Cecil James Nesbitt, Ph.D., F.S.A., M.A.A.A. (1912–2001) was a mathematician who was a Ph.D. student of Richard Brauer and wrote many influential papers in the early history of modular representation theory.
Nesbitt taught actuarial mathematics at the University of Michigan from 1938 to 1980. Nesbitt was born in Ontario, Canada. He received his mathematical education at the University of Toronto and the Institute for Advanced Study in Princeton. He served the Society of Actuaries from 1985 to 1987 as Vice-President for Research and Studies. He developed the Schuette–Nesbitt formula with Donald R. Schuette.
An actuary is a professional with advanced mathematical skills who deals with the measurement and management of risk and uncertainty. The name of the corresponding field is actuarial science which covers rigorous mathematical calculations in areas of life expectancy and life insurance. These risks can affect both sides of the balance sheet and require asset management, liability management, and valuation skills. Actuaries provide assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms.
In representation theory and algebraic number theory, the Langlands program is a web of far-reaching and consequential conjectures about connections between number theory and geometry. Proposed by Robert Langlands, it seeks to relate Galois groups in algebraic number theory to automorphic forms and representation theory of algebraic groups over local fields and adeles. Widely seen as the single biggest project in modern mathematical research, the Langlands program has been described by Edward Frenkel as "a kind of grand unified theory of mathematics."
Actuarial science is the discipline that applies mathematical and statistical methods to assess risk in insurance, pension, finance, investment and other industries and professions. More generally, actuaries apply rigorous mathematics to model matters of uncertainty and life expectancy.
Emil Artin was an Austrian mathematician of Armenian descent.
In mathematics, a Galois module is a G-module, with G being the Galois group of some extension of fields. The term Galois representation is frequently used when the G-module is a vector space over a field or a free module over a ring in representation theory, but can also be used as a synonym for G-module. The study of Galois modules for extensions of local or global fields and their group cohomology is an important tool in number theory.
Richard Dagobert Brauer was a leading German and American mathematician. He worked mainly in abstract algebra, but made important contributions to number theory. He was the founder of modular representation theory.
Modular representation theory is a branch of mathematics, and is the part of representation theory that studies linear representations of finite groups over a field K of positive characteristic p, necessarily a prime number. As well as having applications to group theory, modular representations arise naturally in other branches of mathematics, such as algebraic geometry, coding theory, combinatorics and number theory.
In mathematics, an Artin L-function is a type of Dirichlet series associated to a linear representation ρ of a Galois group G. These functions were introduced in 1923 by Emil Artin, in connection with his research into class field theory. Their fundamental properties, in particular the Artin conjecture described below, have turned out to be resistant to easy proof. One of the aims of proposed non-abelian class field theory is to incorporate the complex-analytic nature of Artin L-functions into a larger framework, such as is provided by automorphic forms and the Langlands program. So far, only a small part of such a theory has been put on a firm basis.
In mathematics, the Brauer–Nesbitt theorem can refer to several different theorems proved by Richard Brauer and Cecil J. Nesbitt in the representation theory of finite groups.
In the business of insurance, statutory reserves are those assets an insurance company is legally required to maintain on its balance sheet with respect to the unmatured obligations of the company. Statutory reserves are a type of actuarial reserve.
James C. Hickman was an American actuary. He was internationally publicized for his work in actuarial education as well as being a major contribution in the development of the actuarial profession. He was a professor emeritus of business and statistics and former dean of the University of Wisconsin–Madison School of Business.
In mathematics, the Schuette–Nesbitt formula is a generalization of the inclusion–exclusion principle. It is named after Donald R. Schuette and Cecil J. Nesbitt.
Jonathan Lazare Alperin is an American mathematician specializing in the area of algebra known as group theory. He is notable for his work in group theory which has been cited over 500 times according to the Mathematical Reviews. The Alperin–Brauer–Gorenstein theorem is named after him.
In mathematics, a Loewy ring or semi-Artinian ring is a ring in which every non-zero module has a non-zero socle, or equivalently if the Loewy length of every module is defined. The concepts are named after Alfred Loewy.
In mathematics, the Artin conductor is a number or ideal associated to a character of a Galois group of a local or global field, introduced by Emil Artin as an expression appearing in the functional equation of an Artin L-function.
Robert Henderson was a Canadian-American mathematician and actuary.
Virginia Ruth Young is the Cecil J. and Ethel M. Nesbitt Professor of Actuarial Mathematics at the University of Michigan, and an expert on the mathematics of insurance.
Robert McDowell Thrall (1914–2006) was an American mathematician and a pioneer of operations research.
Marjorie L. Van Eenam Butcher (1925–2016) was an American mathematician, the first female faculty member in mathematics at the University of Michigan and the first female faculty member at Trinity College (Connecticut).
Andrei Vladimirovich Roiter was a Ukrainian mathematician, specializing in algebra.