Background
O'Meara, Onorato Timothy was born on January 29, 1928 in Cape Town, Republic of South Africa. Arrived in the United States, 1957. Son of Daniel and Fiorina (Allorto) O'M.
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book
Symplectic Groups (Mathematical Survey)
(This volume, the sequel to the author's Lectures on Linea...)
This volume, the sequel to the author's Lectures on Linear Groups, is the definitive work on the isomorphism theory of symplectic groups over integral domains. Recently discovered geometric methods which are both conceptually simple and powerful in their generality are applied to the symplectic groups for the first time. There is a complete description of the isomorphisms of the symplectic groups and their congruence subgroups over integral domains. Illustrative is the theorem $mathrm{PSp}_n(mathfrak o)congmathrm{PSp}_{n_1}(mathfrak o_1)Leftrightarrow n=n_1$ and $mathfrak ocongmathfrak o_1$ for dimensions $geq 4$. The new geometric approach used in the book is instrumental in extending the theory from subgroups of $mathrm{PSp})n(ngeq6)$ where it was known to subgroups of $mathrm{P}Gammamathrm{Sp}_n(ngeq4)$ where it is new. There are extensive investigations and several new results on the exceptional behavior of $mathrm{P}Gammamathrm{Sp}_4$ in characteristic 2. The author starts essentially from scratch (even the classical simplicity theorems for $mathrm{PSp}_n(F)$ are proved) and the reader need be familiar with no more than a first course in algebra.
http://www.amazon.com/gp/product/0821815164/?tag=2022091-20
Introduction to Quadratic Forms (Classics in Mathematics)
( From the reviews: "Anyone who has heard O'Meara lecture...)
From the reviews: "Anyone who has heard O'Meara lecture will recognize in every page of this book the crispness and lucidity of the author's style. ... The organization and selection of material is superb. ... deserves high praise as an excellent example of that too-rare type of mathematical exposition combining conciseness with clarity." Bulletin of the AMS
http://www.amazon.com/gp/product/3540665641/?tag=2022091-20
Introduction to Quadratic Forms (Classics in Mathematics) 2000 edition by O'Meara, O. Timothy (2013) Paperback
http://www.amazon.com/gp/product/B011ME76PY/?tag=2022091-20
Lectures on Linear Groups (CBMS Regional Conference Series in Mathematics)
(The notes in this volume evolved from lectures at the Cal...)
The notes in this volume evolved from lectures at the California Institute of Technology during the spring of 1968, from ten survey lectures on classical and Chevalley groups at an NSF Regional Conference at Arizona State University in March 1973, and from lectures on linear groups at the University of Notre Dame in the fall of 1973. The author's goal in these expository lectures was to explain the isomorphism theory of linear groups over integral domains as illustrated by the theorem $mathrm{PSL}_n({mathfrak o})simeqmathrm{PSL}_{n_1}({mathfrak o}_1)leftrightarrow n=n_1quadmathrm{and}quad{mathfrak o}simeq{mathfrak o}_1$ for dimensions $geqq 3$. The theory that follows is typical of much of the research of the last decade on the isomorphisms of the classical groups over rings. The author starts from scratch, assuming only basic facts from a first course in algebra. The classical theorem on the simplicity of $mathrm{PSL}_n(F)$ is proved, and whatever is needed from projective geometry is developed. Since the primary interest is in integral domains, the treatment is commutative throughout. In reorganizing the literature for these lectures the author extends the known theory from groups of linear transformations to groups of collinear transformations, and also improves the isomorphism theory from dimensions $geqq 3$.
http://www.amazon.com/gp/product/0821816721/?tag=2022091-20
Introduction to Quadratic Forms (Grundlehren der mathematischen Wissenschaften)
http://www.amazon.com/gp/product/3662417758/?tag=2022091-20
- Introduction to Quadratic Forms (Classics in Mathematics) by O. Timothy O'Meara (2000-02-03)
- Introduction to Quadratic Forms
- Introduction to Quadratic Forms (From the reviews: O'Meara treats his subject from th...)
Onorato Timothy O'Meara
Edit Profileacademic administrator mathematician
Education
Bachelor of Science, University Cape Town, 1947. Master of Science, University Cape Town, 1948. Doctor of Philosophy, Princeton University, 1953.
Doctor of Laws (honorary), University Notre Dame, 1987.
Career
Assistant lecturer, U. Natal, Republic South Africa, 1949;
lecturer, U. Otago, New Zealand, 1954-1956;
member, Institute for Advanced Study, Princeton, New Jersey, 1957-1958, 62;
assistant professor, Princeton, 1958-1962;
professor mathematics, U. Notre Dame, Indiana, 1962-1976;
department chairman, U. Notre Dame, 1965-1966, 68-72;
Kenna professor mathematics, U. Notre Dame, 1976-1998;
provost, U. Notre Dame, 1978-1996;
provost emeritus, U. Notre Dame, since 1996;
Kenna professor emeritus, U. Notre Dame, since 1998. Visiting professor California Institute Technology, 1968. Gauss professor Göttingen Academy Science, 1978.
Member of advisory panel mathematics science National Science Foundation, 1974-1977, consultant, since 1960.
Achievements
Works
book
-
Lectures on Linear Groups (CBMS Regional Conference Series in Mathematics)
(The notes in this volume evolved from lectures at the Cal...)
-
Symplectic Groups (Mathematical Survey)
(This volume, the sequel to the author's Lectures on Linea...)
-
Introduction to Quadratic Forms (Classics in Mathematics)
( From the reviews: "Anyone who has heard O'Meara lecture...)
-
Introduction to Quadratic Forms
(From the reviews: O'Meara treats his subject from this po...)
- Introduction to Quadratic Forms (Classics in Mathematics) by O. Timothy O'Meara (2000-02-03)
- Introduction to Quadratic Forms
- Introduction to Quadratic Forms (Classics in Mathematics) 2000 edition by O'Meara, O. Timothy (2013) Paperback
- Introduction to Quadratic Forms (Grundlehren der mathematischen Wissenschaften)
-
Lectures on Linear Groups (CBMS Regional Conference Series in Mathematics)
Membership
Member Catholic Commission Intellectual and Cultural Affairs, since 1962. Board of Governors, trustee U. Notre Dame Australia, since 1990. Life trustee University of Notre Dame, since 1996.
Member American Mathematics Society, American Academy Arts and Sciences, Collegium (board directors 1992-1996, commission on Catholic scholarship since 1997).
Connections
Married Jean T. Fadden, September 12, 1953. Children— Maria, Timothy, Jean, Kathleen, Eileen.
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Born
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Nationality
American South African -
Religion
Roman Catholic