nLab Charles Rezk

Charles Waldo Rezk is a mathematician at the University of Illinois Urbana–Champaign.

He got his PhD degree in 1996 at MIT, advised by Michael J. Hopkins.

His PhD students include Nathaniel Stapleton and Nima Rasekh.

Selected writings

Proof of the canonical model structure on Cat:

On the homotopy theory of homotopy theories (the (infinity,1)-category of (infinity,1)-categories) in terms of complete Segal spaces:

Introducing model toposes/(∞,1)-toposes:

Introducing quasi-elliptic cohomology:

  • Charles Rezk, Quasi-Elliptic Cohomology (2014) [pdf]

    (not publicly available until upload here, in 2023)

Review of higher topos theory:

On complete Segal spaces:

  • Charles Rezk, A model for the homotopy theory of homotopy theory , Trans. Amer. Math. Soc., 353(3), 973-1007 (pdf)

On power operations:

Expressing logarithmic cohomology operations in terms of the Bousfield-Kuhn functor and power operations:

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

On Theta-spaces:

  • Charles Rezk, A cartesian presentation of weak nn-categories Geom. Topol. 14 (2010), no. 1, 521–571 (arXiv:0901.3602)

    Correction to “A cartesian presentation of weak nn-categories” Geom. Topol. 14 (2010), no. 4, 2301–2304. MR 2740648 (pdf)

  • Charles Rezk, Cartesian presentations of weak nn-categories – An introduction to Θ n\Theta_n-spaces (2009) (pdf)

On the string orientation of tmf:

On slices of global equivariant homotopy theory as a cohesive (∞,1)-topoi over GG-equivariant homotopy theory (cohesion of global- over G-equivariant homotopy theory):

On sufficient conditions for geometric realization of simplicial topological spaces to commute with homotopy pullback

  • Charles Rezk, When are homotopy colimits compatible with homotopy base change?, 2014 (pdf, pdf)

On elliptic cohomology:

On classifying spaces for equivariant principal bundles with 1-truncated compact Lie structure group:

On quasi-categories:

  • Charles Rezk, Stuff about quasicategories, Lecture Notes for course at University of Illinois at Urbana-Champaign, 2016, version May 2017 (pdf, pdf)

  • Charles Rezk, Introduction to quasicategories (2022) [pdf, pdf]

On compactly generated topological spaces:

On accessible ( , 1 ) (\infty,1) -categories:

On spectral algebraic geometry:

in higher algebra/stable homotopy theory

in higher category theory:

in higher topos theory:

category: people

Last revised on February 5, 2024 at 15:39:35. See the history of this page for a list of all contributions to it.