Answer the following question: Information: - The colonial colleges are nine institutions of higher education chartered in the American Colonies before the United States of America became a sovereign nation after the American Revolution. These nine have long been considered together, notably in the survey of their origins in the 1907 "The Cambridge History of English and American Literature". Seven of the nine colonial colleges are part of the Ivy League athletic conference: Harvard, Yale, Penn, Princeton, Columbia, Brown, and Dartmouth. (The eighth member of the Ivy League, Cornell University, was founded in 1865.) - The University of Pennsylvania (commonly known as Penn or UPenn) is a private, Ivy League university located in Philadelphia, Pennsylvania, United States. Incorporated as "The Trustees of the University of Pennsylvania", Penn is one of 14 founding members of the Association of American Universities and one of the nine original colonial colleges. - In mathematics, a polynomial is an expression consisting of variables (or indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents. An example of a polynomial of a single indeterminate is . An example in three variables is . - In mathematics and abstract algebra, group theory studies the algebraic structures known as groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as rings, fields, and vector spaces, can all be seen as groups endowed with additional operations and axioms. Groups recur throughout mathematics, and the methods of group theory have influenced many parts of algebra. Linear algebraic groups and Lie groups are two branches of group theory that have experienced advances and have become subject areas in their own right. - In mathematics, more specifically in abstract algebra, Galois theory, named after Evariste Galois, provides a connection between field theory and group theory. Using Galois theory, certain problems in field theory can be reduced to group theory, which is, in some sense, simpler and better understood. - A mathematical problem is a problem that is amenable to being represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems.<br> It can also be a problem referring to the nature of mathematics itself, such as Russell's Paradox. - Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings. Both algebraic geometry and algebraic number theory build on commutative algebra. Prominent examples of commutative rings include polynomial rings, rings of algebraic integers, including the ordinary integers formula_1, and "p"-adic integers. - 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 problems about these sets of zeros. - Mathematics (from Greek "mathma", knowledge, study, learning) is the study of topics such as quantity (numbers), structure, space, and change. There is a range of views among mathematicians and philosophers as to the exact scope and definition of mathematics. - David Harbater ( born December 19 , 1952 ) is an American mathematician at the University of Pennsylvania , well known for his work in Galois theory , algebraic geometry and arithmetic geometry . - In algebra, which is a broad division of mathematics, abstract algebra (occasionally called modern algebra) is the study of algebraic structures. Algebraic structures include groups, rings, fields, modules, vector spaces, lattices, and algebras. The term "abstract algebra" was coined in the early 20th century to distinguish this area of study from the other parts of algebra. - The Association of American Universities (AAU) is an international organization of leading research universities devoted to maintaining a strong system of academic research and education. It consists of 60 universities in the United States (both public and private) and two universities in Canada. - A mathematician is someone who uses an extensive knowledge of mathematics in his/her work, typically to solve mathematical problems. - Evariste Galois (25 October 1811 31 May 1832) was a French mathematician born in Bourg-la-Reine. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem standing for 350 years. His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra, and the subfield of Galois connections. He died at age 20 from wounds suffered in a duel. - The Ivy League is a collegiate athletic conference comprising sports teams from eight private institutions of higher education in the Northeastern United States. The conference name is also commonly used to refer to those eight schools as a group beyond the sports context. The eight institutions are Brown University, Columbia University, Cornell University, Dartmouth College, Harvard University, the University of Pennsylvania, Princeton University, and Yale University. The term "Ivy League" has connotations of academic excellence, selectivity in admissions, and social elitism. Given the information above, choose from the list below the object entity that exhibits the relation 'field of work' with the subject 'david harbater'. Choices: - algebra - commutative algebra - education - french - geometry - group theory - history - literature - mathematician - mathematics - nature - number theory - research
Answer:
group theory