orihuela, J., Smith, R.J. and Troyanski, S.; (2009) Scattered spaces and strictly convex dual norms. [Oral Presentation], Function Theory on Infinite Dimensional Spaces XI, Madrid , 14-DEC-09 - 17-DEC-09.
Hájek, P. and Smith, R.J.; (2009) Operator machines on directed graphs. [Oral Presentation], Modern Functional Analysis: Conference to honour Fernando Bombal on his 65th birthday, Aranjuez, Spain , 08-JUN-09 - 12-JUN-09.
Smith, R.J. and Troyanski, S.; (2008) Unconditional bases and strictly convex dual renormings. [Invited Lecture], CMS Winter Meeting 2008, Ottawa, Canada , 04-DEC-08 - 08-DEC-08.
Smith, R.J.; (2007) Some remarks on Gruenhage spaces. [Invited Lecture], Workshop in Banach Space Theory, University of Murcia, Spain , 17-OCT-07 - 17-OCT-07.
Smith, R.J.; (2006) Gruenhage compacta and strictly convex dual norms. [Oral Presentation], Banach space theory: classical topics and new directions, Cáceres, Spain , 04-SEP-06 - 08-SEP-06.
Smith, R.J.; (2006) Trees, linear orders and renorming. [Oral Presentation], III Workshop in Functional Analysis, La Manga, Spain , 02-MAR-06 - 04-MAR-06.
Smith, R.J.; (2005) Trees, linear orders and renorming. [Oral Presentation], Function Theory on Infinite Dimensional Spaces IX, Madrid, Spain , 13-DEC-05 - 16-DEC-05.
Smith, R.J.; (2004) On Trees and Gâteaux smooth Norms. [Oral Presentation], V Conference on Banach Spaces, Cáceres, Spain , 13-SEP-04 - 17-SEP-04.
Smith, R.J.; (2004) On trees and dual rotund norms. [Oral Presentation], Non-Separable Banach Spaces, Paseky, Czech Republic , 18-APR-04 - 24-APR-04.
 

Employment

Employer: University College Dublin
Position: College Lecturer
Employer: Mathematical Institute, Czech Academy of Sciences
Position: Postdoctoral Researcher
Employer: Queens' College, University of Cambridge
Position: Fellow and Director of Studies

Education

Year 2005 Institution: Oxford University, UK
Qualification: DPhil Subject:
Year 1999 Institution: University of Oxford, UK
Qualification: MMath Subject: Mathematics
     

Journals Edited

Fundamenta Mathematicae: Reviewer.
Bulletin Of The London Mathematical Society: Reviewer.
Proceedings Of The Edinburgh Mathematical Society: Reviewer.
Proceedings Of The American Mathematical Society: Reviewer.
Revista De La Real Academia De Ciencias Exactas: Reviewer.
Journal Of Mathematical Analysis And Applications: Reviewer.
Journal Of The London Mathematical Society: Reviewer.
Quarterly Journal Of Mathematics: Reviewer.
 

Publications

     

Peer Reviewed Journals

Bible, V. and Smith, R. J. (2016) 'Smooth and polyhedral approximation in Banach spaces'. Journal of Mathematical Analysis and Applications, :1262-1272. [DOI] [Details]
Kania, T. and Smith, R. J. (2015) 'Chains of functions in C(K)-spaces'. Journal of the Australian Mathematical Society, 99 :350-363. [DOI] [Details]
Pernecká, E. and Smith, R. J. (2015) 'The metric approximation property and Lipschitz-free spaces over subsets of R^N'. Journal of Approximation Theory, 199 :29-44. [DOI] [Details]
Fonf, V.P., Smith, R.J., Troyanski, S. (2015) 'Boundaries and polyhedral Banach spaces'. Proceedings of the American Mathematical Society, 143 :4845-4849. [DOI] [Details]
Fonf, V.P., Pallares, A.J., Smith, R.J., Troyanski, S. (2014) 'Polyhedrality in pieces'. JOURNAL OF FUNCTIONAL ANALYSIS, . [DOI] [Details]
Hájek, P. and Smith, R.J.; (2012) 'Some duality relations in the theory of tensor products'. Expositiones Mathematicae, 30 (3):239-249. Available Online [DOI] [Details]
Orihuela, J., Smith, R.J. and Troyanski, S.; (2012) 'Strictly convex norms and topology'. Proceedings of the London Mathematical Society, . Available Online [DOI] [Details]
Smith, R.J; (2012) 'Strictly convex norms, Gδ-diagonals and non-Gruenhage spaces'. Proceedings of the American Mathematical Society, . Available Online [DOI] [Details]
Fonf, V.P, Smith, R.J and Troyanski, S.; (2012) 'A note on fragmentability and weak-Gδ sets'. Quarterly Journal of Mathematics, . Available Online [DOI] [Details]
Smith, R.J. and Troyanski, S.; (2010) 'Renormings of C(K) spaces'. Revista de la Real Academia de Ciencias Exactas, 104 (2):375-412. Available Online [DOI] [Details]
Hájek, P. and Smith, R.J.; (2010) 'Operator machines on directed graphs'. Integral Equations and Operator Theory, 67 (1):15-31. [DOI] [Details]
Smith, R.J. and Troyanski, S.; (2009) 'Unconditional bases and strictly convex dual renormings'. Bulletin of the London Mathematical Society, 41 (5):831-840. [DOI] [Details]
Smith, R.J.; (2009) 'Gruenhage compacta and strictly convex dual norms'. Journal of Mathematical Analysis and Applications, 350 (2):745-757. [DOI] [Details]
Fonf, V.P., Pallares, A.J., Smith, R.J. and Troyanski, S.; (2008) 'Polyhedral norms on non-separable Banach spaces'. JOURNAL OF FUNCTIONAL ANALYSIS, 255 (2):449-470. [DOI] [Details]
Smith, R.J.; (2007) 'Trees, linear orders and Gâteaux smooth norms'. Journal of the London Mathematical Society, 76 (3):633-646. [DOI] [Details]
Smith, R.J.; (2007) 'Trees, Gâteaux smooth norms and a problem of Haydon'. Bulletin of the London Mathematical Society, 39 (1):112-120. [DOI] [Details]
Smith, R.J.; (2006) 'On trees and dual rotund norms'. JOURNAL OF FUNCTIONAL ANALYSIS, 231 (1):177-194. [DOI] [Details]
Smith, R.J.; (2005) 'Bounded linear Talagrand operators on ordinal spaces'. Quarterly Journal of Mathematics, 56 (3):383-395. [DOI] [Details]

Other Journals

Smith, R.J.; (2005) 'The Tale of a PhD Mathematician' Mathematics Today 41 :76-77. [Details]
       

Website article

Smith, R. J. (2015) Got the heebie-jeebies? 13 freaky facts about Friday the 13th. Website article Available Online [Details]
Smith, R. J. (2015) Here are 13 facts to mark another Friday the 13th. Website article Available Online [Details]
                                                                                 

Research

Research Interests

I have interests in functional analysis and topology, principally the geometry of Banach spaces.

The natural norm on a general Banach space need not have any good geometrical properties. However, sometimes it is possible to introduce a new norm, topologically equivalent to the original norm, but with, for example, some property of smoothness or strict convexity. In this way, we can improve the geometry of the space.

In general, it is very difficult to decide whether or not such norms can be found, so we try to characterise their existence in terms of more easily determined linear and topological properties of the given space. The techniques involved in this endeavour are wide ranging, and as well as requiring deep results from functional analysis and topology, they bring to bear elements of set theory, combinatorics, smooth function theory, variational methods and much more.

More recently, I have investigated a problem in operator theory which concerned the properties of orbits of points under operators.

More details of my research interests can be found at http://www.maths.ucd.ie/~rsmith.