
Prof. Martin Hairer FRS
University of Warwick, UK
Fields Medal 2014
The Mathematics of Randomness
From the gambling machines in a Casino to the predictions of next
week's weather, the world that surrounds us is governed by seemingly
random events. How do mathematicians make sense of this and what does it
even mean to "predict" something inherently random? We will explore
these questions and see what are the main guiding principles of our
modern understanding of randomness. Along the way, we will see how the
works of an 18th century egyptologist and a 19th century biologist allow
today's banks to model the stock market.
Dienstag, 29. November 2016, 19.30 Uhr
Random Loops
A "rubber band" constrained to remain on a manifold evolves by trying to
shorten its
length, eventually settling on a closed geodesic, or collapsing
entirely. It is natural to try to
consider a noisy version of such a model where each segment of the band
gets pulled in random
directions. Trying to build such a model turns out to be surprisingly
difficult and generates a
number of nice geometric insights, as well as some beautiful algebraic
and analytical objects. We
will survey some of the main results obtained on the way to this
construction.
Mittwoch, 30. November 2016, 17.15 Uhr
Taming Infinities
Some physical and mathematical theories have the unfortunate feature
that if one takes them at face value, many quantities of interest appear
to be infinite! Various techniques, usually going under the common name
of “renormalization” have been developed over the years to address this,
allowing mathematicians and physicists to tame these infinities. We will
tip our toes into some of the mathematical aspects of these techniques
and we will see how they have recently been used to make precise
analytical statements about the solutions of some equations whose
meaning was not even clear until now
Donnerstag, 1. Dezember 2016, 19.30 Uhr
