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Milestone Year
1995
When circles touch
Consider a collection of circles of different sizes in a plane, packed so that they do not intersect. Some pairs of circles may touch each other and others will have no points of contact. Characterizing these relationships (known as tangencies) constitutes an interesting problem of combinatorics, related to other areas of mathematics and its applications.
A Weizmann Institute mathematician made major contributions to this field of research. For example, in 1995, using circle packing as above, he gave a basically combinatorial and constructive proof of Riemann mapping theorem. This 19th century theorem lies in the basis of the area of complex analysis and continues to be relevant even today (and even in applied areas such as image processing). It also lies at the basis for the contribution to SLE. Informally it states that all "hole-free" domains in the plane, except the whole plane, are conformally equivalent; that is, they can be mapped one onto the other by an invertible map that preserve infinitesimal angles. In particular, the shape of small enough region is approximately geometrically preserved, except for possible scaling and rotation.