Charles Waldo Rezk (born 26 January 1969) is an American mathematician, specializing in algebraic topology, category theory, and spectral algebraic geometry.[1]
Education and career
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]
Selected publications
- 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. S2CID 168002.
- 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. S2CID 14472961.
- Goerss, Paul [in German]; 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. arXiv:0706.2175. 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. arXiv:0706.2175. 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 (4): 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. arXiv:0901.3602. 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. S2CID 119141389.
References
- ↑ "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. 9 December 2019.
- ↑ Rezk, Charles (2014). "Isogenies, power operations, and homotopy theory" (PDF). Proceedings of the ICM, Seoul. Vol. 2. pp. 1125–1146. slides
External links
- "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.