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<!DOCTYPE html>
<html lang="en">
<head>
<meta charset="utf-8">
<title>Home</title>
<link rel="icon" href="images/riemann_sphere">
<meta name="viewport" content="width=device-width, initial-scale=1.0">
<meta name="description" content="Visualise transformations on the Riemann sphere.">
<meta name="keywords" content="mathematics, geometry, visualisation, mobius, symplectic, group, veronese, lagrangian">
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<header><a href="index-fr.html"><input type="button" value="Français"></a></header>
<h1>Riemann sphere</h1>
<p>
This website lets you see the action of Möbius transformations or the action of \(\mathrm{PSp}(4, \mathbb{R})\)
on circles, points, etc. on the Riemann sphere. The methods to compute these transformations are described in the corresponding
sections and in detail in [Leb23]. The project is based on ideas developed in [BK21].
</p>
<p id="main_links">
<a href="mobius.html">\(\mathcal{Möb}\)</a><span id="sep"> | </span><a href="psp4r.html">\(\mathrm{PSp}(4, \mathbb{R})\)</a>
</p>
<p>
This site was created by Samuel Leblanc, under the supervision of <a href="https://jpburelle.espaceweb.usherbrooke.ca/index_eng.html" target="_blank">Jean-Philippe Burelle</a>,
as part of the course <i>Experimental Mathematics Lab</i> at Université de Sherbrooke.
The code relating to this site can be found on <a href="https://github.com/samueleblanc" target="_blank">GitHub</a>. The visualisations
were made using <a href="https://cindyjs.org/" target="_blank">CindyJS</a>.
</p>
<p>
[BK21] Jean-Philippe Burelle and Ryan Kirk. <a href="https://arxiv.org/abs/2108.08680" target="_blank">Piecewise circular curves and positivity</a>.
arXiv:2108.08680, 2021.<br>
[Leb23] Samuel Leblanc. <a href="PDF/transformations_cercles_orientes.pdf" target="_blank">Transformations de cercles orientés tangents sur la sphère de Riemann</a> (PDF). 2023.
</p>
</body>
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