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leandrochiarini committed Dec 14, 2023
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4 changes: 4 additions & 0 deletions ReadingGroup-SLE.md
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# Critical and Near-critical Interfaces

<img src='https://upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Schramm-Loewner_Evolution.png/800px-Schramm-Loewner_Evolution.png' width='340' height='340' style='float:right; margin-left:auto; margin-right:auto' >

The reading group will focus on random interfaces that should arise as the scaling limits of massive/near-critical models in statistical mechanics. The most well-known critical interface models are the Schramm-Loewner Evolution (SLE) and Conformal Loop Ensembles (CLE). While the study of critical interfaces has seen many advances in the past two decades, a general theory for near-critical interfaces remains elusive. However, a few rigorous examples of massive interface models have been constructed in the last few years, which we will also explore.

We will begin by discussing the general properties of SLE and providing an overview of the expected properties of massive interfaces. From there, we will explore other important constructions for critical interfaces, followed by descriptions of a few examples of massive interfaces that have already been described. Finally, we will review some results in the physics literature that are related to massive models.
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6. Qian, Werner _"Coupling the Gaussian free fields with free and with zero boundary conditions via common level lines"_. [Link](https://link.springer.com/article/10.1007/s00220-018-3159-z)
7. Sheffield, Werner _"Conformal loop ensembles: the Markovian characterization and the loop-soup construction"_. [Link](https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=da7e6063f7147adb21e81c24fa246b40b75e1b4d)

- Image above from Wikipedia

## Organised by
- [Ellen Powell](https://sites.google.com/view/ellenpowell/home?authuser=0)
- [Léonie Papon](https://www.durham.ac.uk/staff/leonie-b-papon/)
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6 changes: 6 additions & 0 deletions _site/ReadingGroup-SLE.html
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<h1 id="critical-and-near-critical-interfaces">Critical and Near-critical Interfaces</h1>

<p><img src="https://upload.wikimedia.org/wikipedia/commons/thumb/7/7c/Schramm-Loewner_Evolution.png/800px-Schramm-Loewner_Evolution.png" width="340" height="340" style="float:right; margin-left:auto; margin-right:auto" /></p>

<p>The reading group will focus on random interfaces that should arise as the scaling limits of massive/near-critical models in statistical mechanics. The most well-known critical interface models are the Schramm-Loewner Evolution (SLE) and Conformal Loop Ensembles (CLE). While the study of critical interfaces has seen many advances in the past two decades, a general theory for near-critical interfaces remains elusive. However, a few rigorous examples of massive interface models have been constructed in the last few years, which we will also explore.</p>

<p>We will begin by discussing the general properties of SLE and providing an overview of the expected properties of massive interfaces. From there, we will explore other important constructions for critical interfaces, followed by descriptions of a few examples of massive interfaces that have already been described. Finally, we will review some results in the physics literature that are related to massive models.</p>
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<li>Sheffield, Werner <em>“Conformal loop ensembles: the Markovian characterization and the loop-soup construction”</em>. <a href="https://citeseerx.ist.psu.edu/document?repid=rep1&amp;type=pdf&amp;doi=da7e6063f7147adb21e81c24fa246b40b75e1b4d">Link</a></li>
</ol>

<ul>
<li>Image above from Wikipedia</li>
</ul>

<h2 id="organised-by">Organised by</h2>
<ul>
<li><a href="https://sites.google.com/view/ellenpowell/home?authuser=0">Ellen Powell</a></li>
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2 changes: 1 addition & 1 deletion _site/feed.xml
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<?xml version="1.0" encoding="utf-8"?><feed xmlns="http://www.w3.org/2005/Atom" ><generator uri="https://jekyllrb.com/" version="4.2.2">Jekyll</generator><link href="/feed.xml" rel="self" type="application/atom+xml" /><link href="/" rel="alternate" type="text/html" /><updated>2023-12-14T23:29:29+00:00</updated><id>/feed.xml</id><title type="html">Leandro Chiarini</title><author><name>Leandro Chiarini</name></author><entry><title type="html">Events</title><link href="/events/2023/04/11/Events-2023-2024.html" rel="alternate" type="text/html" title="Events" /><published>2023-04-11T09:34:00+01:00</published><updated>2023-04-11T09:34:00+01:00</updated><id>/events/2023/04/11/Events-2023-2024</id><content type="html" xml:base="/events/2023/04/11/Events-2023-2024.html"><![CDATA[<p>Here is a quick list of events in the next year or so that I found interesting. This list reflects my personal preferences, but I think it might be useful to others.</p>
<?xml version="1.0" encoding="utf-8"?><feed xmlns="http://www.w3.org/2005/Atom" ><generator uri="https://jekyllrb.com/" version="4.2.2">Jekyll</generator><link href="/feed.xml" rel="self" type="application/atom+xml" /><link href="/" rel="alternate" type="text/html" /><updated>2023-12-14T23:48:30+00:00</updated><id>/feed.xml</id><title type="html">Leandro Chiarini</title><author><name>Leandro Chiarini</name></author><entry><title type="html">Events</title><link href="/events/2023/04/11/Events-2023-2024.html" rel="alternate" type="text/html" title="Events" /><published>2023-04-11T09:34:00+01:00</published><updated>2023-04-11T09:34:00+01:00</updated><id>/events/2023/04/11/Events-2023-2024</id><content type="html" xml:base="/events/2023/04/11/Events-2023-2024.html"><![CDATA[<p>Here is a quick list of events in the next year or so that I found interesting. This list reflects my personal preferences, but I think it might be useful to others.</p>
<h3 id="march-to-june-2024">March to June 2024</h3>
<ul>
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