One of the nice things in mathematics is that one can play with models which do not necessarily have to do directly with the real world, whatever the later means. We can look at abstract objects, like finite simple groups, number theory in some number field or topology in 1001 …
The energy theorem for simplicial complexes equipped with a complex energy comes with some surpises.
Abstract for this post Analysis had not been my favorite topic at first. The subject appeared to me quite technical and tedious even when sweetened like in analytic number theory. The Sine-Gordon topic and other rather concrete topics in dynamical systems theory changed that a bit and I ended up …
A major open problem in Riemannian geometry is the classification of even dimensional positive curvature manifolds with symmetry. There is a reduction theory which produces a periodic system of elements. This picture has affinity with gauge bosons in physics.
