Gisbert Wüstholz

Gisbert Wüstholz, 2005

Gisbert Wüstholz (born June 4, 1948 in Tuttlingen ) is a German mathematician who is internationally known for his fundamental contributions to number theory (in the field of the theory of transcendent numbers and Diophantine approximations ) and arithmetic algebraic geometry.

Education, Career and Research

Gisbert Wüstholz was born in Tuttlingen (Baden-Württemberg) in 1948 and studied from 1967 to 1973 at the Albert Ludwig University of Freiburg , where he received his doctorate in 1978 under Theodor Schneider . At the invitation of Friedrich Hirzebruch , he spent a year as a postdoc at the Rheinische Friedrich-Wilhelms-Universität Bonn . He then received a postdoc position at the Bergische Universität Wuppertal , where he worked for Walter Borho from 1979 to 1984 and then moved to Bonn as a professor at the newly founded Max Planck Institute for Mathematics . From 1985 to 1987 he was a full professor of mathematics in Wuppertal and was elected full professor of mathematics at the ETH Zurich in 1987 . He founded the Zurich Graduate School in Mathematics in 2003 and was its director until 2008. He has been a professor emeritus at ETH Zurich since 2013.

He is a member of the German Academy of Sciences Leopoldina (since 2000), the Berlin-Brandenburg Academy of Sciences (since 2003), the Academia Europaea (since 2008), where he was chairman of the mathematics section from 2011-2013, and of the European since 2016 Academy of Sciences and Arts . In 1999 he became an Honorary Advisory Professor at Tongji University , Shanghai. From 2011 he was Senator for Mathematics at the Leopoldina. He is honorary professor at the Graz University of Technology (since 2017).

Gisbert Wüstholz spent a long time at various universities and research institutes, for example at the University of Michigan in Ann Arbor (1984, 1988) and at the Institute des Hautes Études Scientifiques in Bures-sur-Yvette (1987). He was a member of the Institute for Advanced Study in Princeton (1986, 1990, 1994/95, 2011), 1992 Visiting Fellow Commoner at Trinity College in Cambridge for research projects with Alan Baker and the following year he attended the Mathematical Sciences Research Institute in Berkeley (1993 ). He was a frequent guest at the Max Planck Institute for Mathematics in Bonn and at the International Erwin Schrödinger Institute for Mathematical Physics (ESI) in Vienna. He has been a guest at the University of Zurich since 2015 . In the academic year 2017/18 he was a Senior Research Fellow at the Freiburg Institute for Advanced Studies (FRIAS) .

Gisbert Wüstholz has had close relationships with a number of universities in Asia since 1980: he spent a few months each at Kyushu University in Fukuoka (1992), the Morningside Center of Mathematics of the Chinese Academy of Sciences in Beijing, and at Hong Kong University of Science and Technology (HKUST) (1996, 1997, 2006, 2010) and at the University of Hong Kong (HKU) (1999, 2011, 2012). Several visits took him to the Vietnam Institute for Advanced Study in Mathematics (VIASM) (2010, 2017), the Korea Institute for Advanced Study (KIAS) and the National Taiwan University in Taipei (2009, 2013, 2016).

In 1986 Gisbert Wüstholz gave an invited lecture at the International Congress of Mathematicians (ICM) in Berkeley, in 1992 the Mordell lecture in Cambridge, in 2001 the 13th Kuwait founding lecture, and an invited lecture at the Leonhard Euler Festival in St. Petersburg in 2007 the 300th birthday of Leonhard Euler and in 2008 the academy lecture at the Berlin-Brandenburg Academy of Sciences .

His research interests are algebraic geometry and number theory (especially Diophantine approximations and transcendence theory) and Hodge theory (periods). Highlights of his scientific work are his Analytical Subgroup Theorem (1989) based on the multiplicity estimates of group variety published in 1989 , his proof for the Abelian analog of Lindemann's famous theorem (wrongly called Lindemann-Weierstrass theorem ), which refuted the square of the circle, and the joint work with Gerd Faltings on Wolfgang Schmidt's subspace theorem as well as the isogeny estimates for Abelian varieties together with David Masser proved that they offer an alternative approach to the Mordell conjecture . The joint work with Alan Baker on linear forms in logarithms should also be mentioned. His Analytical Subgroup Theorem is now a central result of the transcendence theory. It says that the only algebraic points of an analytic subgroup of a commutative algebraic group are above in an algebraic subgroup of . ${\displaystyle A}$ ${\displaystyle {\overline {\mathbb {Q} }}}$ ${\displaystyle A}$

Fonts (selection)

Books

• with G. Faltings: Rational Points . Aspects of Mathematics, E6. Friedr. Vieweg & Sohn, Braunschweig (1st ed. 1984, 2nd ed. 1986), 3rd ed., 1992. Essays from the seminar of the Max Planck Institute for Mathematics, 1983/1984 in Bonn / Wuppertal, with an appendix by Wüstholz in 3. Edition.
• A Panorama of Number Theory or the View from Baker's Garden , editor. Cambridge University Press, Cambridge, 2002. ISBN 0-521-80799-9 .
• with A. Baker: Logarithmic Forms and Diophantine Geometry . New Mathematical Monographs 9 . Cambridge University Press, Cambridge, 2007. ISBN 978-0-521-88268-2 .

Essays

• About the Abelian analog of Lindemann's Theorem I , Inventiones Mathematicae , Volume 72, No. 3, 1983, pp. 363-388. doi: 10.1007 / BF01398393 .
• Algebraic Groups, Hodge Theory and Transcendence , Proceedings of the International Congress of Mathematicians, Vol. 1, 2 (Berkeley, Calif. 1986), pp. 476-483, Amer. Math. Soc., Providence, RI, 1987.
• Multiplicity Estimates on Group Varieties , Annals of Mathematics , Series 2, Volume 129, No. 3, 1989, pp. 471-500. doi: 10.2307 / 1971514 .
• Algebraic Points on Analytic Subgroups of Algebraic Groups , Annals of Mathematics , Series 2, Volume 129, No. 3, 1989, pp. 501-517. doi: 10.2307 / 1971515 .
• with D. Masser: Periods and minimal abelian subvarieties , Annals of Mathematics , Series 2, Volume 137, No. 2, 1993, pp. 407-458. doi: 10.2307 / 2946542 .
• with D. Masser: Isogeny estimates for abelian varieties and finiteness theorems , Annals of Mathematics , Series 2, Volume 137, No. 3, 1993, pp. 459-472. doi: 10.2307 / 2946529 .
• with A. Baker: Logarithmic forms and group varieties , J. Reine. Angew. Math. , Vol. 442, 1993, pp. 19-62. doi: 10.1515 / crll.1993.442.19 .
• with G. Faltings: Diophantine approximations on projective spaces , Inventiones Mathematicae , Volume 116, No. 1-3, 1994, pp. 109-138. doi: 10.1007 / BF01231559 .
• with D. Masser: Factorization estimates for Abelian varieties , Publ. Math. Inst. Hautes Études Sci. , Vol. 81, 1995, pp. 5-24. ISSN: 0073-8301 .
• with PB Cohen: Application of the André-Oort Conjecture to some questions in transcendence , In: A Panorama in Number Theory or The View from Baker's Garden (Zurich 1999), Cambridge University Press, 2002, pp. 89-106. doi: 10.1017 / CBO9780511542961.007 .
• Leibniz 'conjecture, periods & motives , In: Colloquium De Giorgi 2009, Colloquia, 3, Ed. Norm., Pisa, 2012, pp. 33-42. doi: 10.1007 / 978-88-7642-387-1_3 .

Web links

Commons : Gisbert Wüstholz  - Collection of images, videos and audio files

• Gisbert Wüstholz in the Mathematics Genealogy Project (English) .
• Website by Gisbert Wüstholz at the ETH Zurich.
• Gisbert Wüstholz , ETHZ-UZh-Sbg Arithmetic and Geometry Research Group
• Gisbert Wüstholz , Freiburg Institute for Advanced Studies (FRIAS)

Individual evidence

1. ^ Member entry by Gisbert Wüstholz at the German Academy of Natural Scientists Leopoldina , accessed on July 20, 2016.
2. ↑ Gisbert Wüstholz . Member entry at the Berlin-Brandenburg Academy of Sciences , accessed on August 12, 2018.
3. ↑ Directory of members: Gisbert Wüstholz. Academia Europaea , accessed on August 16, 2017 . 
4. ↑ Gisbert Wüstholz. Member of the European Academy of Sciences and Arts , accessed on August 12, 2018.
5. ^ G. Wüstholz: Algebraic points on analytic subgroups of algebraic groups , Annals of Mathematics , Series 2, Volume 129, No. 3, 1989, pp. 501-517. doi: 10.2307 / 1971515 .