Abstract: Arezzo and Pacard proved that if a compact Kahler manifold M admits constant scalar curvature Kahler (cscK) metrics, then the blow-up of M in one or more points admits cscK metrics provided that some stability conditions hold. Later, Arezzo, Pacard and Singer generalized their previous result to the case of extremal metrics. The main goal of this talk is to generalize the result of Arezzo-Pacard-Singer. More precisely, we give conditions under which the blowup of an extremal Kähler manifold along a submanifold of codimension greater than 2 admits an extremal metric. 

Bio-Sketch: Professor Reza Seyyedali is currently a faculty member at the School of Mathematics at the Institute for Research in Fundamental Sciences, Iran. He received his Ph.D. from Johns Hopkins University in 2009. His research interests lie in complex geometry, geometric analysis, and partial differential equations.