Michael J. Hopkins

Michael J. Hopkins's AcademicInfluence.com Rankings

Michael J. Hopkins

Mathematics

#322

World Rank

#683

Historical Rank

#155

USA Rank

Algebraic Topology

World Rank

#13

Historical Rank

USA Rank

Measure Theory

#3065

World Rank

#3637

Historical Rank

#889

USA Rank

mathematics Degrees

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Mathematics

Why Is Michael J. Hopkins Influential?

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According to Wikipedia, Michael Jerome Hopkins is an American mathematician known for work in algebraic topology. Life He received his PhD from Northwestern University in 1984 under the direction of Mark Mahowald, with thesis Stable Decompositions of Certain Loop Spaces. Also in 1984 he also received his D.Phil. from the University of Oxford under the supervision of Ioan James. He has been professor of mathematics at Harvard University since 2005, after fifteen years at the Massachusetts Institute of Technology, a few years of teaching at Princeton University, a one-year position with the University of Chicago, and a visiting lecturer position at Lehigh University.

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Michael J. Hopkins's Published Works

Number of citations in a given year to any of this author's works

Total number of citations to an author for the works they published in a given year. This highlights publication of the most important work(s) by the author

Published Works

Nilpotence and stable homotopy theory II (1988) (398)
Quadratic functions in geometry, topology, and M-theory (2002) (385)
On the nonexistence of elements of Kervaire invariant one (2009) (385)
Equivariant K-theory (1968) (360)
Reflection positivity and invertible topological phases (2016) (244)
Structured Ring Spectra: Moduli spaces of commutative ring spectra (2004) (208)
GENERALIZED GROUP CHARACTERS AND COMPLEX ORIENTED COHOMOLOGY THEORIES (2000) (197)
Elliptic spectra, the Witten genus and the theorem of the cube (2001) (169)
Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups (2004) (150)
Loop groups and twisted K‐theory I (2007) (145)
Algebraic topology and modular forms (2002) (136)
Twisted equivariant K‐theory with complex coefficients (2002) (124)
Homotopy Theory: Proceedings of the Durham Symposium 1985: Global methods in homotopy theory (1987) (116)
Twisted K-theory and loop group representations (2003) (108)
Topological Quantum Field Theories from Compact Lie Groups (2009) (108)
Equivariant vector bundles on the Lubin-Tate moduli space (2009) (90)
MULTIPLICATIVE ORIENTATIONS OF KO-THEORY AND OF THE SPECTRUM OF TOPOLOGICAL MODULAR FORMS (2006) (87)
An ∞‐categorical approach to R‐line bundles, R‐module Thom spectra, and twisted R‐homology (2014) (84)
Construction of elements in Picard groups (1992) (79)
Topological Modular Forms, the Witten Genus, and the Theorem of the Cube (1995) (79)
The rigid analytic period mapping, Lubin-Tate space, and stable homotopy theory (1994) (78)
The sigma orientation is an H∞ map (2004) (71)
FROM ELLIPTIC CURVES TO HOMOTOPY THEORY (1998) (70)
The Action of the Morava Stabilizer Group on the Lubin-Tate Moduli Space of Lifts (1995) (65)
Units of ring spectra and Thom spectra (2008) (65)
Units of ring spectra, orientations, and Thom spectra via rigid infinite loop space theory (2014) (59)
The homotopy theory of cyclic sets (1985) (58)
Splitting Varieties for Triple Massey Products (2012) (56)
Loop groups and twisted $K$-theory II (2005) (54)
Loop groups and twisted K-theory III (2011) (51)
Morava K-theories of classifying spaces and generalized characters for finite groups (1992) (47)
Spin cobordism determines real K-theory (1992) (43)
Equivariant symmetric monoidal structures (2016) (40)
Chern-Weil forms and abstract homotopy theory (2013) (40)
Consistent Orientation of Moduli Spaces (2007) (38)
The slice spectral sequence for the $C_{4}$ analog of real $K$-theory (2015) (33)
On the existence of a $v^{32}_2$-self map on $M(1,4)$ at the prime 2 (2007) (27)
Equivariant Multiplicative Closure (2013) (27)
A Variant of K-theory: K_{+-} (2003) (23)
Suspension spectra are harmonic (1992) (22)
On the structure of spaces representing a landweber exact cohomology theory (1995) (22)
The Arf-Kervaire problem in algebraic topology: Sketch of the proof (2010) (22)
Morava Hopf algebras and spaces K ( n ) equivalent to finite Postnikov systems (1994) (19)
Nilpotence and finite H-spaces (1989) (19)
Vanishing lines in generalized Adams spectral sequences are generic (1999) (17)
Hodge filtered complex bordism (2012) (17)
$\eta$-periodic motivic stable homotopy theory over fields (2020) (15)
Direct synthesis of fluorinated peroxides. V. The preparation of pentafluorosulfurperoxy esters by reactions of pentafluorosulfur hydroperoxide with acyl fluorides (1976) (14)
Higher real K‐theories and topological automorphic forms (2009) (12)
The slice spectral sequence for certain R O(Cpⁿ)-graded suspensions of HZ (2017) (12)
The Arf-Kervaire Invariant Problem in Algebraic Topology: Introduction (2010) (11)
Detecting exotic spheres in low dimensions using coker J (2017) (11)
Advances in Homotopy Theory: Characters and elliptic cohomology (1989) (11)
Localization and nilpotent spaces in A^1-homotopy theory (2019) (10)
Consistency of M-Theory on Non-Orientable Manifolds (2021) (9)
The Kervaire invariant problem (2016) (9)
Strictly commutative complex orientation theory (2016) (9)
Invertible phases of matter with spatial symmetry (2019) (8)
M-Theory anomaly cancellation (2019) (8)
Realizing commutative ring spectra as E8 ring spectra (2001) (8)
The mathematical work of Douglas C. Ravenel (2008) (7)
(1)-local _{∞}-ring spectra (2014) (6)
Intersection forms of spin 4-manifolds and the pin(2)-equivariant Mahowald invariant (2018) (6)
Simplifying Complicated Simplicial Complexes: Discrete Morse Theory and its Applications (2012) (5)
Ellitpic curves and stable homotopy I (2014) (5)
Algebraic vector bundles and $p$-local A^1-homotopy theory. (2020) (5)
Minimal atlases of real projective spaces (1989) (4)
Computational methods for higher real k-theory with applications to tmf (2006) (3)
Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem (2021) (3)
A nilpotence theorem for modules over the mod 2 steenrod algebra (1993) (3)
The Arf-Kervaire problem in algebraic topology: an introduction (2009) (3)
KERVAIRE INVARIANT ONE [ after (2010) (3)
OBSTRUCTIONS TO ALGEBRAIZING TOPOLOGICAL VECTOR BUNDLES (2015) (3)
Real Wilson Spaces I (2018) (2)
Comparing Dualities in the K(n)-local Category (2020) (2)
The Slice Spectral Sequence for certain $RO(C_{p^n})$-graded Suspensions of $H\underline{\mathbb Z}$ (2015) (2)
ON THE 3-PRIMARY ARF-KERVAIRE INVARIANT PROBLEM (2011) (2)
Dualizing spheres for compact p-adic analytic groups and duality in chromatic homotopy (2020) (2)
THE σ-ORIENTATION IS AN H∞ MAP (2002) (2)
The slice spectral sequence for certain $$RO({C_{p^{n}}} )$$RO(Cpn)-graded suspensions of $$H{\underline{\mathbf{Z}}}$$HZ̲ (2015) (2)
THE SLICE SPECTRAL SEQUENCE FOR RO(Cpn)-GRADED SUSPENSIONS OF HZ I (2014) (2)
From spectra to stacks (2014) (1)
THE SLICE SPECTRAL SEQUENCE OF MACKEY FUNCTORS FOR THE C 4 ANALOG OF REAL K-THEORY (2014) (1)
From Elliptic Curves to Homotopy Theory a Preliminary Report (1)
The string orientation (2014) (1)
NORTHWESTERN UNIVERSITY STABLE DECOMPOSITIONS OF CERTAIN LOOP SPACES A DISSERTATION SUBMITTED TO THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS for the degree DOCTOR OF PHILOSOPHY (2020) (0)
A T ] 1 3 N ov 2 00 7 Loop Groups and Twisted K-Theory II (2007) (0)
N ov 2 00 5 Twisted K-theory and Loop Group Representations (0)
On the Whitehead theorem for nilpotent motivic spaces (2022) (0)
Topological Methods in Automorphic Forms (2011) (0)
Kervaire Invariant One Following (2010) (0)
AN ELEMENTARY PROOF OF QUILLEN ’ S THEOREM FOR COMPLEX COBORDISM (2017) (0)
The sigma orientation is an H-infinity map (2002) (0)
A T ] 9 N ov 2 00 5 Loop Groups and Twisted K-Theory II (2005) (0)
Localization and nilpotent spaces in ${\mathbb {A}}^1$-homotopy theory (2022) (0)
Vanishing lines in Adams spectral sequences are generic (1998) (0)
TOWARDS THE CONSTRUCTION OF tmf (2012) (0)
The Kervaire invariant problem (2016) (0)
ec 2 00 3 Twisted equivariant K-theory with complex coefficients (2008) (0)
The sheaf of _{∞}-ring spectra (2014) (0)
SYMMETRIC POWERS OF THE SPHERE March 1, 2018 (2018) (0)
Strictly commutative complex orientation theory (2017) (0)
A NEW ANGLE ON THE STABLE HOMOTOPY GROUPS OF SPHERES JOINT WORK WITH MIKE HILL AND (2007) (0)
Model Category Structures on sC (2006) (0)

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