Lempert, Laszlo, Kolokvij maj 2017

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The cohomological method in complex analysis

Laszlo Lempert, Purdue University

One of the momentous discoveries of twentieth century mathematics was that there is a large class of problems in very different subfields that can, and should, be formulated in a common language, the language of (co)homologies. The talk will be about cohomology groups that arise when trying to solve certain fundamental analytical problems in complex analysis and geometry.

After introducing the central notion of the subject: holomorphic functions, I will pass to the so called Cousin problem and its significance. I will summarize the works of H. Cartan, Oka, and Serre on the solution of the Cousin problem in finite dimensions. The solution is expressed in terms of cohomology groups. Finally, I will discuss twenty--first century developments in infinite dimensional spaces.​

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