Kate Okikiolu

"My mother is British, from a family with a trade union background and a central interest in class struggle; she met my father, who is Nigerian, while both were students of mathematics in London. My father was a very talented mathematician, and after my parents married, he 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."

"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 to me; it was there that my interest in mathematics really began."

"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."

"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."

"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."

"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."

"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."