77 citations · 186 across the 20 of their papers we have counts for
9 papers · 1 filter
Tropical Mirror Symmetry in Dimension One
Janko Böhm, Christoph Goldner, Hannah Markwig
We prove a tropical mirror symmetry theorem for descendant Gromov-Witten invariants of the elliptic curve, generalizing the tropical mirror symmetry theorem for Hurwitz numbers of…
Bad Primes in Computational Algebraic Geometry
Janko Boehm, Wolfram Decker, Claus Fieker +2
Computations over the rational numbers often suffer from intermediate coefficient swell. One solution to this problem is to apply the given algorithm modulo a number of primes and…
Current Challenges in Developing Open Source Computer Algebra Systems
Janko Boehm, Wolfram Decker, Simon Keicher +1
This note is based on the plenary talk given by the second author at MACIS 2015, the Sixth International Conference on Mathematical Aspects of Computer and Information Sciences. Mo…
A Classification Algorithm for Complex Singularities of Corank and Modality up to Two
Janko Boehm, Magdaleen S. Marais, Gerhard Pfister
In (Arnold, 1985), V.I. Arnold has obtained normal forms and has developed a classifier for, in particular, all isolated hypersurface singularities over the complex numbers up to m…
A smoothness test for higher codimensions
Janko Boehm, Anne Frühbis-Krüger
Based on an idea in Hironaka's proof of resolution of singularities, we present an algorithmic smoothness test for algebraic varieties. The test is inherently parallel and does not…
3D printing dimensional calibration shape: Clebsch Cubic
Andre F. van der Merwe, Janko Boehm, Magdaleen S. Marais
3D printing and other layer manufacturing processes are challenged by dimensional accuracy. Several techniques are used to validate and calibrate dimensional accuracy through the c…
The Classification of Real Singularities Using Singular. Part III: Unimodal Singularities of Corank 2
Janko Boehm, Magdaleen S. Marais, Andreas Steenpass
We present a classification algorithm for isolated hypersurface singularities of corank 2 and modality 1 over the real numbers. For a singularity given by a polynomial over the rat…
Local analysis of Grauert-Remmert-type normalization algorithms
Janko Boehm, Wolfram Decker, Mathias Schulze
Normalization is a fundamental ring-theoretic operation; geometrically it resolves singularities in codimension one. Existing algorithmic methods for computing the normalization re…
Tropical mirror symmetry for elliptic curves
Janko Boehm, Kathrin Bringmann, Arne Buchholz +1
Mirror symmetry relates Gromov-Witten invariants of an elliptic curve with certain integrals over Feynman graphs. We prove a tropical generalization of mirror symmetry for elliptic…