Mardi, 13 mars 2007, 18h00, salle BS 0.03,
campus Limpertsberg
Professeur Anton Thalmaier
Faculté des Sciences, de la Technologie et de la Communication, Unité de Recherche en Mathématiques:
Conférence en langue anglaise
"Brownian motion: from pollen grains in water to global geometry",
In 1828 Robert Brown, a famous nineteenth century botanist,
published his microscopical investigations that dust grains suspended
in water perform a rapid and highly irregular motion. With the most
careful scrutiny, he ruled out that these erratic movements were
signatures of life.
In 1905 Albert Einstein, unaware of the work of Brown, predicted the
phenomenon on theoretical grounds, caused through a bombardment by the
molecules of the liquid, and formulated a correct quantitative theory
of it.
It is remarkable that already 5 years before Einstein, in 1900, Louis
Bachelier defended at the Sorbonne his thesis "Théorie de la
Speculation" in which the mathematical theory of Brownian motion is
initiated and used for the modeling of price movements and evaluation
of contingent claims in financial markets.
During the last 100 years Brownian motion became not only the
keystone of a fully probabilistic formulation of statistical mechanics,
as well as for financial engineering on the stock markets, in
mathematics it grew to an universal object that lies at the interface
of Analysis, Geometry and Probability. Brownian motion feels curved
spaces and helps to connect local and global geometry.
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