# Charles Rezk > Mediated Wiki article. Canonical URL: https://mediated.wiki/source/Charles_Rezk > Markdown URL: https://mediated.wiki/source/Charles_Rezk.md > Source: https://en.wikipedia.org/wiki/Charles_Rezk > Source revision: 1346436531 > License: Creative Commons Attribution-ShareAlike 4.0 International (https://creativecommons.org/licenses/by-sa/4.0/) {{short description|American mathematician}} '''Charles Waldo Rezk''' (born 26 January 1969) is an American mathematician, specializing in [algebraic topology](/source/algebraic_topology) and [category theory](/source/category_theory).{{cite web|title=Charles Rezk's homepage|website=Department of Mathematics, University of Illinois at Urbana-Champaign|url=https://rezk.web.illinois.edu/}} ==Education and career== Rezk matriculated at the [University of Pennsylvania](/source/University_of_Pennsylvania) in 1987 and graduated there in 1991 with B.A. and M.A. in mathematics.{{cite web|title=Charles W. Rezk, Curriculum Vitae|website=Department of Mathematics, University of Illinois at Urbana-Champaign|url=https://rezk.web.illinois.edu/cv-rezk-2024.pdf}} In 1996 he received his PhD from [MIT](/source/Massachusetts_Institute_of_Technology) with thesis ''Spaces of Algebra Structures and Cohomology of Operads'' and advisor [Michael J. Hopkins](/source/Michael_J._Hopkins).{{MathGenealogy|id=37595|title=Charles Waldo Rezk}}{{cite web|author=Rezk, C. W.|date=May 1996|title=Spaces of algebra structures and cohomology of operads (Doctoral dissertation, Massachusetts Institute of Technology)|website=dspace.mit.edu|url=https://dspace.mit.edu/bitstream/handle/1721.1/41793/36023226-MIT.pdf?sequence=2}} At [Northwestern University](/source/Northwestern_University) Rezk was a faculty member from 1996 to 2001. At the [University of Illinois](/source/University_of_Illinois) he was an assistant professor from 2001 to 2006 and an associate professor from 2006 to 2014, and has been a full professor since 2014. He was at the [Institute for Advanced Study](/source/Institute_for_Advanced_Study) in the fall of 1999, the spring of 2000, and the spring of 2001.{{cite web|title=Charles Rezk|website=Institute for Advanced Study|date=9 December 2019 |url=https://www.ias.edu/scholars/charles-rezk}} He held visiting positions at MIT in 2006 and at Berkeley's [MSRI](/source/Mathematical_Sciences_Research_Institute) in 2014. Since 2015 he has been a member of the editorial board of ''[Compositio Mathematica](/source/Compositio_Mathematica)''. Rezk was an invited speaker at the [International Congress of Mathematicians](/source/International_Congress_of_Mathematicians) in Seoul in 2014.{{cite book|author=Rezk, Charles|chapter=Isogenies, power operations, and homotopy theory|title=Proceedings of the ICM, Seoul|volume=2|year=2014|pages=1125–1146|chapter-url=https://rezk.web.illinois.edu/rezk-icm-talk-posted.pdf}} [https://rezk.web.illinois.edu/rezk-icm-2014-handout.pdf slides] He was elected a Fellow of the [American Mathematical Society](/source/American_Mathematical_Society) in the class of 2015 (announced in late 2014). ==Selected publications== *{{cite journal|author=Rezk, Charles|title=Notes on the Hopkins-Miller theorem|journal=Contemporary Mathematics|volume=220|year=1998|pages=313–366|url=https://rezk.web.illinois.edu/hopkins-miller-thm.pdf|doi=10.1090/conm/220/03107|isbn=9780821808054}} *{{cite journal|doi=10.1353/ajm.1999.0043|title=Brown-Comenetz duality and the Adams spectral sequence|journal=American Journal of Mathematics|volume=121|issue=6|pages=1153–1177|year=1999|last1=Mahowald|first1=Mark|authorlink=Mark Mahowald|last2=Rezk|first2=Charles|s2cid=168002}} *{{cite journal|doi=10.1090/S0002-9947-00-02653-2|year=2001|last1=Rezk|first1=Charles|title=A model for the homotopy theory of homotopy theory|journal=Transactions of the American Mathematical Society|volume=353|issue=3|pages=973–1008|doi-access=free}} *{{cite journal|doi=10.1353/ajm.2001.0019|title=Simplicial structures on model categories and functors|journal=American Journal of Mathematics|volume=123|issue=3|pages=551–575|year=2001|last1=Rezk|first1=Charles|last2=Schwede|first2=Stefan|last3=Shipley|first3=Brooke|bibcode=2001math......1162R|arxiv=math/0101162|s2cid=14472961}} *{{cite journal|doi=10.4007/annals.2005.162.777|title=A resolution of the K(2)-local sphere at the prime 3|journal=Annals of Mathematics|volume=162|issue=2|pages=777–822|year=2005|last1=Goerss|first1=Paul|author-link=:de:Paul Goerss|last2=Henn|first2=Hans-Werner|last3=Mahowald|first3=Mark|last4=Rezk|first4=Charles|doi-access=free|arxiv=0706.2175}} *{{cite journal|jstor=20159929|title=A Resolution of the K(2)-Local Sphere at the Prime 3|journal=Annals of Mathematics|volume=162|issue=2|pages=777–822|last1=Goerss|first1=P.|last2=Henn|first2=H-.W.|last3=Mahowald|first3=M.|last4=Rezk|first4=C.|year=2005|doi=10.4007/annals.2005.162.777|doi-access=free|arxiv=0706.2175}} *{{cite journal|last1=Rezk|first1=Charles|title=The units of a ring spectrum and a logarithmic cohomology operation|journal=Journal of the American Mathematical Society|volume=19|issue=4|year=2006|pages=969–1015|issn=0894-0347|doi=10.1090/S0894-0347-06-00521-2|doi-access=free}} *{{cite journal|doi=10.2140/gt.2010.14.521|title=A cartesian presentation of weak ''n''–categories|journal=Geometry & Topology|volume=14|pages=521–571|year=2010|last1=Rezk|first1=Charles|doi-access=free|arxiv=0901.3602}} *{{cite journal|doi=10.1112/jtopol/jtt035|title=An ∞-categorical approach to ''R''-line bundles, ''R''-module Thom spectra, and twisted ''R''-homology|journal=Journal of Topology|volume=7|issue=3|pages=869–893|year=2014|last1=Ando|first1=Matthew|last2=Rezk|first2=Charles|last3=Blumberg|first3=Andrew J.|last4=Gepner|first4=David|last5=Hopkins|first5=Michael J.|arxiv=1403.4325|s2cid=119141389}} ==References== ==External links== *{{cite web|title=Calculations in Multiplicative Stable Homotopy Theory at Height 2 (Charles Rezk @ MSRI)|date=17 July 2014|website=YouTube|url=https://www.youtube.com/watch?v=cN_27X1poIQ}} *{{cite web|title=ICM2014 VideoSeries IL6.7: Charles Rezk on Aug18Mon|date=20 August 2014|publisher=Seoul ICM VOD|website=YouTube|url=https://www.youtube.com/watch?v=NzwuY9Rhk5M}} {{Authority control}} {{DEFAULTSORT:Rezk, Charles}} Category:1969 births Category:Living people Category:20th-century American mathematicians Category:21st-century American mathematicians Category:University of Pennsylvania alumni Category:MIT School of Science alumni Category:Northwestern University alumni Category:University of Illinois Urbana-Champaign faculty Category:Fellows of the American Mathematical Society Category:American topologists Category:Category theorists --- Adapted from the Wikipedia article [Charles Rezk](https://en.wikipedia.org/wiki/Charles_Rezk) by Wikipedia contributors ([contributor history](https://en.wikipedia.org/wiki/Charles_Rezk?action=history)). 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