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Michael J. Hopkins

Michael J. Hopkins

D-Index & Metrics

Mathematics

D-Index
41
Citations
6669
World Ranking
1918
National Ranking
820

Research.com Recognitions

  • 2021 - Fellow of the American Mathematical Society For contributions to algebraic topology and related areas of algebraic geometry, representation theory, and mathematical physics.
  • 2010 - Member of the National Academy of Sciences
  • 2002 - Fellow of the American Academy of Arts and Sciences
  • 1987 - Fellow of Alfred P. Sloan Foundation

Overview

Michael J. Hopkins is a researcher affiliated with Harvard University in the United States. Their primary field of study is Mathematics, with substantial contributions in subfields such as Geometry and Topology, Mathematical Physics, Nuclear and High Energy Physics, Computational Theory and Mathematics, and Algebra and Number Theory.

Their research covers a range of main topics, including:

  • Homotopy and Cohomology in Algebraic Topology
  • Algebraic structures and combinatorial models
  • Algebraic Geometry and Number Theory
  • Advanced Algebra and Geometry
  • Advanced Topics in Algebra
  • Black Holes and Theoretical Physics
  • Geometric and Algebraic Topology

Hopkins has published extensively in various scientific venues. Frequent publication sites include:

  • arXiv (Cornell University)
  • Journal of the London Mathematical Society
  • Advances in Theoretical and Mathematical Physics
  • Communications of the American Mathematical Society
  • Journal of Electronic Packaging

Recent papers authored or co-authored by Hopkins demonstrate their involvement in topics combining topology, algebra, and mathematical physics. Selected recent publications include:

  • Intersection forms of spin 4-manifolds and the pin(2)-equivariant Mahowald invariant, 2022, Communications of the American Mathematical Society
  • Detecting exotic spheres in low dimensions using coker J, 2020, Journal of the London Mathematical Society
  • $\eta$-periodic motivic stable homotopy theory over fields, 2020, arXiv (Cornell University)
  • Invertible phases of matter with spatial symmetry, 2020, Advances in Theoretical and Mathematical Physics
  • Investigation of Electromechanical Reliability and Radio Frequency Performance of a Highly Stretchable Liquid Metal Conductor for Wearable Electronics, 2023, Journal of Electronic Packaging

Frequent collaborators include:

  • Michael A. Hill
  • Douglas C. Ravenel
  • Aravind Asok
  • Tom Bachmann
  • Daniel S. Freed

Hopkins has contributed to academic literature beyond journal articles, including a book published by Cambridge University Press:

  • Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem, 2021

Their recognition in the mathematical community includes several awards and honors such as:

  • Fellow of the American Mathematical Society (2021) for contributions to algebraic topology and related areas
  • Member of the National Academy of Sciences (2010)
  • Fellow of the American Academy of Arts and Sciences (2002)
  • Fellow of Alfred P. Sloan Foundation (1987)

Best Publications

  • Quadratic functions in geometry, topology, and M-theory

    M.J. Hopkins;I.M. Singer

  • On the nonexistence of elements of Kervaire invariant one

    Michael Hill;Michael Hopkins;Douglas Ravenel

  • Nilpotence and stable homotopy theory II

    Michael J. Hopkins;Jeffrey H. Smith

  • Nilpotence and Stable Homotopy Theory II

    Unknown

  • Reflection positivity and invertible topological phases

    Daniel S. Freed;Michael J. Hopkins

  • GENERALIZED GROUP CHARACTERS AND COMPLEX ORIENTED COHOMOLOGY THEORIES

    Michael J. Hopkins;Nicholas J. Kuhn;Douglas C. Ravenel

  • Structured Ring Spectra: Moduli spaces of commutative ring spectra

    Unknown

  • Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups

    Ethan S. Devinatz;Michael J. Hopkins

  • Loop groups and twisted K-theory I

    Daniel S. Freed;Michael J. Hopkins;Constantin Teleman

  • Algebraic topology and modular forms

    Michael J. Hopkins

  • Elliptic spectra, the Witten genus and the theorem of the cube

    M. Ando;M. J. Hopkins;N. P. Strickland

  • Twisted K-theory and loop group representations

    Daniel S. Freed;Michael J. Hopkins;Constantin Teleman

  • On Ramond-Ramond fields and K-theory

    Daniel S. Freed;Michael J. Hopkins

  • Homotopy Theory: Proceedings of the Durham Symposium 1985: Global methods in homotopy theory

    Unknown

  • Twisted equivariant K-theory with complex coefficients

    Daniel S. Freed;Michael J. Hopkins;Constantin Teleman

  • Topological Modular Forms, the Witten Genus, and the Theorem of the Cube

    Michael J. Hopkins

  • TQM and CSR nexus

    Abby Ghobadian;David Gallear;Michael Hopkins

  • On the non-existence of elements of Kervaire invariant one

    Michael A. Hill;Michael J. Hopkins;Douglas C. Ravenel

  • The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory

    M. J. Hopkins;B. H. Gross

  • An ∞‐categorical approach to R‐line bundles, R‐module Thom spectra, and twisted R‐homology

    Matthew Ando;Andrew J. Blumberg;David Gepner;Michael J. Hopkins

  • The Action of the Morava Stabilizer Group on the Lubin-Tate Moduli Space of Lifts

    Ethan S. Devinatz;Michael J. Hopkins

  • FROM ELLIPTIC CURVES TO HOMOTOPY THEORY

    Mike Hopkins;Mark Mahowald

  • An $\infty$-categorical approach to $R$-line bundles, $R$-module Thom spectra, and twisted $R$-homology

    Matthew Ando;Andrew J. Blumberg;David Gepner;Michael J. Hopkins

Frequent Co-Authors

Daniel S. Freed
Daniel S. Freed The University of Texas at Austin
Benedict H. Gross
Benedict H. Gross University of California, San Diego

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