Abstract：For the projective line over complex numbers with 4 punctures 0, 1, \infity, \lambda, where lambda is a parameter running in P^-{0, 1, \infty} we construct infinitely many rank-2 local systems with the prescribed local monodromy around those 4 punctures, which come from geometry origin. Consequently, they all are algebraic solutions of the Painleve VI equation. The method is totally d...
AbstractWe will review some recent progress on the general geometric behavior of homologically area-minimizing subvarieties, namely, objects that minimize area with respect to homologous competitors. They are prevalent in geometry, for instance, as holomorphic subvarieties of a Kahler manifold, or as special Lagrangians on a Calabi-Yau, etc. A fine understanding of the geometric structure of ho...
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