nLab Michael Hill (changes)

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• webpage

Selected writings

On string bordism of the classifying space of $E_8$:

• Michael Hill, The $String$ bordism of $B E_8$ and $B E_8 \times B E_8$ through dimension 14, Ill. J. Math. 53 1 (2009) 183-196 [[doi:10.1215/ijm/1264170845](https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-53/issue-1/The-string-bordism-of-BE_8-and-BE_8times-BE_8-through-dimension/10.1215/ijm/1264170845.full)]

On tmf:

• Christopher Douglas, John Francis, André Henriques, Michael Hill, Topological Modular Forms, Mathematical Surveys and Monographs Volume 201, AMS 2014 (ISBN:978-1-4704-1884-7)

with level structure:

• Michael Hill, Tyler Lawson, Topological modular forms with level structure, Inventiones mathematicae volume 203, pages 359–416 (2016) (arXiv:1312.7394, doi:10.1007/s00222-015-0589-5)

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

• Michael Hill, Michael Hopkins, Douglas Ravenel, Equivariant Stable Homotopy Theory and the Kervaire Invariant Problem, New Mathematical Monographs, Cambridge University Press (2021) [[doi:10.1017/9781108917278](https://doi.org/10.1017/9781108917278)]

• Michael Hill, Michael Hopkins, Douglas Ravenel, On the non-existence of elements of Kervaire invariant one, Annals of Mathematics 184 1 (2016)[[doi:10.4007/annals.2016.184.1.1](https://doi.org/10.4007/annals.2016.184.1.1), arXiv:0908.3724, talk slides]

• Michael Hill, Michael Hopkins, Douglas Ravenel, The Arf-Kervaire problem in algebraic topology: Sketch of the proof, Current Developments in Mathematics, 2010: 1-44 (2011) (pdf, doi:10.4310/CDM.2010.v2010.n1.a1)

• Michael Hill, Michael Hopkins, Douglas Ravenel, The Arf-Kervaire invariant problem in algebraic topology: introduction (2016) [[pdf](http://math.ucla.edu/~mikehill/Research/CDMHistory.pdf)]