Umberto Zannier

Umberto Zannier

Umberto Zannier (born May 25, 1957 in Spilimbergo ) is an Italian mathematician who deals with number theory and Diophantine geometry. He is professor of geometry at the Scuola Normale Superiore .

Life

Zannier graduated from the University of Pisa with a Laureate degree and studied with Enrico Bombieri at the Scuola Normale Superiore . From 1983 to 1987 he was at the University of Padua , from 1987 to 1991 assistant professor of algebra at the University of Salerno , from 1991 to 2003 professor of geometry at the Università IUAV di Venezia in Venice and from 2003 professor of geometry at the Scuola Normale Superiore.

In 2010 he gave the Hermann Weyl Lectures at the Institute for Advanced Study and was at the Institut Henri Poincaré in Paris, at the ETH Zurich and at the Erwin Schrödinger Institute in Vienna. He was invited speaker at the 4th European Congress of Mathematicians in Stockholm 2004 (On the integral points on certain algebraic varieties). Zannier became a corresponding member of the Istitutio Veneto in 2004 and he is a member of the Accademia dei Lincei (2006) and the Academia Europaea (2012).

With Jonathan Pila he developed a method of applying O-minimality to number theoretic and algebro-geometric problems, the Pila-Zannier method. With this they proved (after Michel Raynaud and Ehud Hrushovski ) again the Manin-Manford conjecture. Zannier and P. Corvaja 2002 proved Siegel's theorem about the finite number of integer points on curves of gender using Wolfgang Schmidt's subspace theorem . ${\displaystyle g>0}$

In 2005 he received the Mathematics Prize of the Accademia dei XL and in 2011 an Advanced Grant from the European Research Council (ERC). He is editor of the Annali di Scuola Normale Superiore and co-editor of Acta Arithmetica. In 2014 he was invited speaker at the ICM in Seoul (Elementary integration of differentials in families and conjectures of Pink). For 2020/21 he is the plenary speaker at the 8th European Congress of Mathematicians .

Fonts

• Some Applications of Diophantine Approximation to Diophantine Equations. Forum, Udine 2003.
• Lecture Notes on Diophantine Analysis. Edizioni Della Normale (Lecture Notes Scuola Normale Superiore), Appendix Francesco Amoroso, 2009.
• Some Problems of Unlikely Intersections in Arithmetic and Geometry . In: Annals of Math. Studies , Volume 181, Princeton University Press, 2012 (with appendix by David Masser).
• With Enrico Bombieri, David Masser : Intersecting a Curve with Algebraic Subgroups of Multiplicative Groups . In: International Mathematics Research Notices , Volume 20, 1999, pp. 1119-1140.
• A proof of Pisot conjecture ${\displaystyle d^{th}}$ . In: Annals of Mathematics , Volume 151, 2000, pp. 375-383.
• With P. Corvaja: A subspace theorem approach to integral points on curves . In: Compte Rendu Acad. Sci. , 334, 2002, pp. 267-271
• With P. Corvaja: Finiteness of integral values ​​for the ratio of two linear recurrences . In: Inventiones Mathematicae , Volume 149, 2002, pp. 431-451.
• With P. Corvaja: On integral Points on Surfaces . In: Annals of Mathematics , Volume 160, 2004, pp. 705-726.
• With P. Corvaja: Some cases of Vojta's conjecture on integral points over function fields . In: Journal of Algebraic Geometry , Volume 17, 2008, pp. 295-333.
• Editor with F. Amoroso: Diophantine approximation . Lectures given at the CIME 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 . In: Atti Accad. Naz. Lincei, Cl. Sci. F sharp. Mat. Natur., Rend. Lincei (9) Mat. Appl. , Volume 19, 2008, No. 2, pp. 149-162.

Web links

• Homepage. ( Memento from September 19, 2015 in the Internet Archive )
• Academia Europaea

Individual evidence

1. ↑ Umberto Zannier in the Mathematics Genealogy Project (English)
2. ^ Weyl Lectures