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Michael Hopkins in nLab

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Michael Jerome Hopkins is a mathematician at Harvard University. He got his PhD from Northwestern University in 1984, advised by Mark Mahowald.

Hopkins is a world leading researcher in algebraic topology and (stable-)homotopy theory.

Among his notable achievements are his work on the Ravenel conjectures, the introduction and discussion of the generalized cohomology theory tmf and its string orientation, a formalization and construction of differential cohomology, the proof of the Kervaire invariant problem. More recently via Jacob Lurie‘s work on the cobordism hypothesis Hopkins participates in work related to the foundations of quantum field theory.

Selected writings

On stable homotopy theory:

Introducing generalized differential cohomology motivated by the M5-brane partition function:

On topological quantum field theory:

On ambidextrous adjunctions in stable homotopy theory

Introducing the nilpotence theorem in stable homotopy theory:

On the Conner-Floyd isomorphism for the Atiyah-Bott-Shapiro orientation of KU and KO (cobordism theory determining homology theory):

On generalized (transchromatic) group characters via complex oriented cohomology theory:

On elliptic genera, the Witten genus and the string orientation of tmf:

The construction of tmf was originally announced, as joint work with Mark Mahowald and Haynes Miller, in

(There the spectrum was still called “eo 2eo_2” instead of “tmftmf”.) The details of the definition then appeared in

On stacks and complex oriented cohomology theory:

On twisted equivariant K-theory with an eye towards twisted ad-equivariant K-theory:

On twisted ad-equivariant K-theory of compact Lie groups and the identification with the Verlinde ring of positive energy representations of their loop group:

On ∞-groups of units, Thom spectra and twisted generalized cohomology:

Solving the Arf-Kervaire invariant problem with methods of equivariant stable homotopy theory:

Introducing Hodge-filtered differential cohomology and its specialization to Hodge-filtered complex cobordism theory:

On classification of invertible TQFTs via reflection positivity:

Last revised on June 21, 2024 at 08:32:45. See the history of this page for a list of all contributions to it.