This biography, written by J J O’Connor and E F Robertson, has been republished with permission from the School of Mathematics and Statistics at the University of St Andrews, Scotland.
Born: 13 August 1965, United Kingdom
Died: NA
Country most active: United Kingdom, United States
Also known as: NA
Katherine Okikiolu is widely known as Kate Okikiolu. Her parents are George Olatokunbo Okikiolu and Patricia Natasha Edwards. George Okikiolu is a Nigerian who came to England to study for an undergraduate degree in mathematics in 1959. He studied at the Sir John Cass College in London where he met the English girl Patricia Edwards who was studying mathematics and physics. Patricia was:-
… from a family with a trade-union background and a central interest in class struggle.
George and Patricia Okikiolu were married on 19 September 1962 and had two daughters, the first was Jeannie Adetokunbo Okikiolu who went on to study mathematics at the University of Cambridge and was awarded an MA. She then trained as a chartered accountant before working as a forensic accountant. George and Patricia Okikiolu’s second daughter was Katherine Adebola Okikiolu, the subject of this biography, who was born shortly before George Okikiolu took up an appointment as an assistant lecturer in mathematics at the University of Sussex. After one year the family moved to Norwich when George Okikiolu was appointed to the University of East Anglia in Norwich, Sussex. In Norwich they lived at 23 Mile End Road. Kate Okikiolu writes:-
My father … went on to a position in the mathematics department of the University of East Anglia. While I was growing up, the elementary school I attended was extremely ethnically homogeneous. I was unable to escape from heavy issues concerning race, which my mother always explained in a political context.
By 1974, unhappy that he was not being promoted to a professorship despite having published around 30 papers in the ten years 1965-74, George Okikiolu decided to resign his university appointment and concentrate on his inventions. At this point George and Patricia Okikiolu separated and from this time Kate Okikiolu was brought up by her mother:-
My parents separated after my father resigned his university position to focus on his inventions, and my mother then finished her education and became a school mathematics teacher. We moved to a very cosmopolitan area of London, which was like a new birth for me; it was there that my interest in mathematics really began.
At high school Okikiolu developed an interest in mathematics and in art. She was also an outstanding athlete and she won the high school long jump championship for her school in 1985, the year she graduated from the high school. She explains how she came to study mathematics at university rather than art:-
I learned mathematics on my own from textbooks which is perhaps strange given that both my parents were involved in the subject. At the same time, I spent a good deal of time studying art and wanted to follow a career in that direction until I was eventually convinced by my family that I should first work for a mathematics degree to ensure that I could earn a living.
Okikiolu matriculated at Newnham College, University of Cambridge, in 1985. This College is a women’s college, founded in 1871. She writes:-
I went to Cambridge, which represented a second major change in my life. As I learned more mathematics, I saw that it is an entire world of its own which many people choose to live in, a world in many ways more real than the real world; it feels permanent, eternal, and offers a deep sense of security because nearly everyone who understands it agrees on what is truth. By the time I had finished at Cambridge, I was very involved with mathematics and did not consider other careers.
In 1987 Okikiolu graduated with a B.A. in mathematics from the University of Cambridge and she went to the United States to undertake research for a doctorate. She undertook research at the University of California, Los Angeles advised by Sun-Yung Alice Chang and John Brady Garnett. John Garnett (born 1940) had been awarded a Ph.D. by the University of Washington in 1966, appointed an assistant professor at the University of California, Los Angeles in 1968, becoming a full professor there in 1974. Okikiolu was awarded a Ph.D. in 1991 for her thesis The Analogue of the Strong Szego Limit Theorem on the Torus and the 3-Sphere. There is minor inconsistency in the information about Okikiolu’s advisors. All biographies which give her advisors state they are Sun-Yung Alice Chang and John Brady Garnett. Certainly John Garnett advised Okikiolu for in her first publication, the 1992 paper Characterization of subsets of rectifiable curves in Rnmathbb{R}^{n}Rn, she writes:-
I would like to thank John Garnett for a lot of very helpful advice.
The inconsistency occurs in the ProQuest LLC listing of her thesis where her advisors are given as Joseph Rudnik and Alice Chang. Joseph Rudnik is in the Department of Physics and Astronomy at the University of California, Los Angeles, and gives his research interests as follows:-
I do research on a variety of problems in condensed matter physics. My primary interests are in the general field of statistical mechanics.
We suggest that Joseph Rudnik may have been an examiner of the thesis rather than a thesis advisor but we hope a reader of this biography will be able to clarify this.
Let us return to the 1992 paper we mentioned above. In this paper Okikiolu solved a conjecture of Peter Wilcox Jones on the continuous [sometimes called the ‘analyst’s’] version of the ‘travelling salesman problem’ which, in its traditional form, seeks to minimise the route visiting each member of a finite set of cities. Peter Jones of Yale University writes:-
My work in geometric measure theory has centred on results in quantitative rectifiability. I proved [in 1990] that in the plane one can give a geometric multi-scale condition for solving the analyst’s travelling salesman problem: When is a set contained in a curve (connected set) of finite length? One half of that proof works in any dimension; the other half was later [in 1992] proven in all dimensions by Kate Okikiolu.
Okikiolu was an instructor and later assistant professor at Princeton University from 1993 to 1995. Part of this time, from September 1993 to June 1994, she spent at the Institute for Advanced Studies at Princeton. While at Princeton she met the mathematician Hans Lindbad and they were married. She published two further papers while at Princeton, namely The Campbell-Hausdorff theorem for elliptic operators and a related trace formula (1995) and The multiplicative anomaly for determinants of elliptic operators (1995). A third paper, The analogue of the strong SzegQ limit theorem on the 2- and 3-dimensional spheres, published in 1996 also contains results she obtained while at Princeton.
She then worked as a visiting assistant professor at the Massachusetts Institute of Technology from 1995 to 1997 where she began a collaboration with Victor William Guillemin. He had received a B.A. from Harvard in 1959, an M.A. from the University of Chicago in 1960, and a Ph.D. from Harvard in 1962.After working as an instructor at Columbia University, he was appointed to the Massachusetts Institute of Technology in 1966, being promoted to professor in 1973. By the time Okikiolu was appointed to the Massachusetts Institute of Technology, Guillemin was the Norbert Wiener Professor of Mathematics. His research interests are in differential geometry and symplectic geometry. Okikiolu and Guillemin published the three joint papers, Szegő theorems for Zoll operators (1996), Spectral asymptotics of Toeplitz operators on Zoll manifolds (1997), and Subprincipal terms in Szegő estimates (1997).
Okikiolu explains the type of mathematical problems she worked on:-
My research is in the field of spectral geometry, the study of how the shape of an object affects the modes in which it can resonate. A famous question in the field is, can one hear the shape of a drum? Spectral geometry bridges different branches of science, including engineering and physics, as well as a number of different fields of mathematics. However, quite different sorts of questions are studied within each discipline. I am a mathematical analyst, which gives me an appreciation for the infinite and the infinitesimal. At the moment, one of the things I am working on understanding is the total wavelength of a surface like a sphere or something of greater complexity, such as the surface of a bagel or a pretzel. What is this total wavelength? If you strike a surface it can resonate at any one of a list of frequencies, and the wavelength of the sound produced by the vibration is inversely proportional to the frequency. In the mathematically idealized model there are infinitely many possible wavelengths. The total wavelength should be the sum of all of these individual wavelengths except that this infinite sum equals infinity. Fortunately, a finite number can be assigned to it by a slightly elusive process called regularization. (This process is also used in mathematical physics to mysteriously obtain true answers from formulas which do not really make sense!) I first became interested in the total wavelength as a model related to a question which can be roughly stated as, can one hear the shape of the universe? However, the total wavelength shows up in many quite different areas of mathematics and I am finding these connections intriguing.
Okikiolu joined the faculty at the University of California at San Diego in 1997 where she became an associate professor. She received two major awards in 1997, the Sloan Research Fellowship and the Presidential Early Career Award for Scientists and Engineers for her project ‘Determinants of Elliptic and Toeplitz Operators with Applications to Geometry’. The project received $500,00 and ran from August 1997 to December 2006. The Abstract was as follows:-
The research supported in this award lies in the general area of geometric analysis. More specifically, the investigator is to study properties of the determinant of the Laplacian on closed compact Riemannian manifolds under all smooth perturbations in the metric which leave the total volume fixed. This may have implications for the Poincare conjecture. In addition, the investigator is to consider the wave operator on general negatively curved manifolds in connection with quantum chaos theory. This award is made under the Faculty Early Career Development (CAREER) program which funds projects that contain highly meritorious research coupled with a strong educational component. For example, the investigator of this award intends to run summer workshops for students introducing them to various current problems in geometric analysis using numerical methods. Also, she is to help develop inner-city K-12 mathematics and science curricula by producing a series of videos depicting model lessons for the inner-city classroom. The lessons will involve design and construction activities which lead directly to the study of mathematics, and incorporate elements from minority social cultures.
During the years that this project was running, Okikiolu spent two further periods at the Institute for Advanced Study, from September 2003 to December 2003 and from September 2008 to December 2008. She gave three talks at the University of Pennsylvania on 24 March 2005, 3 October 2006 and 14 March 2007. As well as giving her affiliation as the University of California at San Diego, it is also indicated that she is affiliated to the University of Pennsylvania. In 2002 she delivered the Claytor-Woodard lecture at the conference of the National Association of Mathematicians, an organization for African-American mathematicians.
In 2011 she joined the Mathematics Department at Johns Hopkins University. She gave this description in 2011 of her research which repeats some of the above quote but is worth giving in full:-
I am a mathematical analyst, and most of my research is in the area of spectral geometry. Problems in spectral geometry are also studied by various kinds of geometers, number theorists, applied mathematicians, mathematical physicists, and others. What is Spectral geometry? Spectral geometry most usually means the study of how the geometry of an object is related to the natural frequencies of the object. These are the frequencies at which the object can vibrate. A vibrating object often produces a sound, and the frequencies can be heard as the dominant tone and the overtones of the sound. The well known question highlighting what spectral geometry is all about is the question “Can one hear the shape of a drum?” I am a mathematical analyst, and most of my research is in the area of spectral geometry. Problems in spectral geometry are also studied by various kinds of geometers, number theorists, applied mathematicians, mathematical physicists, and others. In mathematical terms, the natural frequencies of an object (or rather their squares) are the eigenvalues of a partial differential operator called the Laplacian. This Laplacian takes each function defined on the object and differentiates it twice to give a new function. The eigenvalues of the Laplacian form an infinite sequence of numbers tending to infinity. In spectral geometry we study how these numbers depends on the shape of the object. For people who like to know the full story, I should mention that many spectral geometers (including me) who work on the Laplacian on smooth manifolds study the whole sequence of eigenvalues of the Laplacian. Now the low eigenvalues can give accurate values for the frequencies at which a real life object vibrates, but the very high eigenvalues do not correspond to genuine physical vibrations of the object because of molecular forces and damping. These effects are not included in the model where the vibration is driven by the Laplacian alone. This means that my research is rather different from that of an engineer who wishes to model precisely the vibrations of a real life object. In actual fact the questions I work on are more closely related to mathematics arising in quantum physics and string theory. In addition, I don’t always study the Laplacian, but also the eigenvalues of other operators, which might represent other physical quantities than the frequencies of vibration. I mostly study spectral geometry for nice smooth objects such as spheres and tori, but some people work on rough objects and even discrete objects like graphs. In the last eight years, I have worked mostly on the spectral zeta function, which is an infinite sum of powers of the eigenvalues. In particular, I have worked on the zeta-regularised determinant, which is used in topology, quantum field theory, and string theory. Recently, I have been very interested in the sum of squares of the wavelength of a surface, which is related to all kinds of different things including vortex theory.
By 2009 she had published 14 very high quality research papers, the 2009 paper being A negative mass theorem for surfaces of positive genus. At the time of writing this biography in 2019, we note that she has not published any further papers. Her husband Hans Lindbad is a member of the Mathematics Department at Johns Hopkins University but Okikiolu does not now appear in the staff lists. We end this biography with a quote from Okikiolu published in 2009:-
Although I cannot claim to find it easy to balance my ambitions in mathematical research with the desire to be a good parent, to be an inspiring teacher, or to effect positive social change in the world, I do feel very fortunate to be able to spend my life tackling these challenges, which are extremely interesting and important to me.