2018-06-08 15:00-16:00 Room 1114, Sciences Building No. 1

Abstract: In this short talk, we shall begin with a concise review on some highlights of equivariant differential geometry such as symmetry theorems on isoperimetric regions, soap bubbles, closed minimal submanifolds of spheres etc. on the one hand, and on the other hand, the construction of some outstanding new examples such as immersed soap bubbles, spherical Bernstein problems, etc. and then following with a brief overview on what kinds of natural roles it is playing in the study of various interplays between symmetries and optimalities in the intrinsic structures of the Nature.

We shall conclude with a brief discussion on its prospects of further developments, mainly by formulating some pertinent problems as well as a few new results, such as the construction of examples of Ricci flows of O(3)-hypersurfaces in E^4 exhibiting the puzzling behavior of non-preservation of positive Ricci curvature everywhere.