John Stembridge is a Professor of

Mathematics Mathematics is a field of study that discovers and organizes methods, Mathematical theory, theories and theorems that are developed and Mathematical proof, proved for the needs of empirical sciences and mathematics itself. There are many ar ...

at the

University of Michigan The University of Michigan (U-M, U of M, or Michigan) is a public university, public research university in Ann Arbor, Michigan, United States. Founded in 1817, it is the oldest institution of higher education in the state. The University of Mi ...

. He received his Ph.D. from the

Massachusetts Institute of Technology The Massachusetts Institute of Technology (MIT) is a Private university, private research university in Cambridge, Massachusetts, United States. Established in 1861, MIT has played a significant role in the development of many areas of moder ...

in 1985 under the direction of Richard P. Stanley. His dissertation was entitled ''Combinatorial Decompositions of Characters of SL''(''n,C''). He has had 8 Ph.D. students. He is one of the participants in the Atlas of Lie Groups and Representations.

Research

His research interests are in

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

, with particular emphasis on the following areas: *Topics related to

algebra Algebra is a branch of mathematics that deals with abstract systems, known as algebraic structures, and the manipulation of expressions within those systems. It is a generalization of arithmetic that introduces variables and algebraic ope ...

, especially

representation theory Representation theory is a branch of mathematics that studies abstract algebra, abstract algebraic structures by ''representing'' their element (set theory), elements as linear transformations of vector spaces, and studies Module (mathematics), ...

Coxeter group In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors). Indeed, the finite Coxeter groups are precisely the finite Euclidean ref ...

s and

root system In mathematics, a root system is a configuration of vector space, vectors in a Euclidean space satisfying certain geometrical properties. The concept is fundamental in the theory of Lie groups and Lie algebras, especially the classification and ...

s *

Enumerative combinatorics Enumerative combinatorics is an area of combinatorics that deals with the number of ways that certain patterns can be formed. Two examples of this type of problem are counting combinations and counting permutations. More generally, given an inf ...

Symmetric function In mathematics, a function of n variables is symmetric if its value is the same no matter the order of its arguments. For example, a function f\left(x_1,x_2\right) of two arguments is a symmetric function if and only if f\left(x_1,x_2\right) = f\ ...

s *

Hypergeometric series In mathematics, the Gaussian or ordinary hypergeometric function 2''F''1(''a'',''b'';''c'';''z'') is a special function represented by the hypergeometric series, that includes many other special functions as specific or limiting cases. It is ...

and

q-series In the mathematical field of combinatorics, the ''q''-Pochhammer symbol, also called the ''q''-shifted factorial, is the product (a;q)_n = \prod_^ (1-aq^k)=(1-a)(1-aq)(1-aq^2)\cdots(1-aq^), with (a;q)_0 = 1. It is a ''q''-analog of the Pochhamme ...

*Computational problems and algorithms in algebra He was awarded a

Guggenheim Fellowship Guggenheim Fellowships are Grant (money), grants that have been awarded annually since by the John Simon Guggenheim Memorial Foundation, endowed by the late Simon Guggenheim, Simon and Olga Hirsh Guggenheim. These awards are bestowed upon indiv ...

in 2000 for work in ''Combinatorial aspects of root systems and Weyl characters.''. He has written Maple packages that can be used for computing

symmetric function In mathematics, a function of n variables is symmetric if its value is the same no matter the order of its arguments. For example, a function f\left(x_1,x_2\right) of two arguments is a symmetric function if and only if f\left(x_1,x_2\right) = f\ ...

poset In mathematics, especially order theory, a partial order on a Set (mathematics), set is an arrangement such that, for certain pairs of elements, one precedes the other. The word ''partial'' is used to indicate that not every pair of elements need ...

s, and

finite Coxeter group In mathematics, a Coxeter group, named after H. S. M. Coxeter, is an abstract group that admits a formal description in terms of reflections (or kaleidoscopic mirrors). Indeed, the finite Coxeter groups are precisely the finite Euclidean refl ...

References

Living people Year of birth missing (living people) 20th-century American mathematicians 21st-century American mathematicians Massachusetts Institute of Technology School of Science alumni University of Michigan faculty {{authority control