Dynamical Systems, Fractal Geometry and Diophantine Approximations Carlos Gustavo Tamm de Araujo Moreira IMPA March 9, 2018

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• Dynamical systems
• Mathematics
• Mathematical analysis
• Geometry
• Jacob Palis
• Homoclinic orbit
• Structural stability
• Stable manifold
• Diffeomorphism
• Cantor set
• Heteroclinic orbit
• Hyperbolic set

Arithmetic and Diophantine Geometry 14Gxx [1] Matthew H. Baker, Enrique Gonz´alez-Jim´enez, Josep Gonz´alez, and Bjorn Poonen, Finiteness results for modular curves of genus at least 2, Amer. J. Math), no.

Source URL: magma.maths.usyd.edu.au

THE THUE-SIEGEL METHOD IN DIOPHANTINE GEOMETRY Paul Vojta University of California, Berkeley 28 June 2014 Abstract. This mini-course described the Thue-Siegel method, as used in the proof of

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On transcendental number theory, classical analytic functions and Diophantine geometry B. Zilber University of Oxford

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The set of non-n-th powers in a number field is diophantine Joint work with Jan Van Geel (Gent) Jean-Louis Colliot-Th´el`ene (CNRS et Universit´e Paris-Sud, Orsay) Second ERC Research period on Diophantine Geometry Cet

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The geometry of model theory and Diophantine geometry London-Paris Number Theory Seminar B. Zilber University of Oxford

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Introduction The present work grew out of an entirely unsuccessful attempt to answer some basic questions about elliptic curves over $. Start with an elliptic curve E over $, say given by a Weierstrass equation E: y2 = 4

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• Mathematics
• Analytic number theory
• Number theory
• Mathematical analysis
• Elliptic curves
• Conjectures
• Diophantine geometry
• Millennium Prize Problems
• Birch and Swinnerton-Dyer conjecture
• Rank of an elliptic curve
• Modular form
• Riemann hypothesis

The Hodge-Arakelov Theory of Elliptic Curves Shinichi Mochizuki Research Institute for Mathematical Sciences Kyoto University

Source URL: www.kurims.kyoto-u.ac.jp

• Mathematics
• Abstract algebra
• Algebra
• Algebraic geometry
• Diophantine geometry
• Number theory
• Group theory
• HodgeArakelov theory
• Arakelov theory
• Elliptic curve

LOCAL-GLOBAL PRINCIPLE FOR RATIONAL POINTS AND ZERO-CYCLES ARIZONA WINTER SCHOOL 2015 ´ ENE ` JEAN-LOUIS COLLIOT-THEL

Source URL: www.math.u-psud.fr

• Algebra
• Abstract algebra
• Mathematics
• Field theory
• Algebraic number theory
• Diophantine geometry
• Algebraic varieties
• Brauer group
• Ring theory
• Approximation in algebraic groups
• Hasse principle
• Rational variety

Algorithmic Number Theory MSRI Publications Volume 44, 2008 Computing Arakelov class groups RENE´ SCHOOF

Source URL: www.mat.uniroma2.it

• Algebra
• Abstract algebra
• Mathematics
• Algebraic geometry
• Algebraic structures
• Diophantine geometry
• Algebraic number theory
• Divisor
• Ring theory
• Picard group
• Arakelov theory
• Ample line bundle