Henryk Iwaniec

{{Infobox scientist

| name = Henryk Iwaniec

| image = Henryk Iwaniec.JPG

| image_size = 200px

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| birth_date = {{Birth date and age|1947|10|9|mf=yes}}

| birth_place = Elbląg, Poland

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| citizenship = Poland, United States

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| fields = Mathematician

| workplaces = Polish Academy of Sciences
Institute for Advanced Study
Rutgers University
University of Michigan

| alma_mater = University of Warsaw

| doctoral_advisor = Andrzej Schinzel

| academic_advisors =

| doctoral_students = Étienne Fouvry
Harald Helfgott

| notable_students =

| known_for = analytic number theory
Friedlander–Iwaniec theorem
automorphic forms
Sieve theory

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| influences =

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| awards = Ostrowski Prize (2001)
Cole Prize (2002)
Steele Prize (2011)
Shaw Prize (2015)

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Henryk Iwaniec (born October 9, 1947) is a Polish-American mathematician, and since 1987 a professor at Rutgers University. He is a member of the American Academy of Arts and Sciences and Polish Academy of Sciences. He has made important contributions to analytic and algebraic number theory as well as harmonic analysis. He is the recipient of Cole Prize (2002), Steele Prize (2011), and Shaw Prize (2015).

Background and education

Iwaniec studied at the University of Warsaw, where he got his PhD in 1972 under Andrzej Schinzel. He then held positions at the Institute of Mathematics of the Polish Academy of Sciences until 1983 when he left Poland. He held visiting positions at the Institute for Advanced Study, University of Michigan, and University of Colorado Boulder before being appointed Professor of Mathematics at Rutgers University. He is a citizen of both Poland and the United States.

{{cite journal

|date=April 2002

| title = 2002 Cole Prize in Number Theory

| journal = Notices of the American Mathematical Society

| volume = 49

| issue = 4

| pages = 476–478

| publisher = American Mathematical Society

| location = Providence

| issn = 0002-9920

| url = https://www.ams.org/notices/200204/comm-coleprz.pdf

}}

He and mathematician Tadeusz Iwaniec are twin brothers.

Work

Iwaniec studies both sieve methods and deep complex-analytic techniques, with an emphasis on the theory of automorphic forms and harmonic analysis.

In 1997, Iwaniec and John Friedlander proved that there are infinitely many prime numbers of the form {{math|a{{sup|2}} + b{{sup|4}}}}.{{Cite journal |last1=Friedlander |first1=John |last2=Iwaniec |first2=Henryk |year=1997 |title=Using a parity-sensitive sieve to count prime values of a polynomial |journal=PNAS |volume=94 |issue=4 |pages=1054–1058 |doi=10.1073/pnas.94.4.1054 | mr=432648 |pmid=11038598 |pmc=19742|bibcode=1997PNAS...94.1054F |doi-access=free }}.{{cite journal|last1 = Friedlander|first1 = John|last2=Iwaniec |first2=Henryk |title = The polynomial X² + Y⁴ captures its primes|journal = Annals of Mathematics|volume = 148|year = 1998|pages = 945–1040|url = http://www.emis.de/journals/Annals/148_3/fried1.pdf|doi = 10.2307/121034|jstor = 121034|issue = 3 | mr=1670065|arxiv = math/9811185|bibcode = 1998math.....11185F|s2cid = 1187277}} Results of this strength had previously been seen as completely out of reach: sieve theory—used by Iwaniec and Friedlander in combination with other techniques—cannot usually distinguish between primes and products of two primes, say. He also showed that there are infinitely many numbers of the form $n^2+1$ with at most two prime factors.{{Cite journal |last=Iwaniec |first=Henryk |year=1978 |title=Almost-primes represented by quadratic polynomials |journal=Inventiones Mathematicae |language=en |volume=47 |issue=2 |pages=171–188 |bibcode=1978InMat..47..171I |doi=10.1007/BF01578070 |issn=0020-9910 |s2cid=122656097}}

In 2001, Iwaniec was awarded the seventh Ostrowski Prize.[https://www.ams.org/notices/200207/comm-ostrowski.pdf "Iwaniec, Sarnak, and Taylor Receive Ostrowski Prize"] The prize citation read, in part, "Iwaniec's work is characterized by depth, profound understanding of the difficulties of a problem, and unsurpassed technique. He has made deep contributions to the field of analytic number theory, mainly in modular forms on {{math|GL(2)}} and sieve methods."

Awards and honors

He became a fellow of the American Academy of Arts and Sciences in 1995. He was awarded the fourteenth Frank Nelson Cole Prize in Number Theory in 2002. In 2006, he became a member of the National Academy of Science. He received the Leroy P. Steele Prize for Mathematical Exposition in 2011. In 2012, he became a fellow of the American Mathematical Society.[https://www.ams.org/profession/fellows-list List of Fellows of the American Mathematical Society], retrieved January 26, 2013. In 2015 he was awarded the Shaw Prize in Mathematics.{{Cite web |url=http://www.shawprize.org/en/shaw.php?tmp=3&twoid=98&threeid=245&fourid=444 |title=Shaw Prize 2015 |access-date=June 1, 2015 |archive-date=October 21, 2019 |archive-url=https://web.archive.org/web/20191021071843/http://www.shawprize.org/en/shaw.php?tmp=3&twoid=98&threeid=245&fourid=444 |url-status=dead }} In 2017, he was awarded the AMS Doob Prize (jointly with John Friedlander) for their book Opera de Cribro, which is about sieve theory.

Publications

{{cite book | last = Iwaniec | first = Henryk | title = Topics in Classical Automorphic Forms | publisher = American Mathematical Society | location = Providence | year = 1997 | isbn = 978-0-8218-0777-4 | url = https://books.google.com/books?id=BJGDAwAAQBAJ }}{{cite journal|last1=Rogawski|first1=Jonathan D.|title=Book Review: Automorphic forms on $SL_{2}(\mathbf{R})$ by A. Borel, Automorphic forms and representations by D. Bump, and Topics in classical automorphic forms by H. Iwaniec|journal=Bulletin of the American Mathematical Society|volume=35|issue=3|year=1998|pages=253–263|issn=0273-0979|doi=10.1090/S0273-0979-98-00756-3|doi-access=free}}
{{cite book | last = Iwaniec | first = Henryk | title = Spectral Methods of Automorphic Forms | edition = 2nd | publisher = American Mathematical Society | location = Providence | year = 2002 | isbn = 978-0-8218-3160-1 | url = https://books.google.com/books?id=GtyFAwAAQBAJ }}
{{cite book | last = Iwaniec | first = Henryk |author2=Emmanuel Kowalski | title = Analytic Number Theory | publisher = American Mathematical Society | location = Providence | year = 2004 | isbn = 978-0-8218-3633-0 | url=https://books.google.com/books?id=CL8jDwAAQBAJ }}{{cite journal|last1=Zaharescu|first1=Alexandru|authorlink=Alexandru Zaharescu|title=Book Review: Analytic number theory|journal=Bulletin of the American Mathematical Society|volume=43|issue=2|year=2006|pages=273–278|issn=0273-0979|doi=10.1090/S0273-0979-06-01084-6|doi-access=free}}
{{cite book | last = Iwaniec | first = Henryk |author2=J. B. Friedlander | author3-link = Roger Heath-Brown |author3=D. R. Heath-Brown |author4=J. Kaczorowski | title = Analytic Number Theory: Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, July 11–18, 2002 | publisher = Springer | location = Berlin | year = 2006 | isbn = 978-3-540-36363-7 | author2-link = John Friedlander | url=https://books.google.com/books?id=NuDimaRIVVsC }}
{{cite book | last1 = Friedlander | first1 = John | author1-link = John Friedlander | last2= Iwaniec | first2 = Henryk | title = Opera de Cribro | publisher = American Mathematical Society | location = Providence | year = 2010 | isbn = 978-0-8218-4970-5 | url=https://books.google.com/books?id=GJSKAwAAQBAJ }}{{cite journal|last1=Thorne|first1=Frank|title=Book Review: An introduction to sieve methods and their applications by Alina Carmen Cojocaru and M. Ram Murty and Opera de cribro by John Friedlander and Henryk Iwaniec|journal=Bulletin of the American Mathematical Society|volume=50|issue=2|year=2012|pages=359–366|issn=0273-0979|doi=10.1090/S0273-0979-2012-01390-3|doi-access=free}}
{{cite book | last1 = Iwaniec | first1 = Henryk | title = Lectures on the Riemann zeta function | publisher = American Mathematical Society | location = Providence | year = 2014 | isbn = 978-1-4704-1851-9 | url = https://books.google.com/books?id=vBe8BAAAQBAJ}}{{cite journal|last1=Conrey|first1=Brian|authorlink=Brian Conrey|title=Book Review: Lectures on the Riemann zeta function|journal=Bulletin of the American Mathematical Society|volume=53|issue=3|year=2016|pages=507–512|issn=0273-0979|doi=10.1090/bull/1525|doi-access=free}}