Junior Number Theory Seminar
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Mon, 23/01/2012 16:00 |
James Maynard |
Junior Number Theory Seminar  |
SR1 |
| We consider the prime k-tuples conjecture, which predicts that a system of linear forms are simultaneously prime infinitely often, provided that there are no obvious obstructions. We discuss some motivations for this and some progress towards proving weakened forms of the conjecture. | |||
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Mon, 30/01/2012 16:00 |
Daniel Kotzen |
Junior Number Theory Seminar |
SR1 |
| I will discuss the structure of the Selberg class - in which certain expected properties of Dirichlet series and L-functions are axiomatised - along with the numerous interesting conjectures concerning the Dirichlet series in the Selberg class. Furthermore, results regarding the degree of the elements in the Selberg class shall be explored, culminating in the recent work of Kaczorowski and Perelli in which they prove the absence of elements with degree between one and two. | |||
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Mon, 06/02/2012 16:00 |
Jan Vonk |
Junior Number Theory Seminar |
SR1 |
| The infamous inverse Galois problem asks whether or not every finite group can be realised as a Galois group over Q. We will see some techniques that have been developed to attack it, and will soon end up in the realms of class field theory, étale fundamental groups and modular representations. We will give some concrete examples and outline the so called 'rigidity method'. | |||
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Mon, 13/02/2012 16:00 |
Jan Tuitman |
Junior Number Theory Seminar |
SR1 |
| In this talk we will give an introduction to the theory of p-adic (or rigid) cohomology. We will first define the theory for smooth affine varieties, then sketch the definition in general, next compute a simple example, and finally discuss some applications. | |||
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Mon, 20/02/2012 16:00 |
Alastair Irving |
Junior Number Theory Seminar |
SR1 |
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Mon, 27/02/2012 16:00 |
Thomas Reuss |
Junior Number Theory Seminar |
SR1 |
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Mon, 05/03/2012 16:00 |
Paul-James White |
Junior Number Theory Seminar |
SR1 |
