Seán Dineen (12 February 1944 – 18 January 2024) was an Irish mathematician specialising in

complex analysis Complex analysis, traditionally known as the theory of functions of a complex variable, is the branch of mathematical analysis that investigates functions of complex numbers. It is helpful in many branches of mathematics, including algebraic ...

. His academic career was spent, in the main, at

University College Dublin University College Dublin (), commonly referred to as UCD, is a public research university in Dublin, Ireland, and a collegiate university, member institution of the National University of Ireland. With 38,417 students, it is Ireland's largest ...

(UCD) where he was Professor of Mathematics, serving as Head of Department and as Head of the School of Mathematical Sciences before retiring in 2009. Dineen died on 18 January 2024, at the age of 79.

Education

Seán Dineen was born in Clonakilty, Co. Cork, Ireland on 12 February 1944. He attended St Mary's, the first secondary school for boys in Clonakilty, which his parents Jerry (Jeremiah) and Margaret Dineen had founded in 1938. His father had died in 1953 and the school was subsequently run by his mother. He entered

University College Cork University College Cork – National University of Ireland, Cork (UCC) () is a constituent university of the National University of Ireland, and located in Cork (city), Cork. The university was founded in 1845 as one of three Queen's Universit ...

(UCC) in 1961 to study mathematics, graduating with honours BSc in mathematics in 1964. While at UCC, he was involved in setting up the student mathematics society there. His tutors and lecturers included Finbarr Holland, Michael Mortell, Tagdh Carey, Paddy Kennedy, Paddy Barry and Siobhán O'Shea (later Siobhán Vernon). He completed his MSc there in 1965, and was awarded a

National University of Ireland The National University of Ireland (NUI) () is a federal university system of ''constituent universities'' (previously called '' constituent colleges'') and ''recognised colleges'' set up under the Irish Universities Act 1908, and signifi ...

Travelling Studentship.An Interview with Professor Seán Dineen
by Gary McGuire, Irish Math. Soc. Bulletin 64 (2009), 65–77. Dineen was the first student of pure mathematics from UCC to travel to the USA to do his doctorate, where he did his coursework in the

University of Maryland The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public land-grant research university in College Park, Maryland, United States. Founded in 1856, UMD is the flagship institution of the Univ ...

. His official supervisor there was John Horvath, but his PhD research was carried out in

Rio de Janeiro Rio de Janeiro, or simply Rio, is the capital of the Rio de Janeiro (state), state of Rio de Janeiro. It is the List of cities in Brazil by population, second-most-populous city in Brazil (after São Paulo) and the Largest cities in the America ...

Instituto Nacional de Matemática Pura e Aplicada The ''Instituto Nacional de Matemática Pura e Aplicada'' (National Institute for Pure and Applied Mathematics) is considered to be the foremost research and educational institution of Brazil in the area of mathematics. It is located in the cit ...

(IMPA) under the supervision of Leopoldo Nachbin. He completed his thesis on "Holomorphy Types on a Banach Space" in 1970.Seán Dineen
at the

Mathematics Genealogy Project The Mathematics Genealogy Project (MGP) is a web-based database for the academic genealogy of mathematicians.. it contained information on 300,152 mathematical scientists who contributed to research-level mathematics. For a typical mathematicia ...

UCD Career

Dineen spent the year 1969-1970 at

Johns Hopkins Johns Hopkins (May 19, 1795 – December 24, 1873) was an American merchant, investor, and philanthropist. Born on a plantation, he left his home to start a career at the age of 17, and settled in Baltimore, Maryland, where he remained for mos ...

as an instructor before returning to Ireland. After two years at the

Dublin Institute for Advanced Studies The Dublin Institute for Advanced Studies (DIAS) () is a statutory independent research institute in Dublin, Ireland. It was established, under the Institute For Advanced Studies Act 1940, by the government of the then Taoiseach, Éamon de Vale ...

(DIAS), he secured a position at University College Dublin. Seven years later, in 1979, he was appointed to the professorship and chair of mathematics vacated by J. R. Timoney. He spent the rest of his career there, formally retiring in 2009.

Mathematics

Dineen's work has principally been in the area of infinite dimensional

and the topological structure of spaces of

Holomorphic function In mathematics, a holomorphic function is a complex-valued function of one or more complex variables that is complex differentiable in a neighbourhood of each point in a domain in complex coordinate space . The existence of a complex de ...

s. He later worked on bounded symmetric domains and

spectral theory In mathematics, spectral theory is an inclusive term for theories extending the eigenvector and eigenvalue theory of a single square matrix to a much broader theory of the structure of operator (mathematics), operators in a variety of mathematical ...

, among other topics. He has said "If you want to stay active as a research mathematician, you have to reinvent yourself regularly". His academic footprint includes 10 books and/or monographs, over 100 peer-reviewed research articles, over 4000 citations, 11 PhD students, over 40 collaborators, and the organisation of numerous mathematical conferences and meetings. In 1987 he was elected to the

Royal Irish Academy The Royal Irish Academy (RIA; ), based in Dublin, is an academic body that promotes study in the natural sciences, arts, literature, and social sciences. It is Ireland's premier List of Irish learned societies, learned society and one of its le ...

.Science Member Seán Dineen
The Royal Irish Academy

Selected papers

* Dineen, Seán "The second dual of a JB∗ triple system. Complex analysis, functional analysis and approximation theory". (Campinas, 1984), 67–69, North-Holland Math. Stud., 125, Notas Mat., 110, North-Holland, Amsterdam, 1986. * Dineen, Seán "Complete holomorphic vector fields on the second dual of a Banach space". Math. Scand. 59 (1986), no. 1, 131–142. * Dineen, Seán "Holomorphy types on a Banach space". Studia Math. 39 (1971), 241–288. * Alencar, Raymundo; Aron, Richard M.; Dineen, Seán "A reflexive space of holomorphic functions in infinitely many variables". Proc. Amer. Math. Soc. 90 (1984), no. 3, 407–411. * Dineen, Seán; Timoney, Richard M. "On a problem of H. Bohr". Bull. Soc. Roy. Sci. Liège 60 (1991), no. 6, 401–404. * Dineen, Seán; Timoney, Richard M.; Vigué, Jean-Pierre "Pseudodistances invariantes sur les domaines d'un espace localement convexe". Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4) 12 (1985), no. 4, 515–529. * Dineen, Seán; Timoney, Richard M. "Absolute bases, tensor products and a theorem of Bohr". Studia Math. 94 (1989), no. 3, 227–234. * Dineen, Seán; Mellon, Pauline "Holomorphic functions on symmetric Banach manifolds of compact type are constant". Math. Z. 229 (1998), no. 4, 753–765. * Dineen, Seán; Mackey, Michael; Mellon, Pauline "The density property for JB∗-triples". Studia Math. 137 (1999), no. 2, 143–160. * Dineen, Seán; Patyi, Imre; Venkova, Milena "Inverses depending holomorphically on a parameter in a Banach space". J. Funct. Anal. 237 (2006), no. 1, 338–349. * Dineen, Seán; Mujica, Jorge "A monomial basis for the holomorphic functions on $c_0$". Proc. Amer. Math. Soc. 141 (2013), no. 5, 1663–1672. * Dineen, Seán; Harte, Robin E. "Banach-valued axiomatic spectra". Studia Math. 175 (2006), no. 3, 213–232. * Dineen, Seán; Galindo, Pablo; García, Domingo; Maestre, "Manuel Linearization of holomorphic mappings on fully nuclear spaces with a basis". Glasgow Math. J. 36 (1994), no. 2, 201–208.

Selected books

* ''Analysis, a Gateway to Understanding''. World Scientific, 2012, 320pp. * ''Black-Scholes Formula''. Second edition. Graduate Studies in Mathematics, 70. American Mathematical Society, Providence, RI, 2013. xiv+305 * ''Probability Theory in Finance. A Mathematical Guide to the Black-Scholes formula''. Graduate Studies in Mathematics, 70. American Mathematical Society, Providence, RI, 2005. xiv+294 pp. * ''Complex Analysis on Infinite-Dimensional Spaces''. Springer Monographs in Mathematics. Springer-Verlag London, Ltd., London, 1999. xvi+543 pp. * ''Multivariate Calculus and Geometry''. Springer Undergraduate Mathematics, Series. Springer-Verlag London, Ltd., London, 1998. xii+262 pp. Third edition 2014. xiv+257 pp. * ''Functions of Two Variables''. Chapman and Hall Mathematics, Series. Chapman & Hall, London, 1995. x+189 pp. Second edition Chapman & Hall/CRC, Boca Raton, FL, 2000. xii+191 pp. * ''The Schwarz Lemma''. Oxford Mathematical Monographs. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1989. x+248 pp.

References

External links

*
Obituary
in Irish Maths Society Bulletin {{DEFAULTSORT:Dineen, Sean 1944 births 2024 deaths Mathematical analysts Complex analysts 20th-century Irish mathematicians 21st-century Irish mathematicians Alumni of University College Cork University System of Maryland alumni Instituto Nacional de Matemática Pura e Aplicada alumni Academics of University College Dublin Johns Hopkins University faculty People from Clonakilty Members of the Royal Irish Academy Academics of the Dublin Institute for Advanced Studies Scientists from County Cork