Computational Mathematics Seminar: Diophantine approximation in positive characteristic and linear complexity profiles
2009.03.11 |
| Date | Tue Apr 14 |
| Time | 15:15 — 16:15 |
| Location | Aud. D1, Department of Mathematics |
Speaker: Simon Kristensen, University of Aarhus, Department of Mathematics
Abstract: Diophantine approximation is the quantitative study of the density of the rational numbers inside the real numbers. A fruitful analogue over function fields in positive characteristic has been developed over the years.
This setup has been applied toproblems in linear complexity profiles. Linear complexity profiles are a refinement of the global linear complexity,a well known complexity measure in the theory of stream ciphers. The linear complexity profile of a sequence gives a measure of the deviation of the sequence from a truly random sequence.
In the talk, I will describe the field of Diophantine approximation in positive characteristic and outline several results. A particular emphasis will be put on the so-called metrical theory, wherein the measure and Hausdorff dimension of involved sets is studied. I will also describe the relation between Diophantine approximation and complexity profiles.
Many of the mathematical technicalities will be omitted, and all key concepts will be definedand explained.
See www.daimi.au.dk/~bjarke/compmath/ for more information on the seminar series.