77 citations · 186 across the 20 of their papers we have counts for
20 papers
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…
Complete sets of logarithmic vector fields for integration-by-parts identities of Feynman integrals
Janko Boehm, Alessandro Georgoudis, Kasper J. Larsen +2
Integration-by-parts identities between loop integrals arise from the vanishing integration of total derivatives in dimensional regularization. Generic choices of total derivatives…
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…
Computing integral bases via localization and Hensel lifting
Janko Boehm, Wolfram Decker, Santiago Laplagne +1
We present a new algorithm for computing integral bases in algebraic function fields of one variable, or equivalently for constructing the normalization of a plane curve. Our basic…
Weak Lefschetz Property and Stellar Subdivisions of Gorenstein Complexes
Janko Boehm, Stavros Argyrios Papadakis
Assume sigma is a face of a Gorenstein* simplicial complex D. We investigate the question of whether the Weak Lefschetz Property of the Stanley-Reisner ring k[D] (over an infinite…
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…
Bounds for the Betti numbers of successive stellar subdivisions of a simplex
Janko Boehm, Stavros Argyrios Papadakis
We give a bound for the Betti numbers of the Stanley-Reisner ring of a stellar subdivision of a Gorenstein* simplicial complex by applying unprojection theory. From this we derive…
The use of Bad Primes in Rational Reconstruction
Janko Boehm, Wolfram Decker, Claus Fieker +1
A standard method for finding a rational number from its values modulo a collection of primes is to determine its value modulo the product of the primes via Chinese remaindering, a…
Decomposition of Monomial Algebras: Applications and Algorithms
Janko Boehm, David Eisenbud, Max Joachim Nitsche
Considering finite extensions K[A] \subseteq K[B] of positive affine semigroup rings over a field K we have developed in [1] an algorithm to decompose K[B] as a direct sum of monom…
Decomposition of semigroup algebras
Janko Boehm, David Eisenbud, Max Joachim Nitsche
Let A \subseteq B be cancellative abelian semigroups, and let R be an integral domain. We show that the semigroup ring R[B] can be decomposed, as an R[A]-module, into a direct sum…
Parallel algorithms for normalization
Janko Boehm, Wolfram Decker, Santiago Laplagne +3
Given a reduced affine algebra A over a perfect field K, we present parallel algorithms to compute the normalization \bar{A} of A. Our starting point is the algorithm of Greuel, La…
Implementing the Kustin-Miller complex construction
Janko Boehm, Stavros Argyrios Papadakis
The Kustin-Miller complex construction, due to A. Kustin and M. Miller, can be applied to a pair of resolutions of Gorenstein rings with certain properties to obtain a new Gorenste…
On the structure of Stanley-Reisner rings associated to cyclic polytopes
Janko Boehm, Stavros Argyrios Papadakis
We study the structure of Stanley-Reisner rings associated to cyclic polytopes, using ideas from unprojection theory. Consider the boundary simplicial complex Delta(d,m) of the d-d…
Stellar subdivisions and Stanley-Reisner rings of Gorenstein complexes
Janko Boehm, Stavros Argyrios Papadakis
Unprojection theory aims to analyze and construct complicated commutative rings in terms of simpler ones. Our main result is that, on the algebraic level of Stanley-Reisner rings,…