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<!DOCTYPE html>
<html>
<head>
<meta charset=utf-8 />
<meta name="description" content="Brice Loustau" />
<title>Brice Loustau - Research</title>
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<body>
<div id="main">
<div id="header">
<p> <a href="/recherche.html">Français</a></p>
</div>
<div id="leftnavbar">
<ul>
<li><a href="/indexen.html">Home</a></li>
<li><a href="/teaching.html">Teaching</a></li>
<li><a href="/book.html">Book</a></li>
<li class="active"><a href="/research.html">Research</a></li>
<li><a href="/code.html">Code</a></li>
<li><a href="/about.html">About</a></li>
</ul>
</div>
<div id="maincontent">
<p class="imgfloatright"><img style="width: 180px" src="/ressources/Harmony5-p.png"></p>
<p class="titre0">Research interests</p>
<p>Differential geometry • Hyperbolic geometry • Moduli Spaces • Discrete Geometry • Math programming and
visualization • Data Science and Machine Learning</p>
<br />
<p class="titre1">Publications</p>
<p class="titre2" id="Papers">Articles</p>
<div id="liste2">
<ol>
<li>
The complex symplectic geometry of the deformation space of complex projective structures.<br>
<i>Geometry & Topology</i> 19 (2015), no. 3, 1737–1775.
<a href="/ressources/CPsymplectic.pdf">Download</a>.
</li>
<li>
Minimal surfaces and symplectic structures of moduli spaces.<br>
<i>Geometriae Dedicata</i> 175 (2015), 309–322.
<a href="/ressources/MinimalSymplectic.pdf">Download</a>.
</li>
<li>
Bi-Lagrangian structures and Teichmüller theory (with <a href="https://www.mathi.uni-heidelberg.de/~asanders/">A. Sanders</a>).<br>
Preprint: <a href="https://arxiv.org/abs/1708.09145">arXiv:1708.09145</a> or
<a href="https://hal.archives-ouvertes.fr/hal-01579284">HAL-01579284</a>.
<a href="/ressources/BiLagrangian.pdf">Download</a>.
</li>
<li>
Computing discrete equivariant harmonic maps (with <a href="https://sites.google.com/view/jonah-gaster/home">J. Gaster</a> and <a href="http://www.iecl.univ-lorraine.fr/~Leonard.Monsaingeon/">L. Monsaingeon<a>).<br>
Preprint: <a href="https://arxiv.org/abs/1810.11932">arXiv:1810.11932</a> or
<a href="https://hal.archives-ouvertes.fr/hal-02054982">HAL-02054982</a>.
<a href="/ressources/DiscreteHarmonic1.pdf">Download</a>.
</li>
<li>
Computing harmonic maps between Riemannian manifolds (with <a href="https://sites.google.com/view/jonah-gaster/home">J.Gaster</a> and <a href="http://www.iecl.univ-lorraine.fr/~Leonard.Monsaingeon/">L. Monsaingeon<a>).<br>
Accepted in <i>Canadian Journal of Mathematics</i> (2022).
<a href="/ressources/DiscreteHarmonic2.pdf">Download</a>.
</li>
<li>
The sum of Lagrange numbers (with <a href="https://sites.google.com/view/jonah-gaster/home">J. Gaster</a>).<br>
<i>Proceedings of the AMS</i> 149 (2021), 5385-5391.
<a href="/ressources/LagrangeSum.pdf">Download</a>.
</li>
<li>
Harmonic maps from Kähler manifolds.<br>
Preprint: <a href="http://arxiv.org/abs/2010.03545">arXiv:2010.03545</a> or
<a href="https://hal.archives-ouvertes.fr/hal-02961444">HAL-02961444</a>.
<a href="/ressources/HarmonicKaehler.pdf">Download</a>.
</li>
<li>
Hyper-Kähler geometry of the Taubes moduli space (with <a href="http://www-dimat.unipv.it/~bonsante/">F. Bonsante<a>,
<a href="https://www.mathi.uni-heidelberg.de/~asanders/">A. Sanders</a>, and <a href="http://seppi.perso.math.cnrs.fr/index.html">A. Seppi</a>).<br>
<i>In preparation.</i>
</li>
<!--
<li>
Complex geometry of the universal moduli space of Higgs bundles (with <a href="https://www.mathi.uni-heidelberg.de/~asanders/">Andy Sanders</a> and
<a href="http://www.math.ens.fr/~tholozan/">Nicolas Tholozan</a>).<br>
<i>We study the complex, Kähler and hyper-Kähler geometry of the universal moduli space of Higgs bundles over Teichmüller space.</i>
</li>
<li>
Symplectic geometry of Wick rotations (with Carlos Scarinci).<br />
<i>We study the symplectic properties of Wick rotations between moduli spaces of Einstein 3-manifolds in relation to bi-Lagrangian structures.</i>
</li>
<li>
Discrete Bochner formula on Riemannian manifolds
(with <a href="https://www2.bc.edu/jonah-gaster/">{Jonah Gaster}</a> and
<a href="http://www.iecl.univ-lorraine.fr/~Leonard.Monsaingeon/">Léonard Monsaingeon</a>).<br>
<i>We establish a discrete Bochner formula for functions on a weighted triangulation taking values in Riemannian manifold.</i>
</li>
-->
</ol>
</div>
<p class="titre2" id="Notes">Notes</p>
<div id="liste2">
<ol>
<li>
Higgs bundles and Hitchin components.<br>
Notes for the workshop <i>Higher Teichmüller-Thurston spaces</i> in Paris XI, France in 2012.
<a href="/ressources/Higgs.pdf">Download</a>.
</li>
<li>
Minimal surfaces and quasi-Fuchsian structures.<br>
Notes for the NSF workshop <i>Higgs bundles and harmonic maps</i> in Asheville, NC in Januray 2015.
<a href="/ressources/Asheville.pdf">Download</a>.
</li>
<li>
Hyperbolic geometry and applications.<br>
Report of the GRG group (HITS). <i>HITS Annual Report 2020</i>.
</li>
</ol>
</div>
<p class="titre2" id="Book">Book</p>
<div id="liste2">
<ol>
<li>
Hyperbolic Geometry. → <a href="book.html"><strong>Book section</strong></a>.
</li>
</ol>
</div>
<p class="titre2">PhD thesis</p>
<div id="liste2">
<ol>
<li>
<em>The symplectic geometry of complex projective structures</em>. <br />
Advisor: Prof. Jean-Marc Schlenker. <a href="/ressources/Thesis.pdf">View/Download.</a>
</li>
</ol>
</div>
<!--
<br />
<p class="imgfloatright"> <a href="https://annales.lebesgue.fr/index.php/AHL/index"><img style="width: 100px" src="https://annales.lebesgue.fr/embed/logoAHL.svg"></a> </p>
<p>"Ad" : I invite you to consider submitting your most beautiful mathematics papers to the free and open journal
<a href="https://annales.lebesgue.fr/index.php/AHL/index"><span class="smallcaps">Annales Henri Lebesgue</span></a>.
(I have no ties to this journal!)</p>
-->
<br />
<p class="titre1">Computational mathematics</p>
<!--<p>I have had a growing interest for discrete differential geometry,
computational mathematics, experimental research, and visualization:</p>-->
<p class="titre2">Heidelberg Experimental Geometry Lab (HEGL)</p>
<p>Within the <a href="https://www.mathi.uni-heidelberg.de/~geodyn/">Research Station: Geometry & Dynamics</a>,
I was in charge of setting up the Lab (HEGL).
The goal of HEGL is to promote the interaction between theoretical math and computational experimentation and visualization.
HEGL provides advanced technology and hosts many student research projects.</p>
<p>→ <a href="https://www.mathi.uni-heidelberg.de/~geodyn/HEGL/projects.html"><strong>HEGL website</strong></a>.</p>
<p class="imgfloatright"> <img src="/ressources/icon.png" height=100px /> </p>
<p class="titre2">Circle Packings</p>
<p>This cross-platform computer software created by <a href="http://www.univ-orleans.fr/mapmo/membres/beeker/index.php?langue=en">Benjamin Beeker</a>
and myself computes and shows circle packings and Riemann conformal mappings.
<p>→ <a href="/code.html#circlepackings"><strong>"Code" section</strong></a>.</p>
<p class="titre2" style="clear: right">Harmony</p>
<p class="imgfloatright"> <img src="/ressources/Harmony.png" width=100px height=100px /> </p>
<p>This cross-platform computer software created with <a href="https://sites.google.com/view/jonah-gaster/home">Jonah Gaster</a> computes and shows equivariant harmonic maps from the hyperbolic plane \(\mathbb{H}^2\) to hyperbolic 3-space
\(\mathbb{H}^3\). </p>
<p>→ <a href="/code.html#harmony"><strong>"Code" section</strong></a>.</p>
<br />
<p class="titre1">Mentoring student research</p>
<div id="liste2">
<ol>
<li>I mentored the Master research project of T. Favier in the Summer 2021. Title: <em>Hyperbolic geometry and graph embeddings</em>.</li>
<li>I mentored the Master thesis of <a href="https://gcd.tuwien.ac.at/?p=2268">Darja Zierau</a> in the Summer 2019. <em> Title: Cross-ratios of torsion points on elliptic curves</em>.</li>
<li>I mentor many undergraduate research projects at HEGL. → <a href="https://www.mathi.uni-heidelberg.de/~geodyn/HEGL/projects.html"><strong>HEGL website</strong></a>.
</ol>
</div>
<br />
<!-- <p class="titre1" id="CVen">CV</p>
<p> <a href="/ressources/CVen.pdf">Download my CV</a> (in English. For French <a href="/ressources/CVfr.pdf">click here</a>).</p>
<p> Please <a href="mailto:[email protected]">contact me</a> for my Research Statement or my Teaching Statement.</p>-->
</div>
<div id="footer">
<p>Brice Loustau. Contact: <a href="mailto:[email protected]">[email protected]</a></p>
</div>
</div>
</body>
</html>