Junior Number Theory Seminar

The weekly Junior Number Theory Seminars provide the opportunity for a structured presentation and informal discussions. The seminars are 50 minutes long and are presented by either a graduate student or a post-doctoral researcher; interested undergraduates are also invited to attend. After the seminar we usually head to the pub where more questions and discussions, mathematical or otherwise take place. 

Forthcoming Seminars 

There are no seminars currently scheduled for this series.

Hilary Term 2009

In previous terms people have talked about their own research, or we have taken turns to present different chapters of a book which might be of common interest. This term we decided to present some introductory ideas, which some of us come across in our day-to-day work. The purpose is not to present exciting and new results, but rather to 'demystify' some of the different techniques of number theory, and aim at broadening people's interest.


PDF icon Week 2: "Galois Cohomology"

PDF icon Week 3: "Jensen's Theorem"  

PDF icon Week 4: "Dirichlet's Approximation Theorem" 

PDF icon Week 5: "Hasse's Theorem for Elliptic Curves" 

PDF icon Week 6: "Ostrowski's Theorem" 

PDF icon Week 7: "Primality Testing"

PDF icon Week 8: "The Chevalley-Warning Theorem"

Trinity Term 2009 

Owing to conferences and other commitments we were not able to run seminars in the first three weeks of term. The format for the remaining five weeks is the same as the previous term, viz. gentle introductions to theorems with some 'problem sheets' attached.

PDF icon Week 4: "An Introduction to the Birch--Swinnterton-Dyer Conjecture. I"

PDF icon Week 5: "An Introduction to the Birch--Swinnterton-Dyer Conjecture. II"

PDF icon Week 6: "An Introduction to the Birch--Swinnterton-Dyer Conjecture. III"

PDF icon Week 7: "A Minimisation Method of W.M. Schmidt" 

PDF icon Week 8: "An Introduction to Tauberian Theorems"  

Notes on these seminars, which is some cases include the "solutions", will appear soon.