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HU Credits:
1
Degree/Cycle:
2nd degree (Master)
Responsible Department:
Mathematics
Semester:
1st Semester
Teaching Languages:
English and Hebrew
Campus:
E. Safra
Course/Module Coordinator:
Prof Ari Shnidman
Coordinator Office Hours:
By appointment
Teaching Staff:
Prof Schneidman Ari
Course/Module description:
The purpose of this lunch seminar is to expose students a wide array of techniques and results in number theory and arithmetic geometry. The theme of the semester will be "explicit number theory". Our aim is to keep prerequisites low though exactly how much background is assumed will depend on the week. Prior exposure to algebraic or analytic number theory or algebraic curves should be sufficient to follow for most weeks.
Course/Module aims:
To describe central topics in number theory and algebraic geometry
Learning outcomes - On successful completion of this module, students should be able to:
To understand central topics in number theory and algebraic geometry
Attendance requirements(%):
100
Teaching arrangement and method of instruction:
Lectures
Course/Module Content:
Possible topics:
Integral points and Runge's method; Skolem's method and Skolem-Mahler-Lech's theorem;
Chaubaty's theorem and Chaubaty-Coleman method;
Siegel's theorem;
Belyi's theorem;
Davenport-Zannier polynomials, dessins, and Hall's conjecture;
Hasse-Minkowski theorem;
Failures of local-to-global principle and Cassels-Tate pairings; Classical algebraic/arithmetic geometry via examples of curves and surfaces
Required Reading:
None
Additional Reading Material:
None
Grading Scheme :
Attendance / Participation in Field Excursion 100 %
Additional information:
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