Arizona Winter School 1998
Course Descriptions and Notes

Alexandru Buium: Differential algebras and diophantine geometry

• Buium's course abstract in html
• The reading list for Buium's course in html
• Lecture notes: dvi, ps, pdf formats.

Henri Darmon: Frey’s method and hyperelliptic curves with real multiplication

• Darmon's course abstract in html
• The reading list for Darmon's course in html
• “Rigid local systems, Hilbert modular forms, and Fermat’s last theorem” This paper is a CICMA preprint which has been submitted for publication. It is available in dvi, ps, and pdf formats, as well as on Henri Darmon's web site.

David Masser: ABC - diophantine approximation aspects

• The reading list for Masser's course in html

Barry Mazur: Visible elements in the Shafarevich-Tate group

• Mazur's course abstract in html
• The reading list for Mazur's course in html
• “Three lectures about the arithmetic of elliptic curves”: dvi, ps, pdf

Lucien Szpiro: Some cases of the discriminant conjecture

• The reading list for Szpiro's course in html

Paul Vojta: A more general ABC conjecture

• Vojta's course abstract in html
• The reading list for Vojta's course in html
• “A more general abc conjecture”: dvi, ps, pdf
• There is also a “Chapter 0” of preliminary material on number theory and algebraic geometry: dvi, ps, pdf

Felipe Voloch: The Brill-Segre formula and the ABC conjecture

• Voloch's course abstract in html
• The reading list for Voloch's course in html
• Lecture notes: dvi, ps, and pdf

Professional Development Component
Cathy Kessel: Teaching lower-division undergraduates

• Kessel spoke on “Removing the discontinuity between high-school and college” and led a workshop on “Tools to teach intuition”. There was also a panel discussion on lower division courses.
• Kessel's course abstract in html
• A relevant paper is “Teaching Mathematical Problem Solving”: ps, pdf
• References: ps, pdf

Contributed talks

• There were contributed talks by Borisov, Frankenhuysen, Luca, Wang, J. Yu, and K. Yu. Abstracts are available in html.
• The following papers are relevant to their talks:
  • Frankenhuysen: “The abc conjecture implies Roth's theorem and Mordell's conjecture”: dvi, ps, pdf
  • Wang: “A note on Wronskians and the abc theorem in function fields of prime characteristic”: dvi, ps, pdf
  • Wang: “ABC estimate, integral points, and geometry of Pn minus hyperplanes”: dvi, ps, pdf
  • J. Yu: “On arithmetic of hyperelliptic curves”: dvi, ps, pdf