Forthcoming Seminars › Seminar Series

Junior Number Theory Seminar

Mon, 10/10/2011
16:00 		James Maynard (Oxford) Junior Number Theory Seminar Add to calendar SR1
Small Gaps Between Primes

We discuss conjectures and results concerning small gaps between primes. In particular, we consider the work of Goldston, Pintz and Yildrim which shows that infinitely often there are gaps which have size an arbitrarily small proportion of the average gap.
Mon, 17/10/2011
16:00 		Jan Vonk Junior Number Theory Seminar Add to calendar SR1
On Maeda's conjecture

The theory of modular forms owes in many ways lots of its results to the existence of the Hecke operators and their nice properties. However, even acting on modular forms of level 1, lots of basic questions remain unresolved. We will describe and prove some known properties of the Hecke operators, and state Maeda's conjecture. This conjecture, if true, has many deep consequences in the theory. In particular, we will indicate how it implies the nonvanishing of certain L-functions.
Mon, 24/10/2011
16:00 		Sebastian Pancratz Junior Number Theory Seminar Add to calendar SR1
Radix conversion for polynomials
We describe various approaches to the problem of expressing a polynomial $ f(x) = \sum_{i=0}^{m} a_i x^i $ in terms of a different radix $ r(x) $ as $ f(x) = \sum_{j=0}^{n} b_j(x) r(x)^j $ with $ 0 \leq \deg(b_j) < \deg(r) $. Two approaches, the naive repeated division by $ r(x) $ and the divide and conquer strategy, are well known. We also describe an approach based on the use of precomputed Newton inverses, which appears to offer significant practical improvements. A potential application of interest to number theorists is the fibration method for point counting, in current implementations of which the runtime is typically dominated by radix conversions.
Mon, 07/11/2011
16:00 		Paul-James White Junior Number Theory Seminar Add to calendar SR1
The Local Langlands correspondence
Mon, 21/11/2011
16:00 		Netan Dogra Junior Number Theory Seminar Add to calendar SR1
P-adic L-functions and their special values
This talk will begin by recalling classical facts about the relationship between values of the Riemann zeta function at negative integers and the arithmetic of cyclotomic extensions of the rational numbers. We will then consider a generalisation of this theory due to Iwasawa, and along the way we shall define the p-adic Riemann zeta function. Time permitting, I will also say something about what zeta values at positive integers have to do with the fundamental group of the projective line minus three points
Mon, 28/11/2011
16:00 		Thomas Reuss Junior Number Theory Seminar Add to calendar SR1
The abc conjecture

For any corrections/updates to these listings, please contact seminars [-at-] maths [dot] ox [dot] ac [dot] uk.

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