O-minimality, Point Counting and Functional Transcendence
O-minimality, Point Counting and Functional Transcendence
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Jacob Tsimerman, University of Toronto and Minerva Distinguished Visitor
In-Person and Online Talk听
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One of the main applications of O-minimality to Number Theory has been via the celebrated Pila-Wilkie theorem. This theorem says, in a precise sense, that transcendental sets听 which are definable in an o-minimal structure contain `few' rational points. Quite unexpectedly, this result has played a huge role in the last 10 years in establishing transcendence theorems for a huge swath of functions, including e^x, modular forms, and even period integrals.听 We will explain this theorem and the idea underlying its proof, and describe some of the functional transcendence applications, including the听classical Ax-Schanuel theorem and its various incarnations.