Unlikely intersection theory and the Ax-Schanuel theorem

Anlong Chua

04-May-2022, 14:00-15:30 (23 months ago)

Abstract: Counting dimensions heuristically tells us whether geometric objects are "likely" or "unlikely" to intersect. For instance, Bezout's theorem tells us that two curves in $\mathbb{P}^2$ always intersect. On the other hand, two curves in $\mathbb{P}^3$ are unlikely to intersect. In number theory, one is often concerned with unlikely intersection problems — for example, when does a subvariety of an abelian variety contain many torsion points?

In this talk, I will try to explain the connections between functional transcendence, unlikely intersections, and number theory. Time permitting, I will discuss the answer to the question posed above and more. On our journey, we will pass through the fascinating world of o-minimality, which I hope to describe in broad strokes.

algebraic geometrynumber theory

Audience: advanced learners


STAGE

Series comments: STAGE (Seminar on Topics in Arithmetic, Geometry, Etc.) is a learning seminar in algebraic geometry and number theory, featuring speakers talking about work that is not their own. Talks will be at a level suitable for graduate students. Everyone is welcome.

Spring 2024 topic: The contents of Serre, Lectures on the Mordell-Weil theorem

Some topics might take more or less time than allotted. If a speaker runs out of time on a certain date, that speaker might be allowed to borrow some time on the next date. So the topics below might not line up exactly with the dates below.

Organizers: Raymond van Bommel*, Edgar Costa*, Bjorn Poonen*, Shiva Chidambaram*
*contact for this listing

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