Benjamin Matschke – Research Summary

Publications and preprints

Diophantine geometry

• Quadratic fields admitting elliptic curves with rational j-invariant and good reduction everywhere, with Abhijit S. Mudigonda, Journal of Number Theory 247, 2023, 162–210., arXiv, github
• Tables of elliptic curves, 2020-21, github, slides
• Tables of number fields, 2020, github
• Elliptic curves with good reduction outside of the first six primes, with Alex Best, Simons Symposia series Arithmetic Geometry, Number Theory, and Computation, 2021, 215–235., arXiv, github
• Proofs by example, 2019, arXiv, slides
• Solving S-unit, Mordell, Thue, Thue-Mahler and generalized Ramanujan-Nagell equations via Shimura-Taniyama conjecture, with Rafael von Känel, Mem. Amer. Math. Soc. Vol. 286, No. 1419., arXiv, github
  Data: elliptic curves with good reduction outside S, abc triples, Mordell equation, S-integral points on elliptic curves of high rank, etc.
• Computing integral points on X_ns⁺(p), with Aurélien Bajolet and Yuri Bilu, Algebra Number Theory 15 (3), 2021, 569–608, arXiv, github

Higher spectral sequences

• Lecture notes for a mini-course on (higher) spectral sequences: pdf, slides
• Higher spectral sequences, 2014-21, arXiv
• Successive spectral sequences, Trans. Amer. Math. Soc. 375(09), 2022, 6205–6254., arXiv

Topological combinatorics

• Quadrilaterals inscribed in convex curves, Trans. Amer. Math. Soc. 374 (8), 2021, 5719–5738., arXiv
• A survey on the Square Peg Problem, Notices Amer. Math. Soc. 61 (4), 2014, 346–352, pdf
• A parametrized version of the Borsuk-Ulam-Bourgin-Yang-Volovikov theorem, J. Topol. Anal. 6 (2), 2014, 263–280, pdf
• Projective center point and Tverberg theorems, with Roman Karasev, Discrete Comput. Geom. 52 (1), 2014, 88–101, pdf, arXiv
• Equivariant topology methods in discrete geometry, 2011, phd thesis, pdf, library copy
• A tight colored Tverberg theorem for maps to manifolds, with Pavle Blagojević and Günter Ziegler, Topol. Appl. 158 (12), 2011, 1445–1452, pdf, arXiv
• Optimal bounds for a colorful Tverberg-Vrećica type problem, with Pavle Blagojević and Günter Ziegler, Adv. Math. 226 (6), 2011, 5198–5215, pdf, arXiv
• Optimal bounds for the colored Tverberg problem, with Pavle Blagojević and Günter Ziegler, J. Eur. Math. Soc. 17 (4), 2015, 739–754, pdf, arXiv, java applet
• Equivariant topology and applications, 2008, diploma thesis, pdf
• A note on masspartitions by hyperplanes, 2009, pdf, arXiv
• On the Square Peg Problem and some relatives, Trans. Amer. Math. Soc. 375(09), 2022, 6255–6280., pdf, arXiv, java applet, github

Polytopes

• The width of 5-dimensional prismatoids, with Francisco Santos and Christophe Weibel, Proc. London Math. Soc. 110 (3), 2015, 647–672, pdf, arXiv, avi
• Prodsimplicial-neighborly polytopes, with Vincent Pilaud and Julian Pfeifle, Discr. Comput. Geom. 46 (1), 2011, 100–131, pdf, arXiv

Extended abstracts (including Oberwolfach reports)

• Kadison-Singer conjecture for strongly Rayleigh measures (2015), Oberwolfach Reports No. 17/2015, 959–962, pdf
• Solving S-unit and Mordell equations via Shimura-Taniyama conjecture (2015), with Rafael von Känel, Oberwolfach Reports No. 5/2015, 348–351, pdf
• Flag algebras (2013), Oberwolfach Reports No. 16/2013, 1013–1015, pdf
• A tight colored Tverberg theorem for maps to manifolds (extended abstract) (2011), with Pavle Blagojević, Günter Ziegler, DMTCS Proc. 23 (FPSAC), 183–190, link
• Curvature and rational homotopy I (2011), Oberwolfach Reports No. 18/2011, 1019–1022, pdf
• On a colored Tverberg-Vrecica type problem (2011), with Pavle Blagojević, Günter Ziegler, Oberwolfach Reports No. 08/2011, 392–395, link
• Survey on random graphs, part 2 (2010), Oberwolfach Reports No. 47/2010, 2700–2702, link
• Optimal bounds for the colored Tverberg problem (2009), with Pavle Blagojević, Günter Ziegler, Oberwolfach Preprints 2009-27, link, pdf
• Square pegs and beyond (2009), Oberwolfach Reports No. 2/2009, 125–127, link

Databases

• I founded NumberDB.
• I contibuted to LMFDB.
• I computed large tables of elliptic curves over number fields and number fields with given places of bad reduction.

Conferences organized

• Journées Algophantiennes Bordelaises 2017, University of Bordeaux, with Yuri Bilu
• Workshop on Big Data in Pure Mathematics 2022, online

Talks

• 09/2008Workshop Topological Combinatorics, TU Berlin.
• 01/2009Workshop on Discrete Differential Geometry, Oberwolfach.
• 05/2009CGTA-Seminar, University of Belgrade.
• 10/2009Cascade Topology Seminar, University of Oregon, Eugene.
• 01/2010Combinatorics-Geometry seminar, University of Washington, Seattle (2 talks).
• 01/2010Algebraic Topology Seminar, PIMS, UBC, Vancouver.
• 06/2010Colloquium talk at Mathematical Institute of the Serbian Academy of Sciences, Belgrad.
• 06/2010Analysis, Topology and Applications 2010, Vrnjačka Banja (Serbia).
• 07/2010Computational topology seminar, Stanford.
• 08/2010Algebra and Discrete Math. seminar, UC Davis.
• 09/2010Topology RTG seminar, UC Berkeley.
• 10/2010Arbeitsgemeinschaft Topological Robotics, Oberwolfach.
• 11/2010Charles University, Prague.
• 02/2011Workshop on Combinatorial and Geometric Topology, Oberwolfach.
• 04/2011Arbeitsgemeinschaft Rational Homotopy Theory, Oberwolfach.
• 04/2011Spring school in discrete probability, ergodic theory and combinatorics, Graz.
• 05/2011Rényi Institut, Budapest (2 talks).
• 06/2011Conference FPSAC'2011, Reykjavik.
• 07/2011Workshop on Modern Graph Theory with Applications to Geometric Group Theory, Bedlewo.
• 07/2011Conference Applied Algebraic Topology, ETH Zürich.
• 09/2011Workshop on Discrete Geometry, Fields Institute Toronto.
• 09/2011School of Mathematics Postdoc talks, IAS, Princeton.
• 10/2011Mathematical Conversations Seminar, IAS, Princeton.
• 11/2011Computational Topology Conference, Fields Institute Toronto.
• 11/2011Algebraic Topology Seminar, Princeton University.
• 11/2011Discrete Mathematics Seminar, Rutgers University.
• 12/2011Colloquium talk, Vassar College, Poughkeepsie.
• 02/2012Workshop on Topology: Identifying Order in Complex Systems, Rutgers University.
• 02/2012Discrete Mathematics Seminar, IAS, Princeton.
• 02/2012Princeton-Rider Workshop on Homotopy theory and toric spaces, Princeton University.
• 03/2012Discrete Geometry Seminar, Cornell University.
• 03/2012Algebraic Topology Seminar, Cornell University.
• 03/2012Discrete Math Seminar, Princeton University.
• 10/2012IHES, Bures-sur-Yvette.
• 11/2012Topology Seminar, Université de Genève.
• 12/2012Topology Seminar, University of Copenhagen.
• 02/2013IHES, Bures-sur-Yvette.
• 04/2013Arbeitsgemeinschaft Limits of Structures, Oberwolfach.
• 05/2013Oberseminar Differentialgeometrie, Augsburg University.
• 07/2013Mittagsseminar Theory of Combinatorial Algorithms, ETH Zürich.
• 07/2013Polynomial Optimization Workshop, Isaac Newton Institute, Cambridge.
• 09/2013Sandia National Labs, Livermore (2 talks).
• 09/2013Geometry Seminar, ETH Zürich.
• 11/2013IST Austria, Vienna.
• 11/2013Oberseminar Geometry and Topology, MPIM Bonn.
• 12/2013Oberseminar Geometry and Topology, MPIM Bonn.
• 12/2013Symposium about Mathematics, University of Zürich.
• 01/2014Geometry Seminar, University of Cologne.
• 02/2014Karlsruhe Institute of Technology.
• 02/2014Winter Workshop, University of Hannover.
• 02/2014Colloquium, University of Rochester.
• 04/2014Mini-course on spectral sequences, MPIM, Bonn.
• 05/2014MPI-Oberseminar, MPIM, Bonn.
• 10/2014Number theory seminar, MPIM, Bonn.
• 11/2014Dutch Intercity Seminar Number Theory, Universiteit Leiden.
• 12/2014Number theory seminar, Bordeaux.
• 12/2014TIFR, Mumbai.
• 01/2015Reinhold-Baer-Kolloquium, Braunschweig.
• 01/2015Algebra and geometry seminar, University of Oldenburg.
• 04/2015Arbeitsgemeinschaft Kadison–Singer conjecture, Oberwolfach.
• 06/2015Topology in pairs seminar, MPIM, Bonn.
• 06/2015Arbeitstagung, MPIM, Bonn.
• 10/2015Likbez Seminar, MPI MIS, Leipzig.
• 01/2016Likbez Seminar, MPI MIS, Leipzig.
• 04/2016Séminaire de Théorie Algorithmique des Nombres, University of Bordeaux.
• 04/2016Special Jerusalem Number theory seminar, Hebrew University.
• 05/2016Number theory seminar, Leiden University.
• 08/2016Combinatorics seminar, Technion, Haifa.
• 01/2017Pontificia Universidad Católica de Chile, Santiago de Chile.
• 01/2017Universidad de los Andes, Bogotá.
• 01/2017American University of Beirut.
• 02/2017Mini-school Topological and Geometric Combinatorics, University of Teheran (3 talks).
• 02/2017Koç University, Istanbul.
• 07/2017Conference Diophantine Approximation and Algebraic Curves, Banff.
• 09/2017IMBM days, Istanbul Center for Mathematical Sciences.
• 02/2018Boğaziçi University, Istanbul (2 talks).
• 05/2018Antalya Algebra Days XX, İzmir.
• 05/2018Sabancı Algebra Seminar, Sabancı University, Istanbul.
• 06/2018Workshop Effective methods for Diophantine problems, Lorentz Center, Leiden.
• 09/2018Conference Approximation diophantienne et transcendance, CIRM, Luminy.
• 10/2018Math seminar, Koç University, Istanbul.
• 11/2018Math seminar, Koç University, Istanbul.
• 01/2019Conference Explicit Number Theory, Universidad de Valparaíso, Valparaíso.
• 03/2019Leiden University, Leiden.
• 03/2019Math seminar, Koç University, Istanbul.
• 07/2019Conference Journées Arithmétiques, Istanbul.
• 09/2019Number theory seminar, Boston University.
• 10/2019Number theory seminar, Harvard University, slides.
• 10/2019Columbia-CUNY-NYU joint Number Theory Seminar (3 talks).
• 08/2020Modern Breakthroughs in Diophantine Problems, BIRS, Banff (online).
• 11/2020Simons collaboration meeting (online).
• 03/2021Colloquium, Yeditepe University, Istanbul (online).
• 05/2021Rational Points and Galois Representations, University of Pittsburgh (online).
• 09/2021Simons collaboration meeting (online).
• 12/2021Oberseminar on algebraic geometry and number theory, Freiburg (online).
• 12/2021Algebraic Number Theory session of CMS Winter Meeting (online).
• 01/2022University College London (online).