Mathematical Sciences: Heat Flow on Riemannian Manifolds

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Using the technique of the Ricci flow evolution equation, the investigator will study the structure of certain classes of complete non-compact Kaehler manifolds with positive bisectional curvature, the smooth structure of compact Riemannian manifolds with positive curvature operator and the existence of Kaehler- Einstein metrics on certain compact Kaehler manifolds. The research covers several topics in modern differential geometry. The geometry of evolution equations is realized in many fields of mathematical physics, areas relating to global change, population studies and the biological sciences. It is expected that the investigator will be active in the training of graduate students.