Mathematisches Institut Georg-August-Universität Göttingen

Clay Mathematics Institute Summer School "Arithmetic geometry" -- Computational Seminar

Week 1

	July 17	July 18	July 19	July 20	July 21
16:00	S. Wiedmann Introduction to computers at the MI	G. Pfister Applying Computer Algebra in Mathematical Research: An example from Group Theory. Lecture Part 1 Lecture Part 2	J. Jahnel Rational points on hypersurfaces Lecture	M. Stoll Computations with genus 2 curves	M. Stoll Computations with genus 2 curves Lecture
17:30-18:30 (Multimediaraum)	Barbecue (17:30)	Exercises Article Singular Scripts ex-magma1.mag	Exercises Simple Magma Exercises from the Book of Joyner, Kreminski, Turisco	Exercises with M. Stoll ellchab.magma kleinquartic.magma g2ff.magma ratcycles.magma	Exercises with M. Stoll

Week 2

	July 24	July 25	July 26	July 27	July 28
16:00	H. Chapdelaine The generalised Fermat equation		S. Wiedmann Zeta functions of regular graphs Lecture Graph movie
17:30-18:30 (Multimediaraum)	Exercises Simple Magma Exercises from the Book of Joyner, Kreminski, Turisco		Exercises ad2Tmatrix LPS.mag terras.mag		P. Charollois Frey's method and ternary Diophantine equations

Week 3

	July 31	August 1	August 2	August 3	August 4
16:00	N. Elkies Newton iteration for simultanous algebraic equations	O. Labs Construction of hypersurfaces with singularities via finite fields	J. Voight Shimura curve computations	J. Schicho Construction of rational points on rational surfaces	M. Greenberg Elliptic curves over imaginary quadratic fields
17:30-18:30 (Multimediaraum)	Exercises with N. Elkies K3family.gp newton.gp	Exercises with O. Labs exercises.pdf searchInFamilies.lib searchInFamilies_cub4_all.sin olitools.lib searchInFamilies_manySings.lib searchInFamilies_quart16_exercise.sin searchInFamilies_quint31_exercise.sin surfex.lib surfex_0_89_03.tar.gz	Exercises with J. Voight	Exercises with J. Schicho dp6.tar dp8.tar Type: tar xfv dp6.tar resp. tar xfv dp8.tar	Exercises

Available Software

Exercises and examples for magma

• Simple Exercises in MAGMA: Basic Syntax, Data Structures
• Number Theory Exercises: Prime numbers, Divisibility, Remainder
• Polynomials and Rings Exercises: Finite Fields, Rings, Polynomials, RSA for Polynomials
• Coding Theory Exercises: Hamming Codes, Reed-Muller Codes, Cyclic Codes

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Multimediaraum

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