Past Junior Number Theory Seminar

11 November 2013
17:00
Alastair Irving
Abstract
I will describe how a sieve method can be used to establish the Hasse principle for the variety $$f(t)=N(x_1,\ldots,x_k),$$ where $f$ is an irreducible cubic and $N$ is a norm form for a number field satisfying certain hypotheses.
  • Junior Number Theory Seminar
28 October 2013
17:00
Netan Dogra
Abstract
Mixed motives turn up in number theory in various guises. Rather than discuss the rather deep foundational questions involved, this talk will aim to give several illustrations of the ubiquity of mixed motives and their realizations. Along the way I hope to mention some of: the Mordell-Weil theorem, the theory of height pairings, special values of L-functions, the Mahler measure of a polynomial, Galois deformations and the motivic fundamental group.
  • Junior Number Theory Seminar
21 October 2013
17:00
Ben Green
Abstract
It is well known that one can attach Galois representations to certain modular forms, it is natural to ask how one might generalise this to produce more Galois representations. One such approach, due to Gross, defines objects called algebraic modular forms on certain types of reductive groups and then conjectures the existence of Galois representations attached to them. In this talk I will outline how for a particular choice of reductive group the conjectured Galois representations exist and are the classical modular Galois representations, thus providing some evidence that this is a good generalisation to consider.
  • Junior Number Theory Seminar
14 October 2013
17:00
Jan Vonk
Abstract
<p>We will discuss some geometric methods to study Diophantine equations. We focus on the case of elliptic curves and their natural generalisations: Abelian varieties, Calabi-Yau manifolds and hyperelliptic curves.&nbsp;</p>
  • Junior Number Theory Seminar

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