Problems related to Monster tower

Research group:
Problems related to Monster tower

16 - 21 September, 2011, Warsaw

Over the last two years, after an exhaustive contribution, coauthored by Montgomery and Zhitomirskii was written, the Monster tower has attracted a considerable amount of attention. The main directions of research are as follows:

1. The classical (1, 2) Monster tower as a universal space for the classical Goursat distributions. In particular, a number of conjectures related to the nilpotent approximations of locally universal Goursat structures living on the stages of that tower.

2. The (1, n) Monster tower, n ≥ 3, and related classification of curves in R^n. A certain amount of results were obtained by P. Mormul, J. Adachi, F. Pelletier, R. Montgomery, A. Castro and some students of R. Montgomery. The main open question: is it possible to reduce the classification of points of the (1, n) Monster tower to the classification of jets of curves in R^n, for any n ≥ 3 (for n = 2 it is possible).

3. The (k, n) Monster tower, k ≥ 2: construction and properties of points and curves [tangent to distributions pertinent to that tower]. Montgomery and Zhitomirskii started this reserach and discovered many surprising facts in the very construction of the relevant tower.

The planned reserach group would firstly focus on the first direction - a direct continuation of the activity of Section No 17 in the joint Israeli-Polish PTM meeting scheduled for September 11 - 15 in Łódź. Several standing conjectures bearing on the nilpotent approximations of Goursat distributions are to be discussed. We also plan to discuss the second and third directions, and related problems, which are closer to the participants J. Adachi and W. Domitrz. Yet within these directions we will concentrate on fixing open interesting problems rather than attacking them.

The main regular fully-fledged lectures will be given by P. Mormul and M. Zhitomirskii. The other participants will give "seminar-style" lectures, while all four of us would take part in the discussions following each lecture.


Piotr Mormul (Polish Academy of Sciences)



  • Jiro Adachi (Hokkaido University, Sapporo, Japan)
  • Wojciech Domitrz (Technical University of Warsaw, Poland)
  • Piotr Mormul (IM PAN)
  • Mikhail Zhitomirskii (Technion, Haifa, Israel)