What is he best known for?
The fields of study he is best known for:
- Algebra
- Pure mathematics
- Topology
The scientist’s investigation covers issues in Discrete mathematics, Pure mathematics, Tight closure, Combinatorics and Algebra.
Much of his study explores Discrete mathematics relationship to Prime characteristic.
His Pure mathematics research includes elements of Von Neumann regular ring, Ring, Noetherian and Ideal.
His research investigates the connection between Tight closure and topics such as Regular ring that intersect with issues in Base change.
His Combinatorics study combines topics from a wide range of disciplines, such as Cup product, De Rham cohomology, Cohomology and Graded ring.
His Local ring study combines topics in areas such as Commutative algebra and Noncommutative ring.
His most cited work include:
- Prime ideal structure in commutative rings (547 citations)
- Tight closure, invariant theory, and the Briançon-Skoda theorem (537 citations)
- Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes (477 citations)
What are the main themes of his work throughout his whole career to date?
His primary scientific interests are in Pure mathematics, Discrete mathematics, Combinatorics, Ideal and Local ring.
His study in Pure mathematics is interdisciplinary in nature, drawing from both Von Neumann regular ring, Commutative ring and Local cohomology.
While the research belongs to areas of Local cohomology, Melvin Hochster spends his time largely on the problem of Group cohomology, intersecting his research to questions surrounding Čech cohomology, De Rham cohomology, Graded ring and Cup product.
He is involved in the study of Discrete mathematics that focuses on Zariski topology in particular.
His Combinatorics research includes themes of Subring and Field.
His Ideal study integrates concerns from other disciplines, such as Ring, Noetherian, Polynomial ring and Domain.
He most often published in these fields:
- Pure mathematics (52.48%)
- Discrete mathematics (34.65%)
- Combinatorics (25.74%)
What were the highlights of his more recent work (between 2014-2021)?
- Pure mathematics (52.48%)
- Combinatorics (25.74%)
- Polynomial ring (17.82%)
In recent papers he was focusing on the following fields of study:
Pure mathematics, Combinatorics, Polynomial ring, Ideal and Local cohomology are his primary areas of study.
In the field of Pure mathematics, his study on Conjecture overlaps with subjects such as In degree.
His Combinatorics research incorporates themes from Field and Algebra.
His Polynomial ring research integrates issues from Regular sequence and Degree.
His research integrates issues of Characterization, Discrete mathematics and Tight closure in his study of Local cohomology.
His Dimension research is multidisciplinary, relying on both Noetherian, Image and Local ring.
Between 2014 and 2021, his most popular works were:
- Small Subalgebras of Polynomial Rings and Stillman's Conjecture (20 citations)
- Small subalgebras of polynomial rings and Stillman’s Conjecture (17 citations)
- Homological Conjectures and Lim Cohen-Macaulay Sequences (8 citations)
In his most recent research, the most cited papers focused on:
- Algebra
- Pure mathematics
- Topology
Melvin Hochster mainly focuses on Pure mathematics, Local cohomology, Ring, Polynomial ring and Ideal.
His studies deal with areas such as Ring theory and Sequence as well as Pure mathematics.
His research in Local cohomology intersects with topics in Discrete mathematics, Tight closure and Perfectoid.
The various areas that Melvin Hochster examines in his Ring study include Degree, Algebraically closed field, Regular sequence, Combinatorics and Bounded function.
His work carried out in the field of Combinatorics brings together such families of science as Noetherian, Image and Maximal ideal.
As part of his studies on Polynomial ring, Melvin Hochster frequently links adjacent subjects like Primary decomposition.
This overview was generated by a machine learning system which analysed the scientist’s
body of work. If you have any feedback, you can
contact us
here.
