7 November 2011

16:00

7 November 2011

16:00

31 October 2011

16:00

24 October 2011

16:00

Sebastian Pancratz

Abstract

<p>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.</p>

17 October 2011

16:00

Jan Vonk

Abstract

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.

10 October 2011

16:00

James Maynard

Abstract

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.

21 June 2011

14:00

Jan Tuitman

Abstract

(Note change in time and location)
The purpose of this talk is to give an introduction to the theory and
practice of integer factorization. More precisely, I plan to talk about the
p-1 method, the elliptic curve method, the quadratic sieve, and if time
permits the number field sieve.

16 May 2011

16:00

9 May 2011

16:00

Frank Gounelas

Abstract

<p>I will describe why e^{\pi\sqrt{163}} is almost an integer and how this is related to Q(\sqrt{-163}) having class number one and why n^2-n+41 is prime for n=0,...,39. Bits and pieces about Gauss's class number problem, Heegner numbers, the j-invariant and complex multiplication on elliptic curves will be discussed along the way.</p>

7 March 2011

16:00

28 February 2011

16:00