讲座内容：

We address the similarity problem for tuples of Cowen-Douglas operators. The unitary equivalence counterpart of this problem was already studied in the 1970s, where geometric concepts such as vector bundles and curvature played a central role in its description. However, as the Cowen-Douglas conjecture suggests, progress on the similarity problem has been relatively limited until recent years. Recent advancements have uncovered a deep connection between complex geometry, the corona problem, and the similarity problem for single Cowen-Douglas operators. Extending these results to the multi-variable setting, we demonstrate that the similarity results for single operators also hold for commuting tuples of Cowen-Douglas operators, even without relying on corona theorems, which are no longer valid in this context.