o-minimality and complex analysis
o-minimality and complex analysis
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Jacob Tsimerman, University of Toronto and Minerva Distinguished Visitor
In-Person and Online Talk听
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Despite o-minimality being inherently a real theory, many听of its applications stem from its synergy with complex analysis, pioneered by the work of Peterzil and Starchenko. Many pathologies of complex analytic functions听 - such as essential singularities - disappear if we only consider functions definable in an o-minimal structure. One of the central results in the subject is a generalization of Chows theorem to a non-projective context: any complex analytic subvariety of听 $\mathbb{C}^n$ which is definable in an o-minimal structure must be algebraic.听Moreover, one may even consider `definable complex analytic spaces' which allow for nilpotent elements, a coherent sheaf theory and GAGA-style results.
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