Pertti Mattila

{{Short description|Finnish mathematician (born 1948)}}

{{for|the Finnish Olympic skier|Pertti Mattila (skier)}}

{{Use dmy dates|date=May 2025}}

{{Infobox scientist

|name = Pertti Mattila

|image = Pertti_Esko_Juhani_Mattila_Finnish_mathematician.jpg

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|birth_date = {{birth date and age|1948|03|28|df=yes}}

|birth_place = Kuusankoski, Finland{{cite book | editor=Paavilainen, Ulla | title=Kuka kukin on: Henkilötietoja nykypolven suomalaisista 2015 | page=545 | location=Helsinki | publisher=Otava | year=2014 | isbn=978-951-1-28228-0 | trans-title=Who’s Who in Finland, 2015 | language=Finnish }}

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|nationality = Finnish

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|fields = Mathematics

|workplaces = Princeton University, University of Jyväskylä, University of Helsinki

|alma_mater = University of Helsinki

|doctoral_advisor = Jussi Väisälä

|thesis_title = Integration in a Space of Measures

|thesis_year = 1973

|academic_advisors =

|doctoral_students = Maarit Järvenpää

|notable_students =

|known_for = Geometric measure theory

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|awards = Magnus Ehrnrooth Foundation Prize (2000)

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Pertti Esko Juhani Mattila (born 28 March 1948) is a Finnish mathematician working in geometric measure theory, complex analysis and harmonic analysis.{{cite web | title=Pertti Mattila's webpage at the University of Helsinki | url=https://wiki.helsinki.fi/display/mathstatHenkilokunta/Mattila,+Pertti}}{{cite web | title=Pertti Mattila's publications in the University of Helsinki database | url=https://tuhat.halvi.helsinki.fi/portal/en/persons/pertti-mattila(a97fc122-0cc4-42b5-98fb-c8bb19f25c5d).html}} He is Professor of Mathematics in the Department of Mathematics and Statistics at the University of Helsinki, Finland.

He is known for his work on geometric measure theory and in particular applications to complex analysis and harmonic analysis. His work include a counterexample to the general Vitushkin's conjecture{{citation|first=Pertti|last=Mattila|author-link=Pertti Mattila|title=Smooth Maps, Null-Sets for Integralgeometric Measure and Analytic Capacity|journal=Annals of Mathematics|volume=123|year=1986|issue=2|pages=303–309|doi=10.2307/1971273|jstor=1971273 }} and with Mark Melnikov and Joan Verdera he introduced new techniques to understand the geometric structure of removable sets for complex analytic functions{{citation|first1=Pertti|last1=Mattila|author1-link=Pertti Mattila|first2=Mark|last2=Melnikov|first3=Joan|last3=Verdera|title=The Cauchy Integral, Analytic Capacity, and Uniform Rectifiability|journal=Annals of Mathematics|volume=144|year=1996|issue=1|pages=127–136|doi=10.2307/2118585|jstor=2118585 }} which together with other works in the field eventually led to the solution of Painlevé's problem by Xavier Tolsa.{{citation | first=Xavier | last=Tolsa | title=Painleve's problem and the semiadditivity of analytic capacity|journal=Acta Mathematica|volume=190|issue=1|year=2003|pages=105–149 | doi=10.1007/bf02393237|arxiv=math/0204027}}{{cite web | title=Personnel page of the Centre of Excellence in Analysis and Dynamics Research | url=https://wiki.helsinki.fi/display/huippu/Personnel}}

His book Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability{{citation | last=Mattila | first=Pertti | authorlink = Pertti Mattila| title = Geometry of Sets and Measures in Euclidean Spaces: Fractals and Rectifiability| publisher = Cambridge University Press| location = London| year = 1995| pages = 356| isbn = 978-0-521-65595-8 }} is now a widely cited{{cite web | title=Geometry of Sets and Measures in Euclidean Spaces citations in Scholarpedia | url=https://scholar.google.com/scholar?cluster=16641930015222637738&hl=en&as_sdt=2005&sciodt=0,5}} and a standard textbook in this field.{{cite web|author=Das, Tushar|title=Review of Fourier Analysis and Hausdorff Dimension by Pertti Mattila|website=MAA Reviews, Mathematical Association of America|date=3 July 2017|url=https://www.maa.org/press/maa-reviews/fourier-analysis-and-hausdorff-dimension}} Mattila has been the leading figure on creating the geometric measure theory school in Finland and the Mathematics Genealogy Project cites he has supervised so far 15 PhD students in the field.

He obtained his PhD from the University of Helsinki under the supervision of Jussi Väisälä in 1973. He worked at the Institute for Advanced Study at the Princeton University for postdoctoral research in 1979 and from 1989 as Professor of Mathematics at the University of Jyväskylä, until appointed as Professor of Mathematics at the University of Helsinki in 2003.{{cite web| title=Institute for Advanced Study records of Pertti Mattila| url=https://www.ias.edu/people/cos/users/pmattila01| access-date=10 December 2014| archive-url=https://web.archive.org/web/20160303230925/https://www.ias.edu/people/cos/users/pmattila01| archive-date=3 March 2016| url-status=dead}} In 1998 he was an Invited Speaker of the International Congress of Mathematicians in Berlin.{{cite book|author=Mattila, Pertti|chapter=Rectifiability, analytic capacity, and singular integrals|title=Doc. Math. (Bielefeld) Extra Vol. ICM Berlin, 1998, vol. II|year=1998|pages=657–664|chapter-url=https://www.elibm.org/ft/10011678000}} Mattila was the director of the Academy of Finland funded Centre of Excellence of Geometric Analysis and Mathematical Physics from 2002 to 2007 and currently part of the Centre of Excellence in Analysis and Dynamics Research in the University of Helsinki.