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Pauline Mellon

Associate Professor

School Of Mathematics & Statistics
Science Centre
Belfield
Dublin 4

Tel: +353 1 7162556
Email: pauline.mellon@ucd.ie

Biography

Pauline Mellon did her undergraduate work at UCD after which she received the Travelling Studentship in Mathematical Sciences from the National University of Ireland. Her doctoral work was at the University of Tuebingen, Germany and UCD. She held a permanent position in the Department of Mathematics at the University of Maynooth for a number of years before returning to a lectureship in UCD. She is currently an Associate Professor in the School of Mathematics and Statistics. She is also currently Vice President of the Irish Mathematical Society (and was earlier a Secretary and ordinary committee member) and a committee member of the Physical, Chemical and Mathematical Sciences Committee of the Royal Irish Academy.





Professional

Honours and Awards

Year: 1996.
Title: Research Fellowship, Mathematisches Institut Oberwolfach, Germany
Year: 1996.
Title: EPSRC Fellowship (UK) University of London
Year: 1986.
Title: NUI Travelling Studentship in Mathematical Science
Year: 1985.
Title: University Prize in Mathematics (UCD)
Year: 1984.
Title: Scholarship in Mathematics (UCD)
Year: 1983.
Title: Scholarship in Mathematics and Chemistry (UCD)
Year: 1982.
Title: Scholarship in Physics and Chemistry (UCD)

Associations

Association: Irish Mathematical Society, 2017-, Function/Role: Vice President
Association: Irish Mathematical Society, 1994-1997, Function/Role: Secretary
Association: Irish Mathematical Society, 1991-1997, , Function/Role: Committee Member
     

Conference Contributions

Mellon, P. (2013) Chair of session on complex analysis. [Chaired Session], Complex Analysis and Dynamical Systems VI, Nahariya, Israel , 21-MAY-13 - 21-MAY-13.
Mellon, P. (2015) Iteration theory on bounded symmetric domains and an extension of Herve's theorem. [Invited Lecture], Complex Analysis and Dynamical Systems VII, Nahariya, Israel , 10-MAY-15 - 15-MAY-15.
Mellon, P. (2014) Denjoy-Wolff Theory on bounded symmetric domains. [Invited Lecture], Jordan Geometric Analysis and Applications, Queen Mary College, University of London , 03-SEP-15 - 05-SEP-15.
Mellon, P. (2013) Jordan theory and holomorphic dynamics. [Invited Lecture], Complex Analysis and Dynamical Systems VI, Nahariya, Israel , 19-MAY-15 - 24-MAY-15.
Mellon P.; (2006) JB*-triples and related topics. [Conference Organising Committee Member], JB*-triples and related topics, UCD , 02-JAN-06 - 02-JAN-06.
Mellon P.; (2001) Jordan Structures in Analysis II (Part I was in UK). [Conference Organising Committee Member], Jordan Structures in Analysis II (Part I was in UK), UK , 01-JAN-01 - 01-JAN-01.
Mellon P.; (1996) Annual Meeting of Irish Mathematical Society. [Conference Organising Committee Member], Annual Meeting of Irish Mathematical Society, N/A , 01-APR-96 - 01-APR-96.
Mellon P.; (1994) Annual Meeting of Irish Mathematical Society. [Conference Organising Committee Member], Annual Meeting of Irish Mathematical Society, N/A , 03-JAN-94 - 03-JAN-94.
Mellon P.; (1994) Polynomials and Holomorphic Functions on Infinite Dimensional Spaces. [Conference Organising Committee Member], Polynomials and Holomorphic Functions on Infinite Dimensional Spaces, UCD , 04-APR-94 - 04-APR-94.

Committees

Committee : Irish Mathematical Society
Committee : Physical, Chemical and Mathematical Sciences Committee of the Royal Irish Academy

Employment

Employer: UCD: 1986-1987 and 1988-1990
Position: Tutor and Part-time Lecturer
Employer: Universität Tübingen: 1987-1988
Position: NUI Travelling Studentship
Employer: NUI Maynooth: 1990-1991
Position: Lecturer Temporary
Employer: NUI Maynooth: 1991-1992
Position: Lecturer Permanent
Employer: UCD: 1992-2002
Position: Lecturer
Employer: UCD: 2002-2003
Position: Senior Lecturer

Education

Year 1985 Institution:
Qualification: BSc Subject:
Year 1990 Institution:
Qualification: PhD Subject:
Year 1986 Institution:
Qualification: MSc Subject:
       

Other Activities

Various funding awards from, among others: Enterprise Ireland, Forbairt, The Spanish Government, The British Council (International Collaboration Scheme) in the period 1992-2002

Undergraduate scholarships (UCD): Physics, Chemistry 1982; Mathematics, Chemistry 1983; Mathematics 1984; Prize in Mathematics 1985.

Other Professional Activities:

Referee for :

Proceedings of The London Mathematical Society, Journal of the London Mathematical Society, Quarterly Journal of Mathematics at Oxford, Mathematical Reviews, Journal of Mathematical Analysis and its Applications, Mathematical Proceedings of the Royal Irish Academy, Manauscripta Mathematica, Mathematica Scandinavica, Proceedings of Edinburgh Mathematical Society (among others).

International Courses Given:

(as part of the 1st and 2nd European Course on Complex Analysis and its Applications. These courses were given for Ph.D students of European universities in the Erasmus program.) 
  • An introduction to Several Complex Variables, Coimbra, Portugal 1995
  • An introduction to Bounded Symmetric Domains, Coimbra, Portugal 1996
Invited Presentations/Lectures/Colloquia:  
  • Heinrich Fabri-Institut der Universität Tübingen, Germany 1991
  • Internation Conference on Operator Algebras, UCC 1991
  • Memphis State University, USA 1991
  • University of Kentucky, USA 1991
  • Irish Math Society Annual Meeting UCG 1991
  • The Banach Center, Warsaw, Poland 1992
  • University of Malaga, Spain 1992
  • University of Granada, Spain 1992
  • Conference on Non-Associative Algebras, Oviedo, Spain 1993
  • Conference on Operator Algebras, UCC 1993
  • Conference on Function Theory, Madrid, Spain 1995
  • University College Cork 1995
  • University of London (Goldsmith's College) 1995
  • Eight lecture course given as part of 1st European Intensive Course on Complex Analysis and its Applications, Coimbra, Portugal 1995
  • Workshop on JB*-triples UCD 1996
  • Universität Tübingen, Germany 1996
  • King's College, University of London 1996
  • University of Reading, UK 1996
  • Kent State University, USA 1996
  • Six lecture course given as part of 2nd European Intensive Course on Complex Analysis and its Applications, Coimbra, Portugal 1996
  • Maynooth College 1997
  • University College Galway 1997
  • Queen's University Belfast 1998
  • Conference on C*-algebras, Queen's University Belfast 1998
  • University of Granada, Spain 2000.
  • Conference on 'Complex Analysis and Dynamical Systems VI', Nahariya, Israel, 2013.
  • Conference on 'Jordan Geometric Analysis and Applications', Univeristy of London, 2014.
  • Conference on 'Complex Analysis and Dynamical Systems VII', Nahariya, Israel, 2015.
  • Invited Lecture, Departamento de Analisis Matematico, University of Granada, Spain, 2017.

Publications

 

Book Chapters

Mellon, P.; (2000) 'An introduction to bounded symmetric domains' In: * (eds). Textos de Matematica. Series B [Texts in Mathematics. Series B]. , pp.22 [Details]
Mellon, P.; (1995) 'An introduction to several comple variables' In: * (eds). Textos de Matematica. Serie B [Texts in Mathematics. Series B]. [Details]
 

Peer Reviewed Journals

M. Mackey and P. Mellon (2018) 'Iterates of a compact holomorphic map on a finite rank homogeneous ball'. Acta Scientiarum Mathematicarum, . [Details]
Mellon, P. (2017) 'A Wolff Theorem for finite rank bounded symmetric domains'. Journal of Mathematical Analysis and Applications, 456 :57-68. [DOI] Link to full text [Details]
Mellon, P (2016) 'A Jordan approach to iteration theory for bounded symmetric domains (Complex Analysis and Dynamical Systems VI)'. Contemporary Mathematics, . [Details]
Mellon, P (2016) 'Denjoy-Wolff theory for finite dimensional bounded symmetric domains'. Annali di Matematica Pura ed Applicata, 195 (3):845-855. [DOI] [Details]
Mellon, P (2015) 'Dynamics of biholomorphic self-maps on bounded symmetric domains'. Mathematica Scandinavica, 117 :203-216. Link to full text [Details]
Mackey, M. and Mellon, P.; (2004) 'A Schwarz lemma and composition operators'. Integral Equations Operator Theory, 48 (4):511-524. Available Online [DOI] Link to full text [Details]
Mellon, P.; (2004) 'A general Wolff theorem for arbitrary Banach spaces'. Mathematical Proceedings of the Royal Irish Academy, 104A (2):127-142. [Details]
Mackey, M. and Mellon, P.; (2003) 'Angular derivatives on bounded symmetric domains'. Israel J. Math, 138 :291-315. Available Online [DOI] Link to full text [Details]
Mackey, M. and Mellon, P.; (2002) 'On an angular derivative result of Fan'. Math. Proc. R. Ir. Acad, 102A (1):115-126. Available Online [DOI] [Details]
Mackey, M. and Mellon, P. (2001) 'Compact-like manifolds associated to JB*-triples'. Manuscripta Mathematica, 106 (2):203-212. [DOI] [Details]
Mackey M. and Mellon, P. (2001) 'Compact-like manifolds associated to JB*-triples'. Manuscripta Mathematica, 106 (2):203-212. [DOI] [Details]
Mellon P.; (2000) 'Holomorphic invariance on bounded symmetric domains'. Journal Fur Die Reine Und Angewandte Mathematik, 523 :199-223. [Details]
Dineen, Seán and Mackey, Michael and Mellon, Pauline (1999) 'The density property for JB*-triples'. Studia Mathematica, 137 (2):143-160. [Details]
Mackey, M. and Mellon, P. (1999) 'The quasi-invertible manifold of a JB*-triple'. Extracta Mathematicae, 14 (1):51-55. [Details]
Dineen, Sean; Mellon, Pauline.; (1998) 'Holomorphic functions on symmetric Banach manifolds of compact type are constant'. Mathematische Zeitschrift, 229 (4):753-765. [Details]
Chu, Cho-Ho; Mellon, Pauline; (1998) 'Jordan structures in Banach spaces and symmetric manifolds'. Expositiones Mathematicae, 16 (2):157-180. [Details]
Chu, Cho-Ho; Mellon, Pauline; (1997) '${\rm JB}\sp *$-triples have Pe\Iczynski's Property V'. Manuscripta Mathematica, 93 (3):337-347. [Details]
Chu, Cho-Ho; Mellon, Pauline; (1997) 'Iteration of compact holomorphic maps on a Hilbert ball'. Proceedings of the American Mathematical Society, 125 (6):1771-1777. [Details]
Chu, Cho-Ho; Mellon, Pauline; (1997) 'The Dunford-Pettis property in $[\rm JB] \sp *$-triples'. Journal of the London Mathematical Society, 55 (3):515-526. [Details]
Mellon, P.; (1996) 'Symmetric manifolds of compact type associated to the $[zrm JB}\sp *$-triples $C\sb 0(X,Z)$'. Mathematica Scandinavica, 78 (1):19-36. [Details]
Mellon, P.; (1996) 'Another look at results of Wolff and Julia type for $J\sp*$-algebras'. Journal of Mathematical Analysis and Applications, 198 (2):444-457. [Details]
Mellon P.; (1994) 'The polarisation constant for ${\rm JB}\sp *$-triples'. Extracta Mathematicae, 9 (3):160-163. [Details]
Mellon P.; (1993) 'Holomorphic curvature of infinite-dimensional symmetric complex Banach manifolds of compact type'. Annales Academiæ Scientiarum Fennicæ Mathematica, 18 (2):299-306. [Details]
Mellon, P.; (1993) 'Dual manifolds fof $[\rm JB}\sp *$-triples of the form $C(X,U)$'. Proceedings of the Royal Irish Academy, 93 (1):27-42. [Details]
P. Mellon (1991) 'Symmetric Banach Manifolds'. Irish Mathematical Society Bulletin, (26):12-14. [Details]
                               

Dissertations/Theses

Mellon, Pauline (1990) Symmetric Banach Manifolds. Dissertations/Theses [Details]
                                                                                                         

Research

Research Interests

Dr. Mellon's research interests are in Complex Analysis, primarily infinite dimensional, studying manifolds with symmetry. These correspond to the Banach spaces whose open unit balls have a transitive group of (biholomorphic) automorphisms, known as the JB*-triples. As such, the area straddles complex analysis, functional analysis and differential geometry. Dr. Mellon has studied these manifolds from several different perspectives: their curvature, the class of holomorphic maps that they admit and differences between the finite and infinite dimensional cases. She has published extensively on JB*-triples. Recent work includes versions of Wolff's classical theorem on these spaces (concerning invariant domains of holomorphic mappings) and work on composition operators. She has several collaborations with C.H. Chu (University College London), S. Dineen and M. Mackey of UCD and M.V. Velasco-Collado of the University of Granada.


Research Projects 

Sponsor : Enterprise Ireland
Title : Composition operators and angular derivatives on bounded symmetric domains
Start Date : 01-OCT-00

Sponsor : Enterprise Ireland
Title : Manifolds of Tripotents in JB*-Triples
Start Date : 01-JUL-99

Sponsor: Forbairt/The British Council
Title: International Collaboration Scheme
Start Date: 01-Oct-1999

Sponsor : Enterprise Ireland
Title : Algebraic and geometric approaches to complex analysis on infinite dimensional spaces II
Start Date : 01-OCT-97

Sponsor: Forbairt/The British Council
Title: International Collaboration Scheme
Start Date: 01-Oct-1996

Sponsor: Enterprise Ireland.
Title: Algebraic and geometric approaches to complex analysis on infinite dimensional spaces I.
Start Date: 01-Oct-1995

Sponsor: Forbairt/The British Council
Title: International Collaboration Scheme
Start Date: 01-Oct-1995

Research Projects

Sponsor : Enterprise Ireland (EI)
Title : Composition operators and angular derivatives on bounded symmetric domains
Start Date / End Date : 01-OCT-00 / 30-SEP-02
Sponsor : Enterprise Ireland (EI)
Title : Manifolds of Tripotents in JB
Start Date / End Date : 01-JUL-99 / 30-JUN-00
Sponsor : Enterprise Ireland (EI)
Title : Algebraic and geometric approaches to complex analysis on infinite dimensional spaces II
Start Date / End Date : 01-OCT-97 / 30-SEP-99
Sponsor : Enterprise Ireland (EI)
Title : No Project title to migrate.
Start Date / End Date : 01-OCT-95 / 08-OCT-95
Sponsor : Enterprise Ireland (EI)
Title : No Project title to migrate.
Start Date / End Date : 01-MAR-96 / 08-MAR-96

Recent Postgraduates

 

Collaborators

Internal Collaborators


Michael Mackey, University College Dublin
Sean Dineen, University College Dublin

External Collaborators

Maria-Victoria Velasco Collado, University of Granada, Spain
Cho-Ho Chu, Queen Mary College, University of London, UK