5 papers
Benchmarks in Leipzig
Andrei Balakin, Miklós Bóna, Marie-Charlotte Brandenburg +45
Between April 1 and May 15, 2026, a group of 49 mathematicians compiled a dataset of research-level mathematics questions with known answers. Most of the work was done during the 3…
Connection Matrices in Macaulay2
Paul Görlach, Joris Koefler, Anna-Laura Sattelberger +4
In this article, we describe the theoretical foundations of the Macaulay2 package ConnectionMatrices and explain how to use it. For a left ideal in the Weyl algebra that is of fini…
Positive Genus Pairs from Amplituhedra
Joris Koefler, Dmitrii Pavlov, Rainer Sinn
A main conjecture in the field of Positive Geometry states that amplituhedra, which are certain semi-algebraic sets in the Grassmannian, are positive geometries. It is motivated by…
Taking the amplituhedron to the limit
Joris Koefler, Rainer Sinn
The amplituhedron is a semialgebraic set given as the image of the non-negative Grassmannian under a linear map subject to a choice of additional parameters. We define the limit am…
Uniqueness of MHV Gravity Amplitudes
Joris Koefler, Umut Oktem, Shruti Paranjape +2
We investigate MHV tree-level gravity amplitudes as defined on the spinor-helicity variety. Unlike their gluon counterparts, the gravity amplitudes do not have logarithmic singular…