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Britton Lecture Series: Functional transcendence in the analytic theory of algebraic geometry through model theory

Hamilton Hall

06/03/2020, 3:30 pm - TO 06/03/2020 - 4:30 pm

Organizer: Mathematics and Statistics

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The final lecture in this year’s Britton lecture series; Thomas Scanlon will speak on “Functional Transcendence In The Analytic Theory Of Algebraic Geometry Through Model Theory”

Abstract:
Complex analytic geometry enters algebraic geometry through such constructions as the uniformization maps of complex algebraic varieties, the corresponding period mappings, and more generally from the period maps associated with variations of Hodge structures. While such constructions are geometrically meaningful, the functions involved are almost always transcendental. The theory of o-minimality has been used to show that the associated geometry is nevertheless tame. We will interpret these results in terms of the model theory of differential equations and then use this interpretation to solve the function field version of a conjecture of Zilber and Pink on algebraic relations in Shimura varieties. (The new results are joint with Jonathan Pila.)

Dr. F. Ronald Britton was a former Professor of Mathematics at McMaster, and served as Chair of the Department of Mathematics. After his retirement, he endowed our annual Britton Lectures in memory of his late wife Helen E. Britton. The Britton Lectures have provided the University with a series of distinguished invited speakers since its beginning in 1978.