World's Best Scientists 2026 revealed!

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Mathematics

D-Index
38
Citations
8504
World Ranking
2294
National Ranking
970

Research.com Recognitions

  • 1992 - Fellow of the American Academy of Arts and Sciences
  • 1992 - Member of the National Academy of Sciences
  • 1981 - Fellow of John Simon Guggenheim Memorial Foundation
  • 1980 - Frank Nelson Cole Prize in Algebra

Overview

Melvin Hochster is affiliated with the University of Michigan-Ann Arbor, located in the United States. Their research primarily falls within the broad field of Mathematics, encompassing 39 publications. The scientist's work spans several subfields, including Algebra and Number Theory, Geometry and Topology, Computational Theory and Mathematics, Mathematical Physics, and Discrete Mathematics and Combinatorics.

The main topics covered in their research include:

  • Algebraic Geometry and Number Theory
  • Algebraic structures and combinatorial models
  • Commutative Algebra and Its Applications
  • Rings, Modules, and Algebras
  • Advanced Topics in Algebra
  • Polynomial and algebraic computation
  • Advanced Algebra and Geometry

Among recent publications authored by Melvin Hochster are the following papers:

  • "The F-rational signature and drops in the Hilbert-Kunz multiplicity," 2022, Algebra & Number Theory
  • "When are the natural embeddings of classical invariant rings pure?," 2023, Forum of Mathematics Sigma
  • "A Jacobian criterion for nonsingularity in mixed characteristic," 2021, arXiv (Cornell University)
  • "Extensions of primes, flatness, and intersection flatness," 2021, Contemporary mathematics - American Mathematical Society
  • "The Eisenbud-Green-Harris conjecture for defect two quadratic ideals," 2020, Mathematical Research Letters

Frequent collaborators of this scientist include Jack Jeffries, Yongwei Yao, Tigran Ananyan, Vaibhav Pandey, and Anurag K. Singh. These coauthors have contributed to multiple joint works, with Jack Jeffries being a collaborator on six publications.

Melvin Hochster has published extensively in several venues that appear frequently in their publication record, including:

  • arXiv (Cornell University)
  • Transactions of the American Mathematical Society
  • Mathematical Research Letters
  • Journal of Algebra
  • Algebra & Number Theory

The scientist has been recognized by several awards and honors, such as:

  • Member of the National Academy of Sciences (1992)
  • Fellow of the American Academy of Arts and Sciences (1992)
  • Fellow of John Simon Guggenheim Memorial Foundation (1981)
  • Frank Nelson Cole Prize in Algebra (1980)

Best Publications

  • Prime ideal structure in commutative rings

    Melvin Hochster

  • Rings of Invariants of Tori, Cohen-Macaulay Rings Generated by Monomials, and Polytopes

    M. Hochster

  • Tight closure, invariant theory, and the Briançon-Skoda theorem

    Melvin Hochster;Craig Huneke;Craig Huneke

  • Cohen-Macaulay Rings, Invariant Theory, and the Generic Perfection of Determinantal Loci

    M. Hochster;John A. Eagon

  • Rings of invariants of reductive groups acting on regular rings are Cohen-Macaulay

    Melvin Hochster;Joel L Roberts

  • Topics in the Homological Theory of Modules over Commutative Rings

    M. Hochster

  • The purity of the Frobenius and local cohomology

    Melvin Hochster;Melvin Hochster;Joel L Roberts;Joel L Roberts

  • $F$-regularity, test elements, and smooth base change

    Melvin Hochster;Craig Huneke

  • Comparison of symbolic and ordinary powers of ideals

    Melvin Hochster;Craig Huneke

  • Tight closure and strong F-regularity

    Melvin Hochster;Craig Huneke

  • Infinite integral extensions and big Cohen-Macaulay algebras

    Melvin Hochster;Craig Huneke

  • Contracted ideals from integral extensions of regular rings

    M. Hochster

  • Cyclic purity versus purity in excellent Noetherian rings

    Melvin Hochster

  • Canonical elements in local cohomology modules and the direct summand conjecture

    Melvin Hochster

  • Criteria for equality of ordinary and symbolic powers of primes

    Melvin Hochster

  • INDECOMPOSABLE CANONICAL MODULES AND CONNECTEDNESS

    Melvin Hochster;Craig Huneke

  • A Nullstellensatz with nilpotents and Zariski's Main Lemma on holomorphic functions

    David Eisenbud;David Eisenbud;Melvin Hochster;Melvin Hochster

  • Applications of the Existence of Big Cohen-Macaulay Algebras

    Melvin Hochster;Craig Huneke

  • The Frobenius structure of local cohomology

    Florian Enescu;Melvin Hochster

  • Modules of finite projective dimension with negative intersection multiplicities.

    Sankar P. Dutta;M. Hochster;J. E. McLaughlin

Frequent Co-Authors

Craig Huneke
Craig Huneke University of Virginia
Luchezar L. Avramov
Luchezar L. Avramov University of Nebraska–Lincoln

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