# 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:

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

Review of higher topos theory:

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

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

On Theta-spaces:

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

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

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

On the string orientation of tmf:

On slices of global equivariant homotopy theory as a cohesive (∞,1)-topoi over $G$-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)
• Charles Rezk, Elliptic cohomology and elliptic curves, Felix Klein Lectures, Bonn (2015) $[$web, pdf, pdf, video rec: part 1, 2, 3, 4$]$
• 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]

category: people

Last revised on December 4, 2022 at 19:04:12. See the history of this page for a list of all contributions to it.