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Svein Olav Nyberg Norwegian citizen, born 1966 |
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| Address supplied upon request
+47-93248331 |
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Email:  Internet: http://www.nonserviam.com/solan/ |
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Key Words
- Strong Innovative and Analytic abilities
- Excellent Communication Skills
- PhD in mathematics: Probability
Education
- PhD, mathematics (1996). Dissertation: "Brownian Motion on Simple Fractal spaces".
- MSc, mathematics (1991). Thesis: "Simple Fractal spaces".
- BSc, mathematics (1988). Other subjects: Physics, programming, statistics, astronomy.
Computing Skills
Languages: Simula, BASIC, Maple.
Operating systems: Macintosh - familiar with most major Mac software. UNIX, Win95.
Work Positions
Computas AS Senior IT engineer 01.10.98-present University of Edinburgh UK EPSRC Post-doc 01.09.96-31.08.98 University of Oslo University Scholarship 16.10.95-31.12.95 University of Oslo NAVF Scholarship 01.07.92-31.06.95 University of Oslo University Scholarship 01.09.91-31.12.91
Presentation
Invited lecturer: BI, a financial college outside Oslo: Two 2-hour lectures covering stochastic analysis in Darrell Duffie: "Dynamic Asset Pricing Theory".
Teaching Assistant: University of Oslo, Autumn 1988 - Spring 1992 and Autumn 1995.
Scientific presentations: A series of presentations / lecture series on my own and others' work in the field of analysis/diffusion on fractals at both
- my home universities: University of Oslo (Norway), University of British Columbia (Vancouver, Canada), University of Edinburgh (Scotland);
- international conferences:
"Fractomorphisms, convergence of fractals and convergence of processes". Lecture held at the International Conference in Probability in Vancouver, August 1997, and later at the North British Probability seminar series November 7th 1997. The talks were based on the paper "Fractomorphisms, Convergence of Fractals and Convergence of Processes" above. At this presentation, I covered new ideas from my thesis on how Brownian motions changes as the underlying (fractal) space changes.
"Brownian motion on Simple fractal spaces", lecture at the conference "Fractal Geometry and Stochastics", in Finsterbergen, Germany, 12-18 June 1994. A presentation of the fundamental ideas behind what happens with the physical properties of a fractal under `continuous' changes. I was one of the few who managed to keep Mandelbrot awake.
"Brownian motion on Simple fractal spaces", lecture at the international conference on Non-Standard Analysis in Blaubeuren, Germany, July 1992. First presentation of my Ph.D. work, covering the subject of diffusions on fractals where `cells' have unequal scaling, and the use of the method of non-standard analysis to prove that such diffusions exist.
Scientific publications:
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"Fractomorphisms, Convergence of Fractals and Convergence of
Processes". Submitted to Annals of Applied Probability. This paper
moves the study of Brownian motion on fractals a closer to applications
by proving that some leeway is permissible when modelling physical
mediums as fractals: Small errors in the choice of give only small
errors in physical properties.
- "The discrete Einstein relation". In "Circuits, Systems and Signal Processing", Vol. 16, No 5, 1997, Pp. 547-557. Introduces a topological notion of graph, and proves a fundamental relation for random walks on graphs connecting commute time, `mass' and `resistance' in a simple relation known as "the Einstein relation". The study of random walks on graphs also has applications to the design of algorithms.
- "Brownian Motion on Simple Fractal Spaces". Stochastics and Stochastics Reports, Vol. 55, pp. 21-45. In this paper the existence of a type of diffusion known as "Brownian motion" was proved for a class of fractals which is composed of parts similar to the whole but where the parts may be differently scaled.
- "The discrete Einstein relation". In "Circuits, Systems and Signal Processing", Vol. 16, No 5, 1997, Pp. 547-557. Introduces a topological notion of graph, and proves a fundamental relation for random walks on graphs connecting commute time, `mass' and `resistance' in a simple relation known as "the Einstein relation". The study of random walks on graphs also has applications to the design of algorithms.
Short description of my work
The emphasis has been on diffusions on fractals, and in particular on the question of how diffusions change under changes of the fractal. The motivation for this are concerns of what happens if we model physical mediums as fractals: Will a small deviance in the medium modelled give approximately correct or totally wrong results? The conclusion in the papers above is that if we have a proper measure of difference between fractals, "similar" fractals will also have "similar" physical characteristics. Other concerns have been to widen the class of fractals on which physical processes are studied so as to come closer to applicability of the theory. For more detail, see my work section
Keywords: Probability, stochastic processes, fractal geometry.
Memberships
- Institute of Mathematical Statistics
- Edinburgh Mathematical Society
- Norwegian Mathematical Society
International experience
Post-doc at the Dept. of Mathematics, University of Edinburgh, 9/96-8/98. Invited to work on an extension of the Ph.D. thesis.
Visiting the Dept. of Mathematics, University of British Columbia, 2/94-12/94 while working on Ph.D. thesis. The main benefit of the stay was the high international standard of their probability group.
References
- Leif Bjørn Skorpen, Volda college, Norway - LeifBjorn.Skorpen@hivolda.no - Phone 7007 5359
- T. Lindstrøm, Dept. of Math., University of Oslo, Norway - lindstro@math.uio.no
- B.M. Hambly, Dept. of Math., University of Edinburgh, UK - bmh@maths.ed.ac.uk
- H. Holden, Dept. of Math., NTNU, Norway - holden@math.ntnu.no
- See also the scanned reference section
