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<!--<h3 class="w3-margin w3-jumbo"><b>Florent Schaffhauser</b></h3>-->
<h1 class="w3-margin"><b>Florent Schaffhauser</b></h1>
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<!--Vertretungsprofessor<br>-->
<a class= "one" href="https://hegl.mathi.uni-heidelberg.de" target="_blank"> HEGL Managing Director </a><br>
<a class= "one" href="https://www.math.uni-heidelberg.de/en" target="_blank"> Institute for Mathematics </a><br>
<a class="one" href="https://www.uni-heidelberg.de/en" target="_blank"> Heidelberg University </a>
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<h1>Research</h1>
<h3 class="w3-padding-32">Mathematics in Heidelberg</h3>
<p class="w3-text-grey" style="text-align: justify;">
The <a class="one" href="https://hegl.mathi.uni-heidelberg.de" target="_blank">Heidelberg Experimental Geometry Lab (HEGL)</a> is part of the <a class = "one" href = "https://geometry-dynamics.mathi.uni-heidelberg.de" target = "_blank"> </a>Research Station <i>Geometry+Dynamics</i></a>, which is part of the <a class="one" href="https://www.math.uni-heidelberg.de/en" target="_blank">Institute for Mathematics</a>, which is part of the <a class= "one" href="https://www.mathinf.uni-heidelberg.de/en" target="_blank">Faculty of Mathematics and Computer Science</a> at <a class= "one" href="https://www.uni-heidelberg.de/en" target ="_blank">Heidelberg University</a>.
</p>
<h3 class="w3-padding-32">Research interests</h3>
<p class="w3-text" style="text-align: justify;">My research interests lie in the area at the intersection of algebraic and differential geometry.
I study Galois and hidden symmetries of Yang-Mills connections, with applications to the topology and geometry of real and complex algebraic varieties.
</p>
<ul>
<li><span>
Fuchsian groups (30F35)
</span>
</li>
<li><span>
Vector bundles on curves and their moduli (14H60)
</span>
</li>
<li><span>
Special connections and metrics on vector bundles (53C07)
</span>
</li>
<li><span>
Topology of real algebraic varieties (14P25)
</span>
</li>
</ul>
<h3 class="w3-padding-32">Publications</h3>
<ol reversed style="font-weight: bold;">
<li>
<span>
With Juan Martín Pérez. <i>Orbifolds and the modular curve.</i><br>
In Ohshika, K., Papadopoulos, A. (eds)
<a class="one" href="https://doi.org/10.1007/978-3-031-43502-7_11" target="_blank">
<b>In the Tradition of Thurston III</b>
</a>, pp 365–421, Springer (First online: 19 March 2024).
<a href="https://arxiv.org/abs/2312.17068" target="_blank">
<i class="fa-regular fa-file-pdf w3-hover-opacity"></i>
</a>
</span>
</li>
<li>
<span>
With Daniele Alessandrini and Gye-Seon Lee. <i>Hitchin components for orbifolds.</i><br>
<a class="one" href="https://www.ems-ph.org/journals/of_article.php?jrn=jems&doi=1210&p403=1" target="_blank">
<b>J. Eur. Math. Soc.</b> 25 (2023), no. 4, pp. 1285–1347.
</a>
<a href="https://arxiv.org/abs/1811.05366" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li>
<span>
With Erwan Brugallé. <i>Maximality of moduli spaces of vector bundles on curves.</i> <br>
<a class="one" href="https://doi.org/10.46298/epiga.2023.8793" target="_blank"><b>Épijournal de Géométrie Algébrique</b> (EPIGA), Volume 6 (2023)</a>.
<a href="https://arxiv.org/pdf/2111.10959v3.pdf" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li>
<span>
<i>Symmetric differentials and the dimension of Hitchin components for orbi-curves.</i> <br> <a class="one" href="https://doi.org/10.1007/978-3-030-87502-2_13" target="_blank"> <b>Current Trends in Analysis, its Applications and Computation</b>, Birkhäuser <i>Trends in Mathematics</i> (2022), pp. 129-140.
<a href="https://arxiv.org/abs/1911.11370" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li>
<span>
With Victoria Hoskins. <i>Rational points of quiver moduli spaces.</i><br>
<a class="one" href="https://aif.centre-mersenne.org/articles/10.5802/aif.3334/" target="_blank">
<b>Ann. Inst. Fourier</b> Volume 70 (2020) no. 3, pp. 1259–1305.
</a>
<a href="https://arxiv.org/abs/1704.08624" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li>
<span>
With Indranil Biswas. <i>Parabolic vector bundles on Klein surfaces.</i><br>
<a class="one" href="https://projecteuclid.org/journals/illinois-journal-of-mathematics/volume-64/issue-1/Parabolic-vector-bundles-on-Klein-surfaces/10.1215/00192082-8165614.short" target="_blank">
<b>Illinois J. Math.</b> 64 (2020), no. 1, pp.105–118.</a>
<a href="https://arxiv.org/abs/1806.09782" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li>
<span>
With Victoria Hoskins. <i>Group actions on quiver varieties and applications.</i><br>
<a class="one" href="https://www.worldscientific.com/doi/abs/10.1142/S0129167X19500071" target="_blank">
<b>Internat. J. Math.</b> 30 (2019), no. 2, p. 1950007, 46.
</a>
<a href="https://arxiv.org/abs/1612.06593" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
<i>Finite group actions on moduli spaces of vector bundles.</i><br>
<a class="one" href="https://tsg.centre-mersenne.org/articles/10.5802/tsg.354/" target="_blank">
<b>Sémin. Théor. Spectr. Géom.</b> (Grenoble) 34 (2016-2017), 33–63.
</a>
<a href="https://arxiv.org/abs/1608.03977" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
<i>On the Narasimhan-Seshadri correspondence for Real and Quaternionic vector bundles.</i><br>
<a class="one" href="https://projecteuclid.org/journals/journal-of-differential-geometry/volume-105/issue-1/On-the-NarasimhanSeshadri-correspondence-for-real-and-quaternionic-vector-bundles/10.4310/jdg/1483655861.full" target="_blank">
<b>J. Differential Geom.</b> (2017) 105 (1), 119–162.
</a>
<a href="https://arxiv.org/abs/1509.02052" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
<i>Lectures on Klein surfaces and their fundamental group.</i> In <i>Geometry and Quantization of Moduli Spaces.</i>
<a class="one" href="https://www.springerprofessional.de/en/geometry-and-quantization-of-moduli-spaces/11961486" target="_blank"> Advanced Courses in Mathematics - CRM Barcelona</a>. Springer (2016), 67–108.
<a href="https://arxiv.org/abs/1509.01733" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
With Indranil Biswas. <i>Vector bundles over a real elliptic curve.</i><br>
<a class="one" href="https://msp.org/pjm/2016/283-1/p03.xhtml" target="_blank">
<b>Pacific J. Math.</b> (2016) 283 (1), 43–62.
</a>
<a href="https://arxiv.org/abs/1410.6845" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
<i>Differential geometry of holomorphic vector bundles on a curve.</i>
In <i>Geometric and Topological Methods for Quantum Field Theory.</i> <a class="one" href="https://www.cambridge.org/core/books/abs/geometric-and-topological-methods-for-quantum-field-theory/differential-geometry-of-holomorphic-vector-bundles-on-a-curve/DD50E870D4EB66745C1AF2B6F8071D3F" target="_blank">
Proceedings of the 2009 Villa de Leyva Summer School</a>. Cambridge University Press (2013), 39–80.
<a href="https://arxiv.org/abs/1509.01734" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
With Chiu-Chu Melissa Liu. <i>The Yang-Mills equations over Klein surfaces.</i><br>
<a class="one" href="https://academic.oup.com/jtopol/article-abstract/6/3/569/949834" target="_blank">
<b>J. Topol.</b> (2013) 6 (3), 569–643.
</a>
<a href="https://arxiv.org/abs/1109.5164" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
<i>Real points of coarse moduli schemes of vector bundles on a real algebraic curve.</i><br>
<a class="one" href="https://www.intlpress.com/site/pub/pages/journals/items/jsg/content/vols/0010/0004/a002/" target="_blank">
<b>J. Symplectic Geom.</b> 10 (2012), no. 4, 503–534.
</a>
<a href="https://arxiv.org/abs/1003.5285" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
<i>Moduli spaces of vector bundles over a Klein surface.</i><br>
<a class="one" href="https://link.springer.com/article/10.1007/s10711-010-9526-3" target="_blank">
<b>Geom. Dedicata<b> 151 (2011), no. 1, 187–206.
</a>
<a href="https://arxiv.org/abs/0912.0659" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
<i>Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surface groups.</i><br>
<a class="one" href="https://link.springer.com/article/10.1007/s00208-008-0241-4" target="_blank">
<b>Math. Ann.</b> 342 (2008), no. 2, 405–447.
</a>
<a href="https://arxiv.org/abs/math/0703869" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
<i>Anti-symplectic involutions on quasi-Hamiltonian quotients.</i><br>
<a class="one" href="https://wwwfr.uni.lu/recherche/fstm/dmath/travaux_mathematiques/tm_2007_schaffhauser_pdf" target="_blank">
<b>Trav. Math.</b> 17 (2007) 57–64.
</a>
<a href="https://wwwfr.uni.lu/content/download/75306/940327/file/TM-2007-Schaffhauser.pdf" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
<i>A note on quasi-Hamiltonian geometry and representation spaces of surface groups.</i><br>
<b>Sem. Math. Sci.</b> 36 (2007), 35–48.
<a href="https://www.researchgate.net/publication/267078750_A_note_on_quasi-Hamiltonian_geometry_and_representation_spaces_of_surfaces_groups" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
<i>Quasi-Hamiltonian quotients as disjoint unions of symplectic manifolds.</i> In <i>Non-Commutative Geometry and Physics 2005.</i>
<a class="one" href="https://doi.org/10.1142/9789812779649_fmatter" target="_blank"> Proceedings of the 2005 International Sendai-Beijing Joint Workshop</a>, 31-54. World Scientific Press (2007).
<a href="https://arxiv.org/abs/math/0701905" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
<i>Un théorème de convexité réel pour les applications moment à valeurs dans un groupe de Lie.</i><br>
<a class="one" href="https://www.sciencedirect.com/science/article/pii/S1631073X07002282" target="_blank">
<b>C. R. Math. Acad. Sci. Paris</b> 345 (2007), no. 1, 25–30.
</a>
<a href="https://arxiv.org/abs/math/0609517" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
<i>Representations of the fundamental group of an L-punctured sphere generated by products of Lagrangian involutions.</i><br>
<a class="one" href="https://www.cambridge.org/core/journals/canadian-journal-of-mathematics/article/representations-of-the-fundamental-group-of-an-l-punctured-sphere-generated-by-products-of-lagrangian-involutions/D512076A0C280C3F3D6DE391003B832E" target="_blank">
<b>Canad. J. Math.</b> 59 (2007), no. 4, 845–879.
</a>
<a href="https://arxiv.org/abs/math/0608682" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li><span>
With Elisha Falbel and Jean-Pierre Marco. <i>Classifying triples of Lagrangians in a Hermitian vector space.</i>
<a class="one" href="https://www.sciencedirect.com/science/article/pii/S0166864104000628" target="_blank">
<br><b>Topology Appl.</b> 144 (2004), no. 1-3, 1–27.
</a>
<a href="https://www.researchgate.net/publication/237332750_Classifying_triples_of_Lagrangians_in_a_Hermitian_vector_space" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
</ol>
<h3 class="w3-padding-32">Preprints</h3>
<ul>
<li>
<span>
<i>Coming soon!</i>
</span>
</li>
</ul>
<h3 class="w3-padding-32">Theses</h3>
<ul>
<li><span>Habilitation Thesis: <i>Topology of representation varieties of Fuchsian groups</i> (2019).
<a href="https://hal.archives-ouvertes.fr/tel-02394282v2" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li><span>
Doctoral Thesis: <i>Decomposable representations and Lagrangian submanifolds of moduli spaces associated to surfaces groups</i> (2005).
<a href="https://hal.archives-ouvertes.fr/tel-00264370" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
</ul>
<h3 class="w3-padding-32">Slides from conference talks and other material</h3>
<ul>
<li>
<span>
<i>
An informal introduction to formal mathematics
</i>
(Waseda University Geometry Seminar).
<a href="FormalMath/Waseda2023.html">
<i class="fa-regular fa-file-lines w3-hover-opacity"></i>
</a>
</span>
</li>
<li>
<span>
<i>
Welcome to HEGL!
</i>
Visiting Day of the 10th
<a class="one" href="https://www.heidelberg-laureate-forum.org" target="_blank">
<b>
Heidelberg Laureate Forum
</b>
</a>(27.09.2023).
<a href="HEGL/HEGL.html">
<i class="fa-regular fa-file-lines w3-hover-opacity"></i>
</a>
</span>
</li>
<li><span> <i>Formally real fields</i>. <a class="one" href="https://www.lorentzcenter.nl/machine-checked-mathematics.html" target="_blank"><b>Machine-checked mathematics</b></a> (Lorentz Center, Leiden).
<a href="slides/Leiden_2023.pdf"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li><span> <i>Hodge numbers of moduli stacks of principal bundles</i>. <a class="one" href="https://conferences.cirm-math.fr/2605.html" target="_blank"><b>Rencontres du GDR GAGC 2022</b></a> (CIRM, Luminy).
<a href="pdf/Hodge_GAGC_2022.pdf"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li><span> <i>Twisted character varieties</i>. <a class="one" href="https://conferences.cirm-math.fr/2622.html" target="_blank"><b>Conference in honour of Elisha Falbel, 2022</b></a> (CIRM, Luminy).
<a href="pdf/Elisha_2022.pdf"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li><span>
Coco's Fest 2016: <i>Categorías abelianas con conjugación</i> (Bogotá, 2016).
<a href="pdf/Coco75.pdf"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li><span>
50 years of the Narasimhan-Seshadri theorem: <i>Real Seifert manifolds and the Narasimhan-Seshadri correspondence</i> (NS@50, Chennai 2015).
<a href="pdf/NS_at_50.pdf"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li><span>
<i>The Yang-Mills equations over Klein surfaces</i> (Seoul ICM 2014, contributed talk).
<a href="pdf/ICM2014.pdf"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li><span>
<i>Monodromy of Knizhnik-Zamolodchikov equations</i> (2007).
<a href="pdf/KZ.pdf"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
</ul>
</div>
<div class="w3-third w3-center">
<a href="https://webusers.imj-prg.fr/~leila.schneps/grothendieckcircle/Allonsnous.pdf" target="_blank"><i class="fa fa-book w3-padding-64 w3-text-grey" title="Dans les cas extrêmes, on va jusqu'à mesurer la productivité des scientifiques au nombre de pages publiées. Dans ces conditions, pour un grand nombre de scientifiques, certainement pour l'écrasante majorité, à l'exception véritablement de quelques uns qui ont la chance d'avoir, disons, un don exceptionnel ou d'être dans une position sociale et une disposition d'esprit qui leur permettent de s'affranchir de ces sentiments de contrainte, pour la plupart la recherche scientifique est une véritable contrainte qui tue le plaisir que l'on peut avoir à l'effectuer (Alexander Grothendieck)."></i></a>
</div>
</div>
</div>
<!-- Second Grid -->
<div id="teaching" class="w3-row-padding w3-light-grey w3-padding-64 w3-container">
<div class="w3-content">
<div class="w3-third w3-center">
<a href="https://webusers.imj-prg.fr/~michele.vergne/ecritsdivers/devenirMath.pdf" target="_blank"><i class="fa-solid fa-person-chalkboard fa-7x w3-padding-64 w3-text-grey w3-margin-right" title="Comme en général, comme c’était la mode, les professeurs passaient très vite sur les détails fastidieux des démonstrations et que moi, je ne voyais pas à quels objets connus, classiques, elles renvoyaient, je ne pouvais pas rétablir les jalons qui manquaient… : “Par un raisonnement standard, on prouve que…”, et je me sentais réduite à l’infériorité totale de ne pas pouvoir deviner quel était ce raisonnement standard. Je pense que quand les professeurs ne font pas un effort pour expliquer d’où viennent leurs idées, leur intuition, (car maintenant, je ne crois plus que dès le berceau, les hommes étaient prédestinés à savoir, comme moi à ignorer) eh bien, ils pratiquent, délibérément ou non, une attitude raciste et sexiste à l’égard des catégories qui n’ont pas baigné toute leur vie dans la culture mathématique et qui n’ont aucun autre moyen de savoir, hors de l’enseignement, d’où viennent les idées en cours (Michèle Vergne)."></i></a>
</div>
<div class="w3-twothird">
<h1>Teaching</h1>
<h3 class="w3-padding-32">Summer Semester 2024</h3>
<ul>
<li>
<span>
With <a class="one" href="https://www.mathi.uni-heidelberg.de/~arandecker/" target="_blank">
Anja Randecker.
</a>
<b>HEGL (Pro)seminar:</b>
<a class="one" href="SoSe_2024/MatheUnterricht.html">
<i>Teaching mathematics.</i>
</a>
<a class="one" href="https://hegl.mathi.uni-heidelberg.de/wp-content/uploads/2024/04/HEGLsem_SS24_Aushang.pdf" target="_blank">
<i class="fa-regular fa-file-pdf w3-hover-opacity"></i>
</a>
</span>
</li>
<li>
<span>
With <a class="one" href="https://www.judith-ludwig.com" target="_blank">
Judith Ludwig.
</a>
<a class="one" href="SoSe_2024/CompAssistedMath2024.html">
(Pro)Seminar on Computer-assisted Mathematics.
</a>
<a class="one" href="SoSe_2024/RechnergestuetzteMathe2024.pdf">
<i class="fa-regular fa-file-pdf w3-hover-opacity"></i>
</a>
</span>
</li>
</ul>
<h3 class="w3-padding-32">Winter Semester 2023-2024</h3>
<ul>
<li>
<span>
With <a class="one" href="https://www.mathi.uni-heidelberg.de/~arandecker/" target="_blank">
Anja Randecker.
</a> <b>HEGL (Pro)seminar:</b>
<a class="one" href="HEGL/WiSe_2023_2024/README.html">
<i>Illustrating mathematics.</i>
<!--
</a>
-->
<a class="one" href="https://hegl.mathi.uni-heidelberg.de/wp-content/uploads/2023/10/HEGLsem_WiSe23-24_v2.pdf" target="_blank">
<i class="fa-regular fa-file-pdf w3-hover-opacity"></i>
</a>
</span>
</li>
<li>
<span>
<a class="one" href="WiSe_2023_2024/LieAlgebrasSeminar.html">
Seminar on Lie algebras.
</a>
<a class="one" href="WiSe_2023_2024/SeminarLieAlgebras.pdf">
<i class="fa-regular fa-file-pdf w3-hover-opacity"></i>
</a>
</span>
</li>
</ul>
<h3 class="w3-padding-32">Summer Semester 2023</h3>
<ul>
<li> <span>Vector bundles on algebraic curves
<a class="one" href="SoSe_2023/Vector_bundles_on_curves.pdf">
<i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li> <span> <a class="one" href="SoSe_2023/comp_assisted_math_seminar.html">(Pro)seminar on Computer-assisted Mathematics
<a class="one" href="SoSe_2023/RechnergestuetzteMathe.pdf">
<i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
</ul>
<h3 class="w3-padding-32">Winter Semester 2022-2023</h3>
<ul>
<li> <span> <a class="one" href="https://padlet.com/matematiflo/real_algebraic_varieties" target="_blank">Real algebraic varieties </a>
<a class="one" href="WiSe_2022_2023/Real_algebraic_varieties_program.pdf">
<i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
<li> <span> <a class="one" href="WiSe_2022_2023/sheaf_theory_seminar.html">Seminar on Sheaf Theory
<a class="one" href="WiSe_2022_2023/Seminar_on_sheaf_theory.pdf">
<i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span></li>
</ul>
<h3 class="w3-padding-32">Online resources</h3>
<ul>
<li> <span><a class="one" href="https://padlet.com/matematiflo/Lineal" target="_blank">Linear algebra</a>  (Padlet)</span></li>
<!--<li> <span>Notes on sheaf theory  (Students project)</span></li>-->
</ul>
<h3 class="w3-padding-32">Past courses</h3>
<ul>
<li> <span>Algebraic topology 1</span></li>
<li> <span>Algebraic topology 2</span></li>
<li> <span>Complex analysis</span></li>
<li> <span>Differential equations</span></li>
<li> <span>Differential geometry 1</span></li>
<li> <span>Geometric invariant theory</span></li>
<li> <span>Measure theory</span></li>
<li> <span>Riemann surfaces</span></li>
<li> <span>Symplectic geometry</span></li>
<li> <span>Vector calculus</span></li>
</ul>
<h3 class="w3-padding-32">Lecture notes, books and other material</h3>
<ul>
<li><span>
<i>Lectures on Klein surfaces and their fundamental group</i> <a class="one" href="https://arxiv.org/abs/1509.01733" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a><br>
</span>
</li>
<li><span>
<i>Differential geometry of holomorphic vector bundles on a curve.</i> <a class="one" href="https://arxiv.org/abs/1509.01734" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a><br>
</span>
</li>
<li><span>
<i>Analyse L3</i>. Pearson Education France (2009). ISBN 9782744073502. <a class="one" href="https://www.researchgate.net/publication/258568061_Mathematiques_L3" target="_blank"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li><span>
<i> El plano hiperbólico, de la geometría a la teoría de números</i>. <a class="one" href="pdf/plan_hip.pdf"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
<li><span>
MCA 2017: A report on the <a class="one" href="https://scm.org.co/gender-and-mathematics-panel-mca-2017/" target="_blank"><i>Gender and Mathematics Panel</i></a> for the Colombian Society of Mathematics.
</span>
</li>
<li><span>
<i>Congreso Internacional de Matemáticos 2014</i>. Hipótesis 17 (2014), 17-18. <a class="one" href="pdf/Hipotesis-ICM-2014.pdf"><i class="fa-regular fa-file-pdf w3-hover-opacity"></i></a>
</span>
</li>
</ul>
<!--<p class="w3-text-grey">List of past courses</p>-->
</div>
</div>
</div>
<!-- Third Grid -->
<div id="students" class="w3-row-padding w3-padding-64 w3-container">
<div class="w3-content">
<div class="w3-twothird">
<h1>Supervision and mentoring</h1>
<p class="w3-text-grey" style="text-align: justify;">
If you want to know what it is like to write a thesis under my supervision (the good <i>and</i> the bad), talk to my students!
</p>
<h3 class="w3-padding-32">Undergraduate students</h3>
<ol>
<li> <span>
Sergio Pedraza-Rodríguez, Uniandes (2011). <i>Hurwitz surfaces.</i>
</span></li>
<li> <span>
Alejandro Rivera, ENS Lyon (2013). <i>Equivariant Morse theory in symplectic geometry.</i>
</span></li>
<li> <span>
Simón Soto-Ochoa, Uniandes (2016). <i>The modular group of a compact orientable surface.</i>
</span></li>
<li> <span>
Santiago Cortés-Gómez, Uniandes (2016). <i>Galois theory of separable algebras over a field.</i>
</span></li>
<li> <span>
Alirio Calderón-Díaz, Universidad Distrital de Bogotá (2017). <i>Gromov's affine non-squeezing theorem.</i>
</span></li>
<li> <span>
David Jaramillo-Duque, Uniandes (2017). <i>Clifford algebras and spin groups.</i>
</span></li>
<li> <span>
Nicolás Betancourt-Cardona, Uniandes (2019). <i>Extensions of field of meromorphic functions.</i>
</span></li>
<li> <span>
Manuel Aragón, Uniandes (2023). <i>Complex projective structures and opers.</i>
</span></li>
<!-- <li> <span>
Subham Das. <i>Harmonic metrics and the Donaldson functional.</i>
</span></li> -->
<li> <span>
Liva Diler, Universität Heidelberg (2024). <i>Equivariant cohomology of real algebraic varieties.</i>
</span></li>
<li> <span>
Chenyi Yang, Universität Heidelberg (2024). <i>Cell complexes in Homotopy Type Theory.</i>
</span></li>
</ol>
<h3 class="w3-padding-32">Master students</h3>
<ol>
<li> <span>
Andrés Jaramillo-Puentes, Uniandes (2012). <i>Uniformisation of real algebraic curves.</i>
</span></li>
<li> <span>
Ramón Urquijo-Novella, Uniandes (2012). <i>GIT quotients and symplectic quotients, the Kempf-Ness theorem.</i>
</span></li>
<li> <span>
Camilo Vargas-Contreras, Uniandes (2013). <i>Higgs bundles and hyper-Kähler reduction in infinite dimension.</i>
</span></li>
<li> <span>
Nicolás Walteros-Vergara, Uniandes (2018). <i>Unitary connexions and holomorphic vector bundles.</i>
</span></li>
<li> <span>
Juan Martín Pérez-Bernal, Uniandes (2019). <i>The moduli stack of elliptic curves.</i>
</span></li>
<li> <span>
Juan Sebastián Numpaque-Roa, Uniandes (2021). <i>The Hitchin fibration.</i>
</span></li>
<li> <span>
Emanuel Roth, Universität Heidelberg (2024). <i>The Harder-Narasimhan reduction of a principal bundle.</i>
</span></li>
<li> <span>
Till Janke, Universität Heidelberg. <i>Real spectrum compactification of Teichmüller space.</i>
</span></li>
</ol>
<h3 class="w3-padding-32">PhD students</h3>
<ol>
<li> <span>
Marwan Benyoussef, Freie Universität Berlin (co-supervision with Alexander Schmitt, since 2020).
</span></li>
</ol>
<h3 class="w3-padding-32">Postdocs</h3>
<ol>
<li> <span>
Leonardo Roa-Leguizamón, Uniandes (2022-2023).
</span></li>
<li> <span>
Zeinab Toghani, Uniandes (2022).
</span></li>
</ol>
</div>
<div class="w3-third w3-center">
<a href="https://www.nytimes.com/interactive/2022/11/14/magazine/brian-eno-interview.html" target="_blank"><i class="fa-regular fa-graduation-cap w3-padding-64 w3-text-grey" title="I think charisma comes out of the sense you have that not only is somebody different but they’re also confident about it, committed to it, obsessed by it even. We don’t find uncertainty charismatic. Uncertainty doesn’t work for anybody very well, because in general the media don’t appreciate people like that. I would like to cultivate a charisma of uncertainty, a charisma of admitting that you’re making it up as you go along (Brian Eno)."></i></a>
</div>
</div>
</div>
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<h3 class="w3-margin w3-xlarge"><small><a href="mailto:fschaffhauser_@_mathi.uni-heidelberg.de">Contact</a><br><sub>(change _@_ to @)</sub></small></h3>
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