Craig Huneke

Last updated
Craig Huneke
Craig Huneke.jpg
Born27 August 1951 (1951-08-27) (age 72)
NationalityAmerican
Alma mater Oberlin College, and Yale University
Scientific career
Institutions University of Purdue, and University of Virginia
Doctoral advisor Nathan Jacobson and David Eisenbud

Craig Lee Huneke (born August 27, 1951) is an American mathematician specializing in commutative algebra. He is a professor at the University of Virginia.

Contents

Huneke graduated from Oberlin College with a bachelor's degree in 1973 and in 1978 earned a Ph.D. from the Yale University under Nathan Jacobson and David Eisenbud (Determinantal ideal and questions related to factoriality). [1] As a post-doctoral fellow, he was at the University of Michigan. In 1979 he became an assistant professor and was at the Massachusetts Institute of Technology and the University of Bonn (1980). In 1981 he became an assistant professor at Purdue University, where in 1984 he became an associate professor and became a professor in 1987. From 1994 to 1995 he was a visiting professor at the University of Michigan and in 1999 was at the Max Planck Institute for Mathematics in Bonn (as a Fulbright Scholar). In 1999, he was Henry J. Bischoff professor at the University of Kansas. In 2002 he was at MSRI. Since 2012 he has been Marvin Rosenblum professor at the University of Virginia.

With Melvin Hochster and others, he developed the theory of tight closure, a device in ring theory that is used to study rings containing a field of characteristic p in which Frobenius endomorphism figures prominently. He also studies linkage theory, Rees algebras, homological theory of modules over Noetherian rings, local cohomology, symbolic powers of ideals, Cohen-Macaulay rings, Gorenstein rings and Hilbert-Kunz functions.

He was an invited speaker at the International Congress of Mathematicians in 1990 in Kyoto (Absolute Integral Closure and Big Cohen-Macaulay Algebras). He is a fellow of the American Mathematical Society. [2]

Huneke's son is historian Samuel Clowes Huneke. [3]

Writings

Related Research Articles

In commutative algebra, the Krull dimension of a commutative ring R, named after Wolfgang Krull, is the supremum of the lengths of all chains of prime ideals. The Krull dimension need not be finite even for a Noetherian ring. More generally the Krull dimension can be defined for modules over possibly non-commutative rings as the deviation of the poset of submodules.

In mathematics, a Cohen–Macaulay ring is a commutative ring with some of the algebro-geometric properties of a smooth variety, such as local equidimensionality. Under mild assumptions, a local ring is Cohen–Macaulay exactly when it is a finitely generated free module over a regular local subring. Cohen–Macaulay rings play a central role in commutative algebra: they form a very broad class, and yet they are well understood in many ways.

In commutative algebra, a Gorenstein local ring is a commutative Noetherian local ring R with finite injective dimension as an R-module. There are many equivalent conditions, some of them listed below, often saying that a Gorenstein ring is self-dual in some sense.

In mathematics, ideal theory is the theory of ideals in commutative rings. While the notion of an ideal exists also for non-commutative rings, a much more substantial theory exists only for commutative rings

<span class="mw-page-title-main">Melvin Hochster</span> American mathematician (born 1943)

Melvin Hochster is an American mathematician working in commutative algebra. He is currently the Jack E. McLaughlin Distinguished University Professor Emeritus of Mathematics at the University of Michigan.

<span class="mw-page-title-main">David Eisenbud</span> American mathematician

David Eisenbud is an American mathematician. He is a professor of mathematics at the University of California, Berkeley and former director of the then Mathematical Sciences Research Institute (MSRI), now known as Simons Laufer Mathematical Sciences Institute (SLMath). He served as Director of MSRI from 1997 to 2007, and then again from 2013 to 2022.

In mathematics, in the area of commutative algebra, tight closure is an operation defined on ideals in positive characteristic. It was introduced by Melvin Hochster and Craig Huneke.

In commutative algebra, an element b of a commutative ring B is said to be integral over a subring A of B if b is a root of some monic polynomial over A.

In mathematics, a commutative ring R is catenary if for any pair of prime ideals p, q, any two strictly increasing chains

Irvin Sol Cohen was an American mathematician at the Massachusetts Institute of Technology who worked on local rings. He was a student of Oscar Zariski at Johns Hopkins University.

Combinatorial commutative algebra is a relatively new, rapidly developing mathematical discipline. As the name implies, it lies at the intersection of two more established fields, commutative algebra and combinatorics, and frequently uses methods of one to address problems arising in the other. Less obviously, polyhedral geometry plays a significant role.

In commutative algebra, an integrally closed domainA is an integral domain whose integral closure in its field of fractions is A itself. Spelled out, this means that if x is an element of the field of fractions of A that is a root of a monic polynomial with coefficients in A, then x is itself an element of A. Many well-studied domains are integrally closed, as shown by the following chain of class inclusions:

In commutative algebra, the Rees algebra of an ideal I in a commutative ring R is defined to be

This is a glossary of commutative algebra.

In algebra, the integral closure of an ideal I of a commutative ring R, denoted by , is the set of all elements r in R that are integral over I: there exist such that

Karen Ellen Smith is an American mathematician, specializing in commutative algebra and algebraic geometry. She completed her bachelor's degree in mathematics at Princeton University before earning her PhD in mathematics at the University of Michigan in 1993. Currently she is the Keeler Professor of Mathematics at the University of Michigan. In addition to being a researcher in algebraic geometry and commutative algebra, Smith with others wrote the textbook An Invitation to Algebraic Geometry.

In algebra, the Hilbert–Kunz function of a local ring (R, m) of prime characteristic p is the function

In algebra and algebraic geometry, given a commutative Noetherian ring and an ideal in it, the n-th symbolic power of is the ideal

In algebra, specifically in the theory of commutative rings, a quasi-unmixed ring is a Noetherian ring such that for each prime ideal p, the completion of the localization Ap is equidimensional, i.e. for each minimal prime ideal q in the completion , = the Krull dimension of Ap.

<span class="mw-page-title-main">Frank-Olaf Schreyer</span>

Frank-Olaf Schreyer is a German mathematician, specializing in algebraic geometry and algorithmic algebraic geometry.

References

  1. ↑ Mathematics Genealogy Project
  2. ↑ List of Fellows of the American Mathematical Society, retrieved 2013-11-24.
  3. ↑ Huneke, Samuel Clowes (2022). States of Liberation: Gay Men between Dictatorship and Democracy in Cold War Germany. University of Toronto Press. p. xiii. ISBN   978-1-4875-4213-9.
This page is based on this Wikipedia article
Text is available under the CC BY-SA 4.0 license; additional terms may apply.
Images, videos and audio are available under their respective licenses.