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'''Umberto Zannier''' (born 25 May 1957 in [[Spilimbergo]]) is an Italian mathematician, specializing in [[number theory]] and [[diophantine geometry]].
'''Umberto Zannier''' (born 25 May 1957 in [[Spilimbergo]]) is an Italian mathematician, specializing in [[number theory]] and [[diophantine geometry]].


==Education==
Zannier earned a [[Laurea]] degree from [[University of Pisa]] and studied at the [[Scuola Normale Superiore di Pisa]] with Ph.D. supervised by [[Enrico Bombieri]].<ref>{{MathGenealogy|id=100093}}</ref> Zannier was from 1983 to 1987 a researcher at the [[University of Padua]], from 1987 to 1991 an associate professor at the [[University of Salerno]], and from 1991 to 2003 a full professor at the [[Università IUAV di Venezia]]. From 2003 to the present he has been a Professor in Geometry at the Scuola Normale Superiore di Pisa.<ref name=CV>[https://web.archive.org/web/20150919105202/http://www.sns.it/didattica/scienze/menunews/personale/docenti/zannierumberto Zannier Umberto, Scuola Normale Superiore]</ref>
Zannier earned a [[Laurea]] degree from [[University of Pisa]] and studied at the [[Scuola Normale Superiore di Pisa]] with Ph.D. supervised by [[Enrico Bombieri]].<ref>{{MathGenealogy|id=100093}}</ref> Zannier was from 1983 to 1987 a researcher at the [[University of Padua]], from 1987 to 1991 an associate professor at the [[University of Salerno]], and from 1991 to 2003 a full professor at the [[Università IUAV di Venezia]]. From 2003 to the present he has been a Professor in Geometry at the Scuola Normale Superiore di Pisa.<ref name=CV>[https://web.archive.org/web/20150919105202/http://www.sns.it/didattica/scienze/menunews/personale/docenti/zannierumberto Zannier Umberto, Scuola Normale Superiore]</ref>


==Career==
In 2010 he gave the Hermann Weyl Lectures at the [[Institute for Advanced Study]].<ref>{{cite web|date=4 May 2010|url=http://video.ias.edu/weyl|title=Weyl Lectures, Umberto Zannier|website=Institute for Advanced Study, Video Lectures}}</ref> He was a visiting professor at several institutions, including the [[Institut Henri Poincaré]] in Paris, the [[ETH Zurich]], and the [[Erwin Schrödinger Institute]] in Vienna. He was an Invited Speaker at the 4th European Mathematical Congress in Stockholm in 2004. Zannier was elected a corresponding member of the [[Istituto Veneto di Scienze, Lettere ed Arti|Istituto Veneto]] in 2004, a member of the [[Accademia dei Lincei]] in 2006, and a member of [[Academia Europaea]] in 2012.<ref name=CV/>
In 2010 he gave the Hermann Weyl Lectures at the [[Institute for Advanced Study]].<ref>{{cite web|date=4 May 2010|url=http://video.ias.edu/weyl|title=Weyl Lectures, Umberto Zannier|website=Institute for Advanced Study, Video Lectures}}</ref> He was a visiting professor at several institutions, including the [[Institut Henri Poincaré]] in Paris, the [[ETH Zurich]], and the [[Erwin Schrödinger Institute]] in Vienna. He was an Invited Speaker at the 4th European Mathematical Congress in Stockholm in 2004. Zannier was elected a corresponding member of the [[Istituto Veneto di Scienze, Lettere ed Arti|Istituto Veneto]] in 2004, a member of the [[Accademia dei Lincei]] in 2006, and a member of [[Academia Europaea]] in 2012.<ref name=CV/>


With [[Jonathan Pila]] he developed a method (now known as the Pila-Zannier method) of applying [[o-minimal theory|O-minimality]] to number-theoretical and algebro-geometric problems. Thus they gave a new proof of the [[Manin–Mumford conjecture]] (which was first proved by [[Michel Raynaud]] and [[Ehud Hrushovski]]). Zannier and Pietro Corvaja in 2002 gave a new proof of [[Siegel's theorem on integral points]] by using a new method based upon the Subspace Theorem of [[Wolfgang M. Schmidt]].
With [[Jonathan Pila]] he developed a method (now known as the Pila-Zannier method) of applying [[o-minimal theory|O-minimality]] to number-theoretical and algebro-geometric problems. Thus they gave a new proof of the [[Manin–Mumford conjecture]] (which was first proved by [[Michel Raynaud]] and [[Ehud Hrushovski]]). Zannier and Pietro Corvaja in 2002 gave a new proof of [[Siegel's theorem on integral points]] by using a new method based upon the Subspace Theorem of [[Wolfgang M. Schmidt]].


==Awards & Service==
In 2005 Zannier received the Mathematics Prize of the [[Accademia dei XL]] and in 2011 an Advanced Grant from the European Research Council (ERC). He is chief editor of the ''Annali di Scuola Normale Superiore'' and a co-editor of ''[[Acta Arithmetica]]''.<ref name=CV/> In 2014 he was at Invited Speaker of the [[International Congress of Mathematicians]] in [[Seoul]].<ref>{{cite web|title=Elementary integration of differentials in families and conjectures of Pink, Wednesday, August 20, 2014 Seoul ICM|author=Zannier, Umberto|website=ICM2014 VideoSeries IL3.11|url=http://www.icm2014.org/vod/ICM-VOD-I03.html}}</ref>
In 2005 Zannier received the Mathematics Prize of the [[Accademia dei XL]] and in 2011 an Advanced Grant from the European Research Council (ERC). He is chief editor of the ''Annali di Scuola Normale Superiore'' and a co-editor of ''[[Acta Arithmetica]]''.<ref name=CV/> In 2014 he was at Invited Speaker of the [[International Congress of Mathematicians]] in [[Seoul]].<ref>{{cite web|title=Elementary integration of differentials in families and conjectures of Pink, Wednesday, August 20, 2014 Seoul ICM|author=Zannier, Umberto|website=ICM2014 VideoSeries IL3.11|url=http://www.icm2014.org/vod/ICM-VOD-I03.html}}</ref>


Revision as of 10:59, 8 December 2018

Umberto Zannier

Umberto Zannier (born 25 May 1957 in Spilimbergo) is an Italian mathematician, specializing in number theory and diophantine geometry.

Education

Zannier earned a Laurea degree from University of Pisa and studied at the Scuola Normale Superiore di Pisa with Ph.D. supervised by Enrico Bombieri.[1] Zannier was from 1983 to 1987 a researcher at the University of Padua, from 1987 to 1991 an associate professor at the University of Salerno, and from 1991 to 2003 a full professor at the Università IUAV di Venezia. From 2003 to the present he has been a Professor in Geometry at the Scuola Normale Superiore di Pisa.[2]

Career

In 2010 he gave the Hermann Weyl Lectures at the Institute for Advanced Study.[3] He was a visiting professor at several institutions, including the Institut Henri Poincaré in Paris, the ETH Zurich, and the Erwin Schrödinger Institute in Vienna. He was an Invited Speaker at the 4th European Mathematical Congress in Stockholm in 2004. Zannier was elected a corresponding member of the Istituto Veneto in 2004, a member of the Accademia dei Lincei in 2006, and a member of Academia Europaea in 2012.[2]

With Jonathan Pila he developed a method (now known as the Pila-Zannier method) of applying O-minimality to number-theoretical and algebro-geometric problems. Thus they gave a new proof of the Manin–Mumford conjecture (which was first proved by Michel Raynaud and Ehud Hrushovski). Zannier and Pietro Corvaja in 2002 gave a new proof of Siegel's theorem on integral points by using a new method based upon the Subspace Theorem of Wolfgang M. Schmidt.

Awards & Service

In 2005 Zannier received the Mathematics Prize of the Accademia dei XL and in 2011 an Advanced Grant from the European Research Council (ERC). He is chief editor of the Annali di Scuola Normale Superiore and a co-editor of Acta Arithmetica.[2] In 2014 he was at Invited Speaker of the International Congress of Mathematicians in Seoul.[4]

Selected publications

  • On the distribution of self-numbers. Proc. Amer. Math. Soc. vol. 85, 1982, 10-14 doi:10.1090/S0002-9939-1982-0647887-4 (See self number.)
  • Some Applications of Diophantine Approximation to Diophantine Equations. Forum, Udine 2003. (69 pages)
  • Lecture Notes on Diophantine Analysis. Edizioni Della Normale (Lecture Notes Scuola Normal Superiore), Appendix Francesco Amoroso, 2009. pbk reprint. 2015.
  • Some Problems of Unlikely Intersections in Arithmetic and Geometry. Annals of Math. Studies, Volume 181, Princeton University Press, 2012 (with appendix by David Masser).[5]
  • With Enrico Bombieri and David Masser: Intersecting a Curve with Algebraic Subgroups of Multiplicative Groups. International Mathematics Research Notices, Vol. 20, 1999, 1119–1140. doi:10.1155/S1073792899000628
  • A proof of Pisot's conjecture. Annals of Mathematics, Vol. 151, 2000, pp. 375–383.
  • with P. Corvaja: "A subspace theorem approach to integral points on curves", Compte Rendu Acad. Sci., 334, 2002, pp. 267–271 doi:10.1016/S1631-073X(02)02240-9
  • with P. Corvaja: Finiteness of Integral Values for the Ratio of Two Linear Recurrences. Inventiones Mathematicae, Vol. 149, 2002, pp. 431–451. doi:10.1007/s002220200221
  • with P. Corvaja: On Integral Points on Surfaces. Annals of Mathematics, Vol. 160, 2004, 705–726. arXiv preprint
  • with P. Corvaja: "On the rational approximations to the powers of an algebraic number: solution of two problems of Mahler and Mendès France." Acta Mathematica vol. 193, no. 2, 2004, 175–191. doi:10.1007/BF02392563
  • with P. Corvaja: "Some cases of Vojta's conjecture on integral points over function fields." Journal of Algebraic Geometry, Vol. 17, 2008, pp. 295–333. arXiv preprint
  • as editor with Francesco Amoroso: Diophantine approximation. Lectures given at the C.I.M.E. summer school held in Cetraro, Italy, June 28–July 6, 2000. Springer 2003.
  • with J. Pila: Rational points in periodic analytic sets and the Manin-Mumford conjecture. Atti Accad. Naz. Lincei, Cl. Sci. Fis. Mat. Nature., Rend. Lincei (9) Mat. Appl., Vol. 19, 2008, No. 2, pp. 149–162. arXiv preprint

References

  1. ^ Umberto Zannier at the Mathematics Genealogy Project
  2. ^ a b c Zannier Umberto, Scuola Normale Superiore
  3. ^ "Weyl Lectures, Umberto Zannier". Institute for Advanced Study, Video Lectures. 4 May 2010.
  4. ^ Zannier, Umberto. "Elementary integration of differentials in families and conjectures of Pink, Wednesday, August 20, 2014 Seoul ICM". ICM2014 VideoSeries IL3.11.
  5. ^ Silverman, Joseph H. (April 2013). "Review of Some Problems of Unlikely Intersections in Arithmetic and Geometry by Umberto Zannier" (PDF). Bull. Amer. Math. Soc. (N.S.). 50 (2): 353–358.
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