o-minimality and complex analysis

Jacob Tsimerman, University of Toronto and Minerva Distinguished Visitor
Fine Hall 314

In-Person and Online Talk 

Register at: https://math.princeton.edu/minerva-2021

Despite o-minimality being inherently a real theory, many of its applications stem from its synergy with complex analysis, pioneered by the work of Peterzil and Starchenko. Many pathologies of complex analytic functions  - 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  $\mathbb{C}^n$ which is definable in an o-minimal structure must be algebraic. Moreover, one may even consider `definable complex analytic spaces' which allow for nilpotent elements, a coherent sheaf theory and GAGA-style results.