mathematics

Umberto Zannier

Umberto Zannier is a mathematics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Umberto Zannier rather than just read about it. In short: Umberto Zannier (born 25 May 1957, in Spilimbergo, Italy) 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.

Key takeaways

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Reference excerpt

Umberto Zannier (born 25 May 1957, in Spilimbergo, Italy) 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.

Career 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. In 2010 he gave the Hermann Weyl Lectures at the Institute for Advanced Study. 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. 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.

Awards & Service Zannier 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. In 2014 he was an Invited Speaker of the International Congress of Mathematicians in Seoul. 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.

Selected publications Zannier, U. (1982). "On the distribution of self-numbers". Proceedings of the American Mathematical Society. 85: 10–14. doi:10.1090/S0002-9939-1982-0647887-4. (See self number.) Zannier, U. (2003). Some Applications of Diophantine Approximation to Diophantine Equations (with Special Emphasis on the Schmidt Subspace Theorem). Forum Editrice. Zannier, U. (2015) [2009]. Lecture Notes on Diophantine Analysis (Reprint ed.). Springer. ISBN 978-88-7642-517-2. Zannier, U.; Masser, D. W. (2012). Some Problems of Unlikely Intersections in Arithmetic and Geometry. Annals of Mathematics Studies. Vol. 181. Princeton University Press. ISBN 978-0-691-15371-1. Bombieri, E.; Masser, D.; Zannier, U. (1999). "Intersecting a curve with algebraic subgroups of multiplicative groups". International Mathematics Research Notices (20): 1119. doi:10.1155/S1073792899000628.{{cite journal}}: CS1 maint: unflagged free DOI (link) Zannier, U. (2000). "A Proof of Pisot's dth Root Conjecture" (PDF). Annals of Mathematics. 151 (1): 375–383. doi:10.2307/121122. JSTOR 121122. Corvaja, P.; Zannier, U. (2002). "A subspace theorem approach to integral points on curves". Comptes Rendus. Mathématique. 334 (4): 267–271. doi:10.1016/S1631-073X(02)02240-9. Corvaja, P.; Zannier, U. (2002). "Finiteness of integral values for the ratio of two linear recurrences". Inventiones Mathematicae. 149 (2): 431–451. Bibcode:2002InMat.149..431C. doi:10.1007/s002220200221. Corvaja, P.; Zannier, U. (2004). "On integral points on surfaces". Annals of Mathematics. 160 (2): 705–726. arXiv:math/0206100. doi:10.4007/annals.2004.160.705. Corvaja, P.; Zannier, U. (2004). "On the rational approximations to the powers of an algebraic number: Solution of two problems of Mahler and Mendès France". Acta Mathematica. 193 (2): 175–191. doi:10.1007/BF02392563. Corvaja, P.; Zannier, U. (2007). "Some cases of Vojta's conjecture on integral points over function fields". Journal of Algebraic Geometry. 17 (2): 295–333. arXiv:math/0512074. doi:10.1090/S1056-3911-07-00489-4. Amoroso, F.; Zannier, U., eds. (2003). Diophantine Approximation: Lectures Given at the C.I.M.E. Summer School Held in Cetraro, Italy, June 28 – July 6, 2000. Lecture Notes in Mathematics. Vol. 1819. Springer. doi:10.1007/3-540-44979-5. ISBN 978-3-540-40392-0. Zannier, U.; Pila, J. (2008). "Rational points in periodic analytic sets and the Manin-Mumford conjecture". Rendiconti Lincei. Scienze Fisiche e Naturali. 19 (2): 149. arXiv:0802.4016. Bibcode:2008RLSFN..19..149Z. doi:10.4171/rlm/514.

References

External links Umberto Zannier at the Mathematics Genealogy Project Academia Europaea Hermann Weyl Lectures delivered at the Institute for Advanced Study, 2010 "An Overview of Some Problems of Unlikely Intersections - Umberto Zannier". YouTube. 1 September 2016. (Tuesday, May 4th, 2010) "Unlikely Intersections in Multiplicative Groups and the Zilber Conjecture - Umberto Zannier". YouTube. 1 September 2016. (Wednesday, May 5th, 2010) "Unlikely Intersections in Elliptic Surfaces and Problems of Masser - Umberto Zannier". YouTube. 1 September 2016. (Tuesday, May 11th, 2010) "About the André-Oort Conjecture - Umberto Zannier". YouTube. 1 September 2016. (Wednesday, May 12th, 2010)

Illustrations

Worked examples

Example 1 — a first encounter with Umberto Zannier

Start with the simplest possible case. Write down what Umberto Zannier claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In mathematics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Umberto Zannier before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Umberto Zannier ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Umberto Zannier

In research: Umberto Zannier appears in mathematics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Umberto Zannier in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Umberto Zannier is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1957 births, 20th-century Italian mathematicians, 21st-century Italian mathematicians, so understanding it makes those chapters shorter.
In everyday life: Look for Umberto Zannier outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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Frequently asked questions

What is Umberto Zannier in simple terms?

Umberto Zannier (born 25 May 1957, in Spilimbergo, Italy) 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 Bombier…

Why does Umberto Zannier matter?

Because it connects several mathematics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Umberto Zannier?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Umberto Zannier.