Stieltjes Afternoon

date: Friday 26 January, 2001
location: Van Trier zaal, Traverse (former Bestuursgebouw), TUE.
Den Dolech 2, Eindhoven

The lectures on a Stieltjes Afternoon are intended for a broad audience.


13.00 - 13.30 Welcome with coffee and tea
13.30 - 14.15 Prof.dr. W.Th.F. den Hollander (Eurandom):
"Random polymers"
14.30 - 15.15 Prof.dr. C.J. van Duijn (TUE/CWI):
"Entropy conditions and transitional waves in hyperbolic conversation laws"
15.15 - 15.45 Coffee and tea break
15.45 - 16.30 Dr. P.J.C. Spreij (UvA):
"Mathematics in Finance"
16.45 - 17.30 Prof.dr. A. Schrijver (UvA/CWI):
"Permantents and edge-colourings"
17.30 - 18.30 Reception

Summary talk Prof.dr. W.Th.F. den Hollander

This talk is a mini-review on random polymers. Random polymers represent a new area of probability theory, because they are modelled by random processes with a long-range interaction in space and/or time. This leads to a remarkable dependence on dimension and on the interaction parameters.
Six models will be discussed, describing various aspects of the problem area. The main theorems and conjectures will be discussed for each of them. The talk is for a general audience.

Summary talk Prof.dr. C.J. van Duijn

In this lecture we discuss some fundamental concepts related to Riemann problems for hyperbolic conservation laws. We start with shocks, weak solutions, Rankine-Hugoniot and entropy (or uniqueness) conditions for the scalar equation. Then we generalize these issues to systems of equations involving the Hugoniot locus, rarefaction curves and the geometrical contruction of the solution. Introducing travelling waves as viscous profiles we show that a new class of waves can arise in the solution. These waves (leading to transitional shock waves) turn out to be saddle - saddle connections of the corresponding dynamical system.

Summary talk Dr. P.J.C. Spreij.

For decades research in Finance belonged to the realm of economists. A change took place after the publication in 1973 of the famous paper by Black and Scholes on option pricing. Shortly after that mathematiciens, many of them probabilists, became interested in financial models and the methods by which these are analyzed became more and more advanced. In particular it was soon discovered that the field of Mathematical Finance was a fruitful application area of stochastic calculus. In the talk we review some basic concepts in Finance, their mathematical counterparts and discuss some of the mathematical methods that are currently used in Finance. If time permits we will also say something on more recent developments. The talk should be accessible for a general mathematical audience, no knowledge of finance is presupposed.
Last modified: Thu Jan 11 14:30:24 MET 2001