EXCHANGE

"The Cows and Colleges Symposium"

Miklos Laczkovich

A member of the Hungarian National Academy and a recipient of academic prizes and awards by The Hungarian Mathematics Society and the Hungarian Academy of Sciences, Laczkovich was awarded the Ostrowski Prize in 1993, sharing the prize that year with Marina Ratner (University of California--Berkeley). Laczkovich was an invited hour speaker at the First European Congress of Mathematics in Paris, 1992. He has served as a Visiting Professor at the University of Waterloo, the University of Naples and Michigan State University as well as the University of California--Santa Barbara. In 1986 he was a Fullbright Research Scholar at St. Olaf College in Minnesota. He currently holds joint appointments at Eotvos Lorand University, Budapest and University College, London University.

His main research interests cover much of combinatorial and set theoretic analysis. Some particular areas are as follows:

- Problems in geometric measure theory; e.g. is it true that the ball in Rn is the Lipschitz image of every measurable set of positive Lebesgue measure?
- Problems of equidecomposability: Is it true that two bounded measurable sets of the same positive measure and with rectifiable boundaries are always equidecomposable with finitely many measurable pieces? Is this true for the cube and the tetrahedron in R3? Is it true that if two measurable sets are equidecomposable under a commutative group of isometries then they are equidecomposable with measurable pieces?
- Problems concerning the difference operator: can we characterise those topological groups where it is true that if the differences of a function are continuous then it is the sum of a continuous function and an additive function? Can we represent every Lp function on the circle with vanishing integral as the sum of finitely many differences of Lp functions?
- Miscellaneous Problems: Does there exist an algorithm that decides, for every given polynomial with integer coefficients of the functions sin(xn) and cos(xn) whether or not it has a real root?