Burt James Totaro, FRS (b. 1967), is an American

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

, currently a professor at the

University of California, Los Angeles The University of California, Los Angeles (UCLA) is a public land-grant research university in Los Angeles, California. UCLA's academic roots were established in 1881 as a teachers college then known as the southern branch of the California St ...

, specializing in

algebraic geometry Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials. Modern algebraic geometry is based on the use of abstract algebraic techniques, mainly from commutative algebra, for solving geometrical ...

and

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

Education and early life

Totaro participated in the

Study of Mathematically Precocious Youth The Study of Mathematically Precocious Youth (SMPY) is a prospective longitudinal survey study of persons (mostly in the United States) identified by scores of 700 or higher on a section of the SAT Reasoning Test before age 13 years. It is one of th ...

while in grade school and enrolled at

Princeton University Princeton University is a private university, private research university in Princeton, New Jersey. Founded in 1746 in Elizabeth, New Jersey, Elizabeth as the College of New Jersey, Princeton is the List of Colonial Colleges, fourth-oldest ins ...

at the age of thirteen, becoming the youngest freshman in its history. He scored a perfect 800 on the math portion and a 690 on the verbal portion of the

SAT-I The SAT ( ) is a standardized test widely used for college admissions in the United States. Since its debut in 1926, its name and scoring have changed several times; originally called the Scholastic Aptitude Test, it was later called the Schol ...

exam at the age of 12. He graduated in 1984 and went on to graduate school at the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California) is a public land-grant research university in Berkeley, California. Established in 1868 as the University of California, it is the state's first land-grant u ...

, receiving his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is a ...

in 1989.

Career and research

Since 2009, he has been one of three managing editors of the journal ''

Compositio Mathematica ''Compositio Mathematica'' is a monthly peer-reviewed mathematics journal established by L.E.J. Brouwer in 1935. It is owned by the Foundation Compositio Mathematica, and since 2004 it has been published on behalf of the Foundation by the London M ...

''; he is also on the editorial boards of Forum of Mathematics, Pi and Sigma, the

Journal of the American Mathematical Society The ''Journal of the American Mathematical Society'' (''JAMS''), is a quarterly peer-reviewed mathematical journal published by the American Mathematical Society. It was established in January 1988. Abstracting and indexing This journal is abstr ...

, and the

Bulletin of the American Mathematical Society The ''Bulletin of the American Mathematical Society'' is a quarterly mathematical journal published by the American Mathematical Society. Scope It publishes surveys on contemporary research topics, written at a level accessible to non-experts. I ...

. In 2012, he became a Professor in the UCLA Department of Mathematics. Totaro's work is influenced by the

Hodge conjecture In mathematics, the Hodge conjecture is a major unsolved problem in algebraic geometry and complex geometry that relates the algebraic topology of a non-singular complex algebraic variety to its subvarieties. In simple terms, the Hodge conjectur ...

, and is based on the connections and application of topology to algebraic geometry. His work has applications in a number of diverse areas of mathematics, from

representation theory Representation theory is a branch of mathematics that studies abstract algebraic structures by ''representing'' their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures. In essen ...

Lie theory In mathematics, the mathematician Sophus Lie ( ) initiated lines of study involving integration of differential equations, transformation groups, and contact of spheres that have come to be called Lie theory. For instance, the latter subject is L ...

and

group cohomology In mathematics (more specifically, in homological algebra), group cohomology is a set of mathematical tools used to study groups using cohomology theory, a technique from algebraic topology. Analogous to group representations, group cohomology loo ...

Selected works

* *

Recognition

In 2000, he was elected

Lowndean Professor of Astronomy and Geometry The Lowndean chair of Astronomy and Geometry is one of the two major Professorships in Astronomy (alongside the Plumian Professorship) and a major Professorship in Mathematics at Cambridge University. It was founded in 1749 by Thomas Lowndes, an ...

at the

University of Cambridge , mottoeng = Literal: From here, light and sacred draughts. Non literal: From this place, we gain enlightenment and precious knowledge. , established = , other_name = The Chancellor, Masters and Schola ...

. In the same year, he was awarded the

Whitehead Prize The Whitehead Prize is awarded yearly by the London Mathematical Society to multiple mathematicians working in the United Kingdom who are at an early stage of their career. The prize is named in memory of homotopy theory pioneer J. H. C. Whiteh ...

by the

London Mathematical Society The London Mathematical Society (LMS) is one of the United Kingdom's learned societies for mathematics (the others being the Royal Statistical Society (RSS), the Institute of Mathematics and its Applications (IMA), the Edinburgh Mathematical S ...

. In 2009, Totaro was elected

Fellow of the Royal Society Fellowship of the Royal Society (FRS, ForMemRS and HonFRS) is an award granted by the judges of the Royal Society of London to individuals who have made a "substantial contribution to the improvement of natural science, natural knowledge, incl ...

. He was included in the 2019 class of fellows of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

"for contributions to algebraic geometry, Lie theory and cohomology and their connections and for service to the profession".

References

20th-century American mathematicians 21st-century American mathematicians Algebraic geometers Fellows of the Royal Society Fellows of the American Mathematical Society Whitehead Prize winners University of California, Los Angeles faculty Cambridge mathematicians Lowndean Professors of Astronomy and Geometry Princeton University alumni University of California, Berkeley alumni Living people 1967 births Topologists {{US-mathematician-stub