**Associate professor of mathematics, University of Texas at Austin**

(blumberg(at)math.utexas.edu)

Jump to synopses of my work in algebraic K-theory, Thom spectra, string topology, or equivariant homotopy theory.

The localization sequence for the algebraic K-theory of topological K-theoryjoint with Michael Mandell Acta Mathematica 200 (2008) 155-179. |
arxiv (published version) |

Algebraic K-theory and abstract homotopy theoryjoint with Michael Mandell Advances in Mathematics 226 (2011) 3760-3812 |
arxiv (published version) |

Localization theorems in topological Hochschild homology and topological cyclic homology joint with Michael Mandell Geometry and Topology 16 (2012) 1053–1120 |
arxiv (published version) |

Derived Koszul duality and involutions in the algebraic K-theory of spacesjoint with Michael Mandell Journal of Topology (2011). |
arxiv (published version) |

Localization for THH(ku) and topological Hochschild and cyclic homology of Waldhausen categoriesjoint with Michael Mandell |
arxiv |

The homotopy theory of cyclotomic spectrajoint with Michael Mandell |
arxiv |

A universal characterization of higher algebraic K-theoryjoint with David Gepner and Goncalo Tabuada Geometry and Topology 17 (2013) 733–838. |
arxiv |

Uniqueness of the multiplicative cyclotomic tracejoint with David Gepner and Goncalo Tabuada To appear in Advances in Mathematics. |
arxiv |

K-theory of endomorphisms via noncommutative motivesjoint with David Gepner and Goncalo Tabuada |
arxiv |

THH of Thom spectra and the free loop space joint with Ralph Cohen and Christian Schlichtkrull Geometry and Topology 14 (2010) 1165-1242. |
arxiv (published version) |

THH of Thom spectra which are E_\infty-ring spectra Journal of Topology 3 (2010) 535-560. |
arxiv |

Units of ring spectra and Thom spectra joint with Matt Ando, David Gepner, Michael Hopkins, and Charles Rezk (split into two papers for submission) Units of ring spectra and orientations via structured ring spectraTo appear in the Journal of Topology. Parametrized spectra, units, and Thom spectra via infinity categories
To appear in the Journal of Topology. |
arxiv |

Twists of K-theory and TMFjoint with Matt Ando and David Gepner To appear in "Superstrings, Geometry, Topology, and $C^*$-algebras", edited by Robert S. Doran, Greg Friedman, and Jonathan Rosenberg. |
arxiv |

Parametrized spectra, multiplicative Thom spectra, and the twisted Umkehr mapjoint with Matt Ando and David Gepner |
arxiv |

Open-closed field theories, string topology, and Hochschild homology joint with Ralph Cohen and Constantin Teleman "Alpine perspectives on algebraic topology", edited by C. Ausoni, K. Hess, and J. Scherer, Contemp. Math. 504 (2009) 53-76 |
arxiv |

A discrete model of S^1-homotopy theory Journal of Pure and Applied Algebra 210 (2007) 29-41. |
arxiv (published version) |

Continuous functors as a model of the equivariant stable category Algebraic and Geometric Topology 6 (2006) 2257-2295. |
arxiv (published version) |