{{short description|American mathematician}} '''Charles Waldo Rezk''' (born 26 January 1969) is an American mathematician, specializing in algebraic topology and category theory.<ref>{{cite web|title=Charles Rezk's homepage|website=Department of Mathematics, University of Illinois at Urbana-Champaign|url=https://rezk.web.illinois.edu/}}</ref>
==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.<ref name=CV>{{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}}</ref> In 1996 he received his PhD from MIT with thesis ''Spaces of Algebra Structures and Cohomology of Operads'' and advisor Michael J. Hopkins.<ref>{{MathGenealogy|id=37595|title=Charles Waldo Rezk}}</ref><ref>{{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}}</ref> 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 has been a full professor since 2014.<ref name=CV/>
He was at the Institute for Advanced Study in the fall of 1999, the spring of 2000, and the spring of 2001.<ref>{{cite web|title=Charles Rezk|website=Institute for Advanced Study|date=9 December 2019 |url=https://www.ias.edu/scholars/charles-rezk}}</ref> 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''.<ref name=CV/>
Rezk was an invited speaker at the International Congress of Mathematicians in Seoul in 2014.<ref>{{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]</ref> He was elected a Fellow of the American Mathematical Society in the class of 2015 (announced in late 2014).<ref name=CV/>
==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== <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}}
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{{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