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