**Charles Waldo Rezk** (born 26 January 1969) is an American mathematician, specializing in algebraic topology, category theory, and spectral algebraic geometry.^{ [1] }

Rezk matriculated at the University of Pennsylvania in 1987 and graduated there in 1991 with B.A. and M.A. in mathematics.^{ [2] } In 1996 he received his PhD from MIT with thesis *Spaces of Algebra Structures and Cohomology of Operads* and advisor Michael J. Hopkins.^{ [3] }^{ [4] } At Northwestern University Rezk was a faculty member from 1996 to 2001. At the University of Illinois he was an assistant professor from 2001 to 2006 and an associate professor from 2006 to 2014 and is a full professor since 2014.^{ [2] }

He was at the Institute for Advanced Study in the fall of 1999, the spring of 2000, and the spring of 2001.^{ [5] } He held visiting positions at MIT in 2006 and at Berkeley's MSRI in 2014. Since 2015 he has been a member of the editorial board of * Compositio Mathematica *.^{ [2] }

Rezk was an invited speaker at the International Congress of Mathematicians in Seoul in 2014.^{ [6] } He was elected a Fellow of the American Mathematical Society in the class of 2015 (announced in late 2014).^{ [2] }

- Rezk, Charles (1998). "Notes on the Hopkins-Miller theorem" (PDF).
*Contemporary Mathematics*.**220**: 313–366. doi:10.1090/conm/220/03107. ISBN 9780821808054. - Mahowald, Mark; Rezk, Charles (1999). "Brown-Comenetz duality and the Adams spectral sequence".
*American Journal of Mathematics*.**121**(6): 1153–1177. doi:10.1353/ajm.1999.0043. - Rezk, Charles (2001). "A model for the homotopy theory of homotopy theory".
*Transactions of the American Mathematical Society*.**353**(3): 973–1008. doi: 10.1090/S0002-9947-00-02653-2 . - Rezk, Charles; Schwede, Stefan; Shipley, Brooke (2001). "Simplicial structures on model categories and functors".
*American Journal of Mathematics*.**123**(3): 551–575. arXiv: math/0101162 . Bibcode:2001math......1162R. doi:10.1353/ajm.2001.0019. - Goerss, Paul; Henn, Hans-Werner; Mahowald, Mark; Rezk, Charles (2005). "A resolution of the K(2)-local sphere at the prime 3".
*Annals of Mathematics*.**162**(2): 777–822. doi: 10.4007/annals.2005.162.777 . - Goerss, P.; Henn, H-.W.; Mahowald, M.; Rezk, C. (2005). "A Resolution of the K(2)-Local Sphere at the Prime 3".
*Annals of Mathematics*.**162**(2): 777–822. doi: 10.4007/annals.2005.162.777 . JSTOR 20159929. - Rezk, Charles (2006). "The units of a ring spectrum and a logarithmic cohomology operation".
*Journal of the American Mathematical Society*.**19**(04): 969–1015. doi: 10.1090/S0894-0347-06-00521-2 . ISSN 0894-0347. - Rezk, Charles (2010). "A cartesian presentation of weak
*n*–categories".*Geometry & Topology*.**14**: 521–571. doi: 10.2140/gt.2010.14.521 . - Ando, Matthew; Rezk, Charles; Blumberg, Andrew J.; Gepner, David; Hopkins, Michael J. (2014). "An ∞-categorical approach to
*R*-line bundles,*R*-module Thom spectra, and twisted*R*-homology".*Journal of Topology*.**7**(3): 869–893. arXiv: 1403.4325 . doi:10.1112/jtopol/jtt035.

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- ↑ "Charles Rezk's homepage".
*Department of Mathematics, University of Illinois at Urbana-Champaign*. - 1 2 3 4 "Charles W. Rezk, Curriculum Vitae" (PDF).
*Department of Mathematics, University of Illinois at Urbana-Champaign*. - ↑ Charles Waldo Rezk at the Mathematics Genealogy Project
- ↑ Rezk, C. W. (May 1996). "Spaces of algebra structures and cohomology of operads (Doctoral dissertation, Massachusetts Institute of Technology)" (PDF).
*dspace.mit.edu*. - ↑ "Charles Rezk".
*Institute for Advanced Study*. - ↑ Rezk, Charles (2014). "Isogenies, power operations, and homotopy theory" (PDF).
*Proceedings of the ICM, Seoul*. vol. 2. pp. 1125–1146. slides

- "Calculations in Multiplicative Stable Homotopy Theory at Height 2 (Charles Rezk @ MSRI)".
*YouTube*. 17 July 2014. - "ICM2014 VideoSeries IL6.7: Charles Rezk on Aug18Mon".
*YouTube*. Seoul ICM VOD. 20 August 2014.

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