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#painleve

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Nalini Joshi<p>There has been enormous interest in these maps, as they arose from <a href="https://mathstodon.xyz/tags/integrable" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>integrable</span></a> systems, like the Sine-Gordon equation. The interest grew with the construction of discrete <a href="https://mathstodon.xyz/tags/Painlev%C3%A9" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Painlevé</span></a> equations. The autonomous cases of such equations are QRT maps.</p>
Nalini Joshi<p>There is a mysterious connection between <a href="https://mathstodon.xyz/tags/algebraic" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>algebraic</span></a> <a href="https://mathstodon.xyz/tags/surfaces" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>surfaces</span></a> and solutions of non-linear differential equations called the <a href="https://mathstodon.xyz/tags/Painlev%C3%A9" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Painlevé</span></a> equations. Marta Mazzocco <br><span class="h-card" translate="no"><a href="https://birdsite.wilde.cloud/users/unibirmingham" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>unibirmingham</span></a></span> Pieter Roffelsen and I <br><span class="h-card" translate="no"><a href="https://bird.makeup/users/sydney_uni" class="u-url mention" rel="nofollow noopener noreferrer" target="_blank">@<span>sydney_uni</span></a></span> show surprising variations on this connection: <a href="https://arxiv.org/abs/2405.10541" rel="nofollow noopener noreferrer" translate="no" target="_blank"><span class="invisible">https://</span><span class="">arxiv.org/abs/2405.10541</span><span class="invisible"></span></a></p>
Nalini Joshi<p>So very pleased to have our results appear on one of the most famous equations in <a href="https://mathstodon.xyz/tags/mathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathematics</span></a>, famous because it acts as the fulcrum of so many celebrated developments and theories, in <a href="https://mathstodon.xyz/tags/collaboration" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>collaboration</span></a> with Victoria Heu and Milena Radnovic … <a href="https://mathstodon.xyz/tags/openaccess" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>openaccess</span></a> <a href="https://mathstodon.xyz/tags/ForumInMathematics" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>ForumInMathematics</span></a> Space <a href="https://cup.org/3IG7jJB" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="">cup.org/3IG7jJB</span><span class="invisible"></span></a> <a href="https://mathstodon.xyz/tags/Painlev%C3%A9" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Painlevé</span></a></p>
Nalini Joshi<p>Are you interested in the deeply beautiful <a href="https://mathstodon.xyz/tags/mathematical" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>mathematical</span></a> properties of the sixth <a href="https://mathstodon.xyz/tags/Painlev%C3%A9" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>Painlevé</span></a> equation? See our paper (with Viktoria Heu and Milena Radnovic) in Forum of Mathematics, Sigma now available through <a href="https://mathstodon.xyz/tags/open" class="mention hashtag" rel="nofollow noopener noreferrer" target="_blank">#<span>open</span></a> access 👉🏼 <a href="https://doi.org/10.1017/fms.2023.11" rel="nofollow noopener noreferrer" target="_blank"><span class="invisible">https://</span><span class="">doi.org/10.1017/fms.2023.11</span><span class="invisible"></span></a></p>
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