Professor Emeritus Barrett O'Neill died on June 16, 2011, at age 87. O'Neill joined the department in 1951, directly from MIT, where he had just received his PhD under the direction of Witold Hurewicz. O'Neill retired in 1991, but he continued his mathematical work, with a major book on relativity, The Geometry of Kerr Black Holes, published in 1995. O'Neill began his mathematical life as an algebraic topologist: his dissertation was on fixed point theory and he made further contributions to that subject, developing a generalization of the Lefschetz Fixed Point Theorem to multi-valued (set-valued) mappings. But quite early on, he turned primarily to Riemannian geometry and to semi-Riemannian geometry, the geometry of non-degenerate quadratic forms on the tangent spaces that are not positive definite.
O'Neill had a long and distinguished career, exerting a notable influence on his fields of work. The list of citations of his work is enormous, with over 1,000 citations in the Science Citation Index.
In a famous paper on Riemannian submersions, he developed a formula, now known as ONeill's formula, showing that the sectional curvature of the base manifold was always at least as large as the associated vertically-lifted sectional curvature of the larger-dimensional domain manifold. The elegance and power of this paper brought the idea of Riemannian submersion into a prominent position, which it has retained ever since, and is the fundamental tool in particular in the construction of examples of manifolds of positive curvature.
A second highly influential work was O'Neill's investigation of manifolds of negative curvature. His paper with R.L. Bishop on this topic introduced a new viewpoint on the whole subject and also formalized the idea of warped products and bundles, an idea that has been of vital importance also in the construction of manifolds of positive curvature. In a second paper on negative curvature, joint work with his student, P. Eberlein, O'Neill introduced the important concepts of visibility and of geometry at infinity for negatively curved manifolds. These two papers together revitalized the subject of manifolds of negative curvature and led to a long sequence of developments by Eberlein, Ballmann, Spazier, Gromov, among others.
O'Neill wrote three books, each of great distinction. One was an undergraduate text book on differential geometry, Elementary Differential Geometry, which was notable for its systematic use of differential forms - unusual in an undergraduate book at that time - and also notable for the elegance of its illustrations at a time before computer graphics. His book Semi-Riemannian Geometry was one of the first books to treat indefinite metric geometry systematically on an equal footing and in modern notation with the more usual positive definite Riemannian geometry. This book was so superbly done that it has often been used as a text even when only the Riemannian case is at issue. His last book The Geometry of Kerr Black Holes is a masterpiece of exposition and mathematical insight, managing to get to deep matters indeed while being accessible to readers with only limited background in differential geometry, so that its readership has been very broad. O'Neill used to remark that whereas he had written his first two books for the benefit of other people, he had written The Geometry of Kerr Black Holes to please himself. Fortunately, he ended up pleasing a wide variety of readers as well.
O'Neill had eight PhD students, several of whom became distinguished geometers (Patrick Eberlein, Alfred Gray).
O'Neill was an encouraging, intellectually stimulating, and cheerful presence in our department, who was in particular extraordinarily kind and helpful to his younger colleagues. He had a fine dry sense of humor. He delighted, for example, in a wry way in showing people a copy of a book in which another author had unceremoniously stolen without credit the remarkable illustrations in his own Elementary Differential Geometry. The slings and arrows of life never dimmed his enthusiasm for it and for the life of mathematics in particular. He will be much missed by us all.
He is survived by his wife Hope, their three children Eric, Evelyn, and Jean, and two grandchildren.
Adjunct Professor Emeritus Herbert B. Enderton died at his home in Santa Monica on October 22, 2010, after battling leukemia for nearly a year. Enderton received his PhD in mathematics in 1962 at Harvard University under the supervision of Hilary Putnam. He had a postdoctoral appointment at MIT from 1962 to 1964, and he was an assistant professor at UC Berkeley from 1964 to 1968. In 1968 he came to UCLA, where he took on two half-time positions, one in the mathematics department and the other as an editor of the reviews section of the Journal of Symbolic Logic. In 1980 the latter job became a more important one when he was made the coordinating editor of the reviews section. As such he was in charge of a major function of the Association for Symbolic Logic, and he remained in this role until 2002. Enderton retired from department in 2003, but he continued to teach regularly until he became ill in 2009. He similarly continued being in charge of the UCLA Logic Colloquium, as he had been for decades.
Enderton’s thesis and the majority of his published research were on recursion theoretic hierarchies of sets of integers. This subject, which Enderton characterized as “little steps for little feet,” was a very active part of mathematical logic in the 1950s, 1960s, and 1970s, and Enderton was a major contributor to it. In the early 1970s, he began devoting himself to teaching, writing expository articles, and—with great success—writing textbooks. His first book, A Mathematical Introduction to Logic, was published in 1972. It is the most popular logic text at the advanced undergraduate/beginning graduate level, and it is often used (especially by computer scientists) as “the” standard reference to logic. It is still going strong in its second edition, published in 2001. Spanish and Chinese translations appeared in 2004 and 2006 respectively. His 1977 Elements of Set Theory has also been very successful. A new undergraduate text, Computability Theory: an Introduction to Recursion Theory, was completed after he had become ill and was published in 2011.
Herb Enderton was an active participant in the life of the logic group at UCLA, and he will be sorely missed. He is survived by his wife Catherine, his sons Eric and Herbert (“Bert”), and his granddaughter Evelyn.
The department's "California Research Training Program in Computational and Applied Mathematics" proposal to the National Science Foundation (NSF) was ranked at the top of 35 mathematical sciences workforce proposals and funded at the level of $2 million over five years. UCLA applied math professor Andrea Bertozzi leads the program with fellow applied math faculty Stanley Osher, Luminita Vese and Joseph Teran to engage California math undergraduates and master's students in summer research on topics such as crime modeling, fluid dynamics experiments and modeling, robotics and control, medical imaging, cancer stem cells, bone growth, remote sensing applications, alcohol biosensors, photovoltaic cells, and algorithm design for microscopy. The program, which is a state-wide expansion of the department's successful applied math summer research program, involves cross-disciplinary collaboration with UCLA and partnering California university faculty in medicine, anthropology, engineering, chemistry, and other fields. The new award also includes a training program for postdocs and junior faculty to learn how to involve pre-PhD students in publication-level research, and supports training of some PhD students in both research and mentoring.
Professor Greg Hjorth died of a heart attack in his birth city of Melbourne, Australia, on Jan. 13. He was 47. Hjorth was recognized as a young chess whiz in his primary school years. He quickly advanced to tournament chess, becoming joint Commonwealth Champion in 1983 and earning his International Master title in 1984. He played Garry Kasparov, among other accomplished chess rivals, but took his own later advice that “if you’re not in the top 100 by 21, get out.” Hjorth’s passion for chess played over to mathematical logic, a field that saw him reach great heights with high academic honors and wide recognition. After receiving his undergraduate degree in mathematics and philosophy at the University of Melbourne, Hjorth continued his studies at UC Berkeley, where he received his PhD in mathematics under the supervision of Hugh Woodin in 1993. As a graduate student, Hjorth was recognized for his exceptional talent, and his brilliant thesis was awarded the first Sacks Prize in 1994 by the Association for Symbolic Logic for his research in descriptive set theory and its surprising consequences concerning the relationship between projective sets and large cardinals. Hjorth pursued his postdoctoral studies at Caltech for two years then joined the mathematics faculty at UCLA in 1995, where he was made full professor in 2001. Since 2006, he spent two quarters of each year at the University of Melbourne appointed to a prestigious Australian Research Council professorial fellowship. Over his 16 years at UCLA, Hjorth has been acknowledged as a world leader in the field of mathematical logic and its applications to other fields of mathematics. He has made a series of stunning and far reaching contributions, in particular to ergodic theory and orbit equivalence of group actions. These included the development of entirely new theories, including what is now called Hjorth’s theory of turbulence, which has had a major impact in contemporary work in set theory and its applications. Hjorth was known as a brilliant problem solver, having been able to achieve major breakthroughs in problems that were previously considered intractable, including his remarkable work on the famous topological Vaught Conjecture and most recently, his results on the incomparability of treeable equivalence relations. His work consistently amazed his colleagues with its uncanny originality and technical wizardry and has been recognized by many honors, including a Sloan Foundation Fellowship in 1997, an invited lecture at the International Congress of Mathematicians in 1998, the ASL Karp Prize in 2003 (joint with Alexander Kechris), and last year, an invitation to deliver one of the major lecture series in logic, the Alfred Tarski Lectures at UC Berkeley. Hjorth supervised eight PhD students at UCLA, including 2008 UCLA Math PhD Inessa Epstein, who also received the prestigious Sacks prize. Hjorth will be richly remembered by fellow colleagues as a brilliant mathematician in constant pursuit of solutions to intractable problems, and as a committed and caring teacher. He is survived by his parents Noela and Robert, and his sister Larissa.
UCLA Mathematics Professor Chandrashekhar Khare and his collaborator Jean-Pierre Wintenberger were awarded the 2011 Frank Nelson Cole Prize in Number Theory by the American Mathematical Society (AMS) for their remarkable proof of Serre's modularity conjecture. The conjecture was first proposed in 1973 by Fields Medalist Jean-Pierre Serre and has had an important impact in number theory. In the mid-1980s, Gerhard Frey and Serre realized that the conjecture implies Fermat's Last Theorem, the landmark problem that was solved by Andrew Wiles in the 1990s. Wiles used ideas relating to Serre's conjecture to prove the theorem, but at that time the conjecture seemed out of reach. In 2004 Khare and Wintenberger astonished the mathematical community when they found an extremely beautiful strategy to attack Serre's conjecture. The Cole prize was founded in 1931 in honor of Professor Cole. It is the most eminent prize in number theory and is awarded every three years.
UCLA Mathematics collaborative research that uses sophisticated mathematics in predictive policing made The New York Times Magazine 10th Annual Year in Ideas and DISCOVER Magazine Top 100 Stories of 2010. Two different models were developed by UCLA mathematicians and statisticians in conjunction with anthropologists and criminologists. Work by former UCLA Math postdoc George Mohler (Santa Clara University), UCLA Math Assistant Adjunct Professor Martin Short, UCLA anthropologist Jeffrey Brantingham, UCLA Statistics Associate Professor Frederic Schoenberg and criminologist George Tita (UC Irvine) on self-exciting point process models was included in The Times’ selection of ingenuity and innovation. Joint work by UCLA Math Professor Andrea Bertozzi, Short and Brantingham that applies bifurcation theory to crime hot spot models was number 60 (Fighting Crime with Mathematics) on the DISCOVER top stories list.
Professor Emeritus Lowell J. Paige died on his birthday in Carmichael, Calif., on Dec. 10. He was 91. Paige served as a lieutenant in the U.S. Naval Reserve during World War II from 1942 to 1946. He received his PhD in mathematics in 1947 at the University of Wisconsin-Madison under the supervision of Richard Hubert Bruck. Paige’s research interest was abstract algebra. In 1947 Paige joined the faculty of the UCLA mathematics department, where he served as chair from 1964 to 1968. At that time, the Mathematical Sciences Building was being built. Paige added the 5th floor Mathematics Department Reading Room to the building plans and rescued the book collection from the old Institute for Numerical Analysis to establish the reading room.Paige launched his university leadership career with his election as vice-chairman of the Academic Senate in 1966, then chairman in 1968.
He served as the dean of the Division of Physical Sciences in the College of Letters and Science from 1968 to 1973. Paige was appointed by President Richard Nixon to be assistant director of the National Science Foundation in 1973, a position he held for two years before returning to the University of California in 1975 to become special assistant for governmental relations to the president of the UC. Paige retired from UCLA in 1983. From 1983 to1987, he was Gov. George Deukmejian’s assistant adviser for higher education. In 1987 he was appointed to a six-year term on the California Postsecondary Education Commission. During his academic career, Paige spent a year at the Institute for Advanced Study and a year at Yale University, and held a special Fulbright Award in Australia. Paige published Elements of Linear Algebra in 1961 and a second edition in 1974 with J. Dean Swift. Paige is survived by his wife Betty, sons Michael and Steve, and niece Judy Monaco.
The Infosys Science Foundation named UCLA Mathematics Professor Chandrashekhar Khare the winner of the Infosys Prize 2010 in mathematical sciences. The prize recognizes outstanding contributions to scientific research that have impacted India across five categories: mathematical sciences, physical sciences, engineering and computer science, life sciences and social sciences. Established in February 2009, the annual prize is one of the largest in terms of prize money for any such honor in India and seeks to elevate the prestige of scientific research in India and to inspire young Indians to pursue a career in scientific research. The award ceremony will be held on January 6, 2011 in Mumbai, where Dr. Manmohan Singh, Prime Minister of India will present the awards to the winners.
UCLA Mathematics Professor Christoph Thiele is the recipient of a prestigious Humboldt Research Award granted in 2009 across scientific disciplines. The Humboldt Research Award honors a scholar’s scientific work to date, which is recognized as having significant impact on the scholar’s discipline. Named after Prussian scientist and explorer Alexander von Humboldt, the Humboldt Foundation promotes academic cooperation between exceptional scientists and scholars from Germany and abroad. Thiele works in harmonic analysis and is a leading expert on modulation invariant singular integral theory. He will use the award to support a research year at the University of Bonn in Germany.