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			<h1>Raymond van Bommel</h1>
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				Research associate at University of Bristol				
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						<h1>Menu</h1>
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								<a href="#contact">Contact details</a>				  
								<a href="#publications">Publications</a>				
								<a href="#talks">Talks</a>	
								<a href="#other_texts">Other mathematical texts</a>
								<a href="#teaching">Teaching</a>	
								<a href="#seminar">Seminars</a>						 
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						<h1><a name="contact" id="contact"></a>Contact details</h1>
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							<img src="foto.jpg" alt="picture of me" width="300px" /><br />
								Office: Fry Building, office 1.10 (directions are <a href="https://www.bristol.ac.uk/maths/contacts/">here</a>)<br />
								E-mail: <tt><a class="hidemail">click here</a></tt><br />
								Public key: <tt><a href="VanBommel.asc">click here</a></tt><br />
								Mail address: Fry Building, Woodland Road, Bristol, BS8 1UG, United Kingdom
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						<h1><a name="publications" id="publications"></a>Publications</h1>

						<ul>
							<li><a href="https://arxiv.org/abs/2506.14026">&#8220;Curve equations from expansions of 1-forms at a nonrational point&#8221;</a> (preprint, joint with Edgar Costa, Bjorn Poonen, Padmavathi Srinivasan, accepted in Contemporary Mathematics: LuCaNT 2025)</li>
							<li><a href="https://arxiv.org/abs/2411.07857">&#8220;17T7 is a Galois group over the rationals&#8221;</a> (preprint, joint with Edgar Costa, Noam D. Elkies, Timo Keller, Sam Schiavone, John Voight)</li>
							<li><a href="https://doi.org/10.1007/s40993-024-00590-x">&#8220;Reduction of Plane Quartics and Dixmier-Ohno invariants&#8221;</a> (published in Research in Number Theory, joint with Jordan Docking, Reynald Lercier, Elisa Lorenzo Garc&iacute;a, preprint on <a href="https://arxiv.org/abs/2401.13902">ArXiV</a>)</li>
							<li><a href="https://doi.org/10.1007/s10208-025-09704-y">&#8220;Reduction of Plane Quartics and Cayley Octads&#8221;</a> (published in Foundations of Computational Mathematics, joint with Jordan Docking, Vladimir Dokchitser, Reynald Lercier, Elisa Lorenzo Garc&iacute;a, preprint on <a href="https://arxiv.org/abs/2309.17381">ArXiv</a>)</li>
							<li><a href="https://doi.org/10.1090/conm/796/16002">&#8220;Computing isogeny classes of typical principally polarized abelian surfaces over the rationals&#8221;</a> (published in AMS Contemporary Mathematics book &#8220;LuCaNT: LMFDB, Computation, and Number Theory&#8221;, joint with Shiva Chidambaram, Edgar Costa, Jean Kieffer, preprint on <a href="https://arxiv.org/abs/2301.10118">ArXiV</a>)</li>
							<li><a href="https://arxiv.org/abs/2301.08312">&#8220;Computing torsion for plane quartics without using height bounds&#8221;</a> (preprint)</li>
							<li><a href="https://doi.org/10.1007/s00208-024-03084-4">&#8220;Abelian varieties of prescribed order over finite fields&#8221;</a> (published in Mathematische Annalen, joint with Edgar Costa, Wanlin Li, Bjorn Poonen, and Alexander Smith, preprint on <a href="<a href="https://arxiv.org/abs/2106.13651">ArXiV</a>)</li>
							<li><a href="https://doi.org/10.1112/blms.12604">&#8220;A user&apos;s guide to the local arithmetic of hyperelliptic curves&#8221;</a> (published in Bulletin of the London Mathematical Society, preprint on <a href="https://arxiv.org/abs/2007.01749">ArXiv</a>, joint with Alex J. Best, L. Alexander Betts, Matthew Bisatt, Vladimir Dokchitser, Omri Faraggi, Sabrina Kunzweiler, C&eacute;line Maistret, Adam Morgan, Simone Muselli, and Sarah Nowell)</li>
							<li><a href="https://doi.org/10.1007/978-3-030-80914-0_6">&#8220;Efficient computation of BSD invariants in genus 2&#8221;</a> (published in Simons Symposia, Arithmetic Geometry, Number Theory, and Computation, preprint on <a href="https://arxiv.org/abs/2002.04667">ArXiv</a>)</li>
							<li><a href="https://doi.org/10.1112/jlms.12847">&#8220;Boundedness in families with applications to arithmetic hyperbolicity&#8221;</a> (published in Journal of the London Mathematical Society, preprint on <a href="https://arxiv.org/abs/1907.11225">ArXiv</a>, joint with Ariyan Javanpeykar and Ljudmila Kamenova)</li>
							<li><a href="https://doi.org/10.1090/mcom/3441">&#8220;Explicit arithmetic intersection theory and computation of N&eacute;ron-Tate heights&#8221;</a> (published in Math. Comp., preprint on <a href="https://arxiv.org/abs/1809.06791">ArXiv</a>, joint with David Holmes and Steffen M&uuml;ller)</li>
							<li><a href="https://hdl.handle.net/1887/66673">&#8220;Models of curves: The Birch and Swinnerton-Dyer conjecture &amp; ordinary reduction&#8221;</a>, PhD thesis</li>
							<li><a href="https://doi.org/10.1007/s00013-019-01383-w">&#8220;The Birch and Swinnerton-Dyer conjecture for an elliptic curve over &#x0211A;(&#8732;5)&#8221;</a> (published in Arch. Math., preprint on <a href="https://arxiv.org/abs/1805.05862">ArXiv</a>)</li>
							<li><a href="https://doi.org/10.1080/10586458.2019.1592035">&#8220;Numerical verification of the Birch and Swinnerton-Dyer conjecture for hyperelliptic curves of higher genus over &#x0211A; up to squares&#8221;</a> (published in Exp. Math., preprint on <a href="https://arxiv.org/abs/1711.10409">ArXiv</a>)</li>
							<li><a href="https://doi.org/10.1142/S1793042118500811">&#8220;Inverse Galois problem for ordinary curves&#8221;</a> (published in IJNT, preprint on <a href="https://arxiv.org/abs/1704.07608">ArXiv</a>)</li>
						</ul>

						<h1><a name="talks" id="talks"></a>Talks</h1>
						<ul>
							<li><a href="talks/Cambridge2025.pdf">&#8220;17T7 as a Galois group over Q through Hilbert modular forms&#8221;</a>, Number Theory Seminar, Cambridge (UK), February 2025</li>
							<li><a href="talks/Heilbronn2024.pdf">&#8220;17T7 as a Galois group over Q through Hilbert modular forms&#8221;</a>, Heilbronn Number Theory Seminars, October 2024</li>
							<li><a href="talks/ANTS2024.pdf">&#8220;Reduction of plane quartics and Dixmier-Ohno invariants&#8221;</a>, Sixteenth Algorithmic Number Theory Symposium (ANTS XVI), July 2024</li>
							<li><a href="talks/Simons2024.pdf">&#8220;Reduction of Plane Quartics and Cayley Octads&#8221;</a>, 
2024 Simons Collaboration on Arithmetic Geometry, Number Theory, and Computation Annual Meeting, January 2024</li>
							<li><a href="talks/roazhon.pdf">&#8220;Isogeny classes of typical, principally polarized abelian surfaces over Q&#8221;</a>, IRMAR, Rennes, November 2023</li>
							<li><a href="talks/LuCaNT.pdf">&#8220;Isogeny classes of typical, principally polarized abelian surfaces over Q&#8221;</a>, LMFDB, Computation, and Number Theory (LuCaNT), July 2023</li>
							<li><a href="talks/Linfoot.pdf">&#8220;Abelian varieties of prescribed order&#8221;</a>, Linfoot Number Theory Seminars, December 2021</li>
							<li><a href="talks/Leiden2020.pdf">&#8220;Computation of BSD invariants in higher genus&#8221;</a>, Algebra, geometry and number theory seminar, Leiden, December 2020</li>
							<li><a href="talks/BombieriStepanov.pdf">&#8220;The Bombieri-Stepanov approach to the Riemann hypothesis for curves over finite fields&#8221;</a>, <a href="https://math.mit.edu/nt/index_stage.html">STAGE</a>, November 2020</li>
							<li><a href="talks/vantage.pdf">&#8220;Cluster pictures for hyperelliptic curves&#8221;</a>, VaNTAGe seminar, November 2020 (<a href="https://www.youtube.com/watch?v=_fIJVnVnpz8">video</a>)</li>
							<li>&#8220;Boundedness in families of projective varieties with applications to arithmetic hyperbolicity&#8221;, BU number theory seminar, Boston University, January 2020</li>
							<li><a href="talks/JMM_2020.pdf">&#8220;Explicit arithmetic intersection theory and computation of N&eacute;ron-Tate heights&#8221;</a>, Joint mathematics meeting, Denver, January 2020</li>
							<li>&#8220;Boundedness in families of projective varieties with applications to arithmetic hyperbolicity&#8221;, Number theory seminar, MIT, Autumn 2019</li>
							<li><a href="talks/SFB2.pdf">&#8220;Boundedness in families of projective varieties with
applications to arithmetic hyperbolicity&#8221;</a>, SFB Kolloquium, Mainz, Summer 2019</li>
							<li><a href="talks/Kobayashi.pdf">&#8220;Kwack's theorem and its applications&#8221;</a>, Seminar: Algebraic properties of hyperbolic varieties, Mainz, Winter 2018/2019</li>
							<li>&#8220;De Rham cohomology for physicists&#8221;, joint seminar between mathematics and physics, Mainz, Winter 2018/2019</li>
							<li><a href="talks/SFB1.pdf">&#8220;How to compute regulators using Arakelov intersection theory&#8221;</a>, SFB Kolloquium, Mainz, Autumn 2018</li>
							<li><a href="talks/Trieste1.pdf">&#8220;Numerical verification of BSD&#8221;</a>, <a href="https://people.maths.bris.ac.uk/~matyd/Trieste2017.html">Curves and L-functions, Trieste</a>, September 2017</a></li>
							<li><a href="talks/modelsofcurves.pdf">&#8220;Models of curves&#8221;</a>, N&eacute;ron model seminar, Leiden, Autumn 2017</li>
							<li><a href="talks/Bristol1.pdf">&#8220;Numerical verification of BSD&#8221;</a>, <a href="https://people.maths.bris.ac.uk/~matyd/BSDData/">BSD Data &#64; Bristol</a>, March 2017</li> 
							<li><a href="talks/duality_av.pdf">&#8220;Duality of abelian varieties&#8221;</a>, Good Reduction of Abelian Varieties seminar, Amsterdam, Autumn 2016</li>
							<li><a href="talks/Leiden1.pdf">&#8220;Inverse Galois problem for ordinary curves: construction of some examples&#8221;</a>, Algebra seminar, Leiden, Autumn 2016</li>
							<li><a href="talks/bsdtalk.pdf">&#8220;The Birch and Swinnerton-Dyer conjecture&#8221;</a>, Seminar on rational points on elliptic curves, Leiden, Spring 2016</li>
							<li><a href="talks/algant_essen.pdf">&#8220;N&eacute;ron models&#8221;</a>, joint with M. Derickx, G. Orecchia, M. Tzortzakis, ALGANT presentation, Essen, Spring 2016</li>		
							<li><a href="talks/modstack2.pdf">&#8220;The algebraic stack Mg&#8221;</a>, Moduli stacks seminar, Leiden, Autumn 2015</li>
							<li><a href="talks/padic1.pdf">&#8220;The Grothendieck monodromy theorem&#8221;</a>, Local Galois representations seminar, Leiden, Spring 2015</li>
							<li><a href="talks/etale3.pdf">&#8220;Cohomology on quasi-coherents, torsors, H1 and
the Picard group&#8221;</a>, Etale cohomology seminar, Leiden, Autumn 2014</li>	
							<li><a href="talks/Tannaka.pdf">&#8220;Jordan decomposition and Tannaka duality&#8221;</a>, Master student seminar, Paris-Sud, Spring 2013.</li>			
						</ul>	

						<h1><a name="other_texts" id="other_texts"></a>Other mathematical texts</h1>
										<ul>
							<li><a href="Pythagoras_Wie_is_de_dief.pdf">&#8220;Wie is de dief?&#8221;</a>, Pythagoras (April 2016)</li>
							<li><a href="Master.pdf">&#8220;Almost all hyperelliptic Jacobians have a bad semi-abelian prime&#8221;</a>, master's thesis (2014)</li>
							<li><a href="TER.pdf">&#8220;The Grothendieck group of GL(n)&#8221;</a>, Travaux encadr&eacute; de recherche (2013)</li>
							<li><a href="Bachelor.pdf">&#8220;Using the Chebotarev density theorem to calculate the size of Galois groups&#8221;</a>, bachelor's thesis (2012)</li>
							<li><a href="Pythagoras_Reekssommen_en_tweemachten.pdf">&#8220;Reekssommen en tweemachten&#8221;</a>, Pythagoras (November 2010)</li>
							<li><a href="lpc-artikel.pdf">&#8220;Dualiteit&#8221;</a>, Dutch article for the second year student seminar LPC (April 2010)</li>
						</ul>
					
						<h1><a name="teaching" id="teaching"></a>Teaching</h1>
												
														<ul>
								<li>Spring 2025: <a href="teaching/tcc2025.htm">The Birch and Swinnerton-Dyer conjecture explained</a> (<a href="https://www.maths.ox.ac.uk/groups/tcc">Taught Course Centre</a> course, University of Bristol)
								<li>Autumn 2021: <a href="https://math.mit.edu/classes/18.721/Fall2021/">Introduction To Algebraic Geometry (18.721)</a> (Massachusetts Institute of Technology)</li>
								<li>Summer 2019: <a href="https://www.mathematik.uni-mainz.de/lehrveranstaltungen/?event_id=366564671866814">Computeralgebra</a> (Johannes Gutenberg-Universit&auml;t Mainz)</li>
								<li>Winter 2018/2019: <a href="https://ilias.uni-mainz.de/goto.php?client_id=JOGU&target=crs_634588">Zahlentheorie</a> (Johannes Gutenberg-Universit&auml;t Mainz)</li>
								<li>Spring 2018: <a href="https://studiegids.leidenuniv.nl/en/courses/show/74021/mathematical-reasoning">Mathematical Reasoning</a> (Leiden University College)</li>
								<li>Autumn 2017: <a href="https://pub.math.leidenuniv.nl/~griffonrmm/CFF.html">Curves over Finite Fields</a> (<a href="LectureNotes_CodingTheory.pdf">notes coding theory</a>, <a href="LectureNotes_EllipticCurveCryptography.pdf">notes elliptic curve crypto</a>, <a href="Homework3.pdf">homework 3</a> (small typo has been corrected on 6 December), Universiteit Leiden)</li>
								<li>Spring 2017: <a href="https://studiegids.leidenuniv.nl/en/courses/show/62715/Mathematical-Reasoning">Mathematical Reasoning</a> (Leiden University College)</li>
								<li>Autumn 2016 &amp; Spring 2017: <a href="http://pub.math.leidenuniv.nl/~lyczakjt/teaching/wwt1617.html">Wiskundewedstrijdtraining</a> (Universiteit Leiden)</li>
								<li>Autumn 2016: Wiskundige Structuren (Universiteit Leiden)</li>
								<li>Autumn 2016: <a href="http://pub.math.leidenuniv.nl/~edixhovensj/teaching/2016-2017/LA1/index.html">Lineaire Algebra I voor wiskunde</a> (Universiteit Leiden)</li>
								<li>Spring 2016: <a href="http://www.few.vu.nl/~sdn249/modularforms16/index.html">Modular Forms</a> (Mastermath)</li>
								<li>Autumn 2015 &amp; Spring 2016: <a href="http://pub.math.leidenuniv.nl/~lyczakjt/teaching/wwtnj2015.html">Wiskundewedstrijdtraining</a> (Universiteit Leiden)</li>							
								<li>Autumn 2015: <a href="https://studiegids.leidenuniv.nl/courses/show/46915/statistiek_lst">Statistiek voor Life Science and Technology</a> (Universiteit Leiden)</li>				
								<li>Spring 2015: <a href="http://pub.math.leidenuniv.nl/~lyczakjt/teaching/wwtvj2015.html">Wiskundewedstrijdtraining</a></li>							
								<li>Autumn 2014: <a href="http://www.math.leidenuniv.nl/~desmit/edu/ant_2014/">Algebraic Number Theory</a> (Mastermath)</li>
								<li>Spring 2014: <a href="http://pub.math.leidenuniv.nl/~edixhovensj/teaching/2013-2014/algebra3/">Algebra 3</a> (Universiteit Leiden)</li>
								<li>Autumn 2013: Introduction to Manifolds (Universiteit Leiden) &amp; Besliskunde 2 (Universiteit Leiden)</li>
								<li>Spring 2012: Numerieke Methoden 1 (Universiteit Leiden)</li>
								<li>Autumn 2011: <a href="http://pub.math.leidenuniv.nl/~jongrsde/olderteaching/LA1NA2011/">Lineaire Algebra 1 voor Natuur- en Sterrenkundigen</a> (Universiteit Leiden)</li></ul>
						
						<h1><a name="seminar" id="seminar"></a>Seminars</h1>
							<ul>
							<li><a href="https://www.ntwebseminar.org/">Number Theory Web Seminar</a> (Continuously, online)</li>
							<li><a href="https://sites.google.com/view/vantageseminar">VaNTAGe</a> (Continuously, online)</li>
							<li><a href="https://math.mit.edu/nt/">MIT number theorey seminar</a> (Continuously, MIT)</li>
							<li><a href="https://math.mit.edu/nt/">STAGE</a> (Continuously, MIT)</li>
							<li><a href="http://www.staff.uni-mainz.de/dfesti/QuantumSeminar.html">Quantum computation and quantum information seminar</a> (Summer 2019, Mainz, organising)</li>
							<li><a href="https://www.agtz.mathematik.uni-mainz.de/seminar-algebraic-properties-of-hyperbolic-varieties/">Seminar: Algebraic properties of hyperbolic varieties</a> (Winter 2018/2019, Mainz)</li>
							<li><a href="https://www.agtz.mathematik.uni-mainz.de/aktuelles/sfbtrr45-kolloquium/">SFB/TRR45 Kolloquium</a> (Continuously, Mainz)</li>
							<li><a href="http://pub.math.leidenuniv.nl/~winterrl/TropicalGeometry.html">Tropical geometry seminar</a> (Spring 2018, Leiden)</li>
							<li><a href="http://pub.math.leidenuniv.nl/~akeyrgj/neron.html">N&eacute;ron models seminar</a> (Autumn 2017, Leiden)</li>
							<li><a href="http://pub.math.leidenuniv.nl/~akeyrgj/seminar.html">Logarithmic Geometry seminar</a> (Spring 2017, Leiden)</li>
							<li><a href="https://staff.fnwi.uva.nl/w.p.bindt/seminar.html">Good Reduction of Abelian Varieties seminar</a> (Autumn 2016, Amsterdam)</li>
							<li><a href="https://staff.fnwi.uva.nl/a.l.kret/seminar.html">Arithmetic and Algebraic Geometry Seminar</a> (Autumn 2016, Amsterdam)</a></li>
							<li><a href="http://www.math.leidenuniv.nl/~streng/calendar/">Rational points on elliptic curves</a> (Spring 2016, Leiden)</li>
							<li><a href="http://pub.math.leidenuniv.nl/~lyczakjt/seminar/knots2016.html">Knot theory</a> (Spring 2016, Leiden)</li>
							<li><a href="https://shotanimoto.wordpress.com/">Copenhagen K3-surfaces</a> (Autumn 2015, Copenhagen)</li>
							<li><a href="http://www.math.ku.dk/english/research/tfa/alg/ntseminar/">Copenhagen number theory</a> (Autumn 2015, Copenhagen)</li>
							<li><a href="2015/modstack.htm">Moduli stacks</a> (Autumn 2015, organising, Leiden)</li>
							<li><a href="http://pub.math.leidenuniv.nl/~vissehd/k3seminar/">K3 surfaces and their automorphisms</a> (Autumn 2014 / Spring 2015, Leiden)</li>
							<li>Local Galois representations (Spring 2015)</li>
							<li><a href="http://jinbijin.nl/2014/ec/">&Eacute;tale cohomology</a> (Autumn 2014, Leiden)</li>
							<li><a href="http://pub.math.leidenuniv.nl/~strengtc/algseminar/">Algebra, geometry and number theory</a> (Continuously, Leiden)</li>
							<li><a href="http://www.math.leidenuniv.nl/~desmit/ic/general.html">Intercity Number Theory</a> (Continuously, Leiden)</li>
							<li><a href="http://pub.math.leidenuniv.nl/~strengtc/colloquium/">General Mathematics Colloquium</a> (Continuously, Leiden)</li>
							</ul>
										
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