50 citations · 163 across the 15 of their papers we have counts for
16 papers
Higher spectral sequences
Benjamin Matschke
In this article we construct what we call a higher spectral sequence for any chain complex (or topological space) that is filtered in compatible ways. For this we extend the pr…
Quadratic Fields Admitting Elliptic Curves with Rational -Invariant and Good Reduction Everywhere
Benjamin Matschke, Abhijit S. Mudigonda
Clemm and Trebat-Leder (2014) proved that the number of quadratic number fields with absolute discriminant bounded by over which there exist elliptic curves with good reduction…
Elliptic curves with good reduction outside of the first six primes
Alex J. Best, Benjamin Matschke
We present a database of rational elliptic curves, up to Q-isomorphism, with good reduction outside {2,3,5,7,11,13}. We provide a heuristic involving the abc and BSD conjectures th…
Proofs by example
Benjamin Matschke
We study the proof scheme "proof by example" in which a general statement can be proved by verifying it for a single example. This strategy can indeed work if the statement in ques…
Quadrilaterals inscribed in convex curves
Benjamin Matschke
We classify the set of quadrilaterals that can be inscribed in convex Jordan curves, in the continuous as well as in the smooth case. This answers a question of Makeev in the speci…
Solving S-unit, Mordell, Thue, Thue-Mahler and generalized Ramanujan-Nagell equations via Shimura-Taniyama conjecture
Rafael von Känel, Benjamin Matschke
In the first part we construct algorithms which we apply to solve S-unit, Mordell, cubic Thue, cubic Thue-Mahler and generalized Ramanujan-Nagell equations. As a byproduct we obtai…
Successive Spectral Sequences
Benjamin Matschke
In this paper, we develop a structure theory for generalized spectral sequences, which are derived from chain complexes that are filtered over arbitrary partially ordered sets. Als…
Computing integral points on X_ns^+(p)
Aurélien Bajolet, Yuri Bilu, Benjamin Matschke
We describe an algorithm for computing integral points on the modular curve of prime level p associated to the normalizer of a non-split Cartan subgroup of GL_2(F_p). Using our met…
Projective center point and Tverberg theorems
Roman Karasev, Benjamin Matschke
We present projective versions of the center point theorem and Tverberg's theorem, interpolating between the original and the so-called "dual" center point and Tverberg theorems. F…
The width of 5-dimensional prismatoids
Benjamin Matschke, Francisco Santos, Christophe Weibel
Santos' construction of counter-examples to the Hirsch Conjecture (2012) is based on the existence of prismatoids of dimension d of width greater than d. Santos, Stephen and Thomas…
A tight colored Tverberg theorem for maps to manifolds
Pavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler
We prove that any continuous map of an N-dimensional simplex Delta_N with colored vertices to a d-dimensional manifold M must map r points from disjoint rainbow faces of Delta_N to…
On the Square Peg Problem and Its Relatives
Benjamin Matschke
Toeplitz's Square Peg Problem asks whether every continuous simple closed curve in the plane contains the four vertices of a square. It has been proved for various classes of suffi…
A Note on Masspartitions by Hyperplanes
Benjamin Matschke
A triple of positive integers (d,h,m) is admissible if for any m given masses in R^d there exist h hyperplanes that cut each of these masses into 2^h equal pieces. We present an el…
Optimal bounds for a colorful Tverberg--Vrecica type problem
Pavle Blagojevic, Benjamin Matschke, Gunter Ziegler
We prove the following optimal colorful Tverberg-Vrecica type transversal theorem: For prime r and for any k+1 colored collections of points C^l of size |C^l|=(r-1)(d-k+1)+1 in R^d…
Optimal bounds for the colored Tverberg problem
Pavle V. M. Blagojević, Benjamin Matschke, Günter M. Ziegler
We prove a "Tverberg type" multiple intersection theorem. It strengthens the prime case of the original Tverberg theorem from 1966, as well as the topological Tverberg theorem of B…
Prodsimplicial-Neighborly Polytopes
Benjamin Matschke, Julian Pfeifle, Vincent Pilaud
Simultaneously generalizing both neighborly and neighborly cubical polytopes, we introduce PSN polytopes: their k-skeleton is combinatorially equivalent to that of a product of r s…