Algebra and Algebraic Geometry Seminar - Jaydeep Chipalkatti - The Pappus-Steiner map
- Calendar
- Mathematics & Statistics
- Date
- 10.25.2021 12:30 pm - 1:30 pm
Description
Speaker: Jaydeep Chipalkatti (University of Manitoba)
Title: The Pappus-Steiner map
Abstract: Pappus' theorem is one of the oldest results in classical projective geometry. Given a pair of lines in the plane with three points on each, it produce the so-called Pappus line of the configuration. Steiner's theorem says that the six Pappus lines obtained by permuting the points are concurrent in threes. This leads to a geometrically defined dynamical system.
We use class-field theory to characterise all primes $p$ for which this system admits periodic points of order $3$ or $4$ modulo $p$. This relies upon some highly unusual Galois-theoretic phenomena.
All the relevant ideas will be explained in detail during the course of the talk; in particular, no serious knowledge of algebraic number theory will be assumed.
Location: Virtual
Zoom Link: https://mcmaster.zoom.us/j/96350226417?pwd=UkpXbXVZVnFnb2puOVpCVFlJSk1RZz09
Title: The Pappus-Steiner map
Abstract: Pappus' theorem is one of the oldest results in classical projective geometry. Given a pair of lines in the plane with three points on each, it produce the so-called Pappus line of the configuration. Steiner's theorem says that the six Pappus lines obtained by permuting the points are concurrent in threes. This leads to a geometrically defined dynamical system.
We use class-field theory to characterise all primes $p$ for which this system admits periodic points of order $3$ or $4$ modulo $p$. This relies upon some highly unusual Galois-theoretic phenomena.
All the relevant ideas will be explained in detail during the course of the talk; in particular, no serious knowledge of algebraic number theory will be assumed.
Location: Virtual
Zoom Link: https://mcmaster.zoom.us/j/96350226417?pwd=UkpXbXVZVnFnb2puOVpCVFlJSk1RZz09
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