Ten problems I care most

by Michel Deza, Ecole Normale Superieure, Paris

The following 10 problems of Applied Geometry will be presented:

I.  Perfect matroid designs
II. a) Infinite hypermetrics
    b) $l_1$-embedding of complexes
III.a) Fullerenes: $IQ$, Skyrmions, viruses
    b) Space fullerenes
IV. a) Zigzags and railroads in fullerenes
    b) Zigzags and Lins triality of maps
V.  a) Three classes of exotic plane graphs
    b) Ambiguous boundaries of polycycles
VI. Extreme physical distances

Not all of above problems mine and not all are purely mathematical.
But they represent my main areas of interest in recent years.