38 citations · 192 across the 18 of their papers we have counts for
21 papers
Effective Whitney Stratification of Real Algebraic Varieties
Martin Helmer, Anton Leykin, Vidit Nanda
We describe new algorithms to compute Whitney stratifications of real algebraic varieties. Using either conormal or polar techniques, these algorithms stratify a complexification o…
Symbol Alphabets from the Landau Singular Locus
Christoph Dlapa, Martin Helmer, Georgios Papathanasiou +1
We provide evidence through two loops, that rational letters of polylogarithmic Feynman integrals are captured by the Landau equations, when the latter are recast as a polynomial o…
Segre-Driven Radicality Testing
Martin Helmer, Elias Tsigaridas
We present a probabilistic algorithm to test if a homogeneous polynomial ideal defining a scheme in is radical using Segre classes and other geometric notion…
Cohen-Macaulay Property of Feynman Integrals
Felix Tellander, Martin Helmer
The connection between Feynman integrals and GKZ -hypergeometric systems has been a topic of recent interest with advances in mathematical techniques and computational tools ope…
Conormal Spaces and Whitney Stratifications
Martin Helmer, Vidit Nanda
We describe a new algorithm for computing Whitney stratifications of complex projective varieties. The main ingredients are (a) an algebraic criterion, due to Lê and Teissier, whic…
Complex Links and Hilbert-Samuel Multiplicities
Martin Helmer, Vidit Nanda
We describe a framework for estimating Hilbert-Samuel multiplicities for pairs of projective varieties from finite point samples rather than defining equations…
On the Uniqueness Problem for Quadrature Domains
Yacin Ameur, Martin Helmer, Felix Tellander
We study questions of existence and uniqueness of quadrature domains using computational tools from real algebraic geometry. These problems are transformed into questions about the…
Probabilistic Saturations and Alt's Problem
Jonathan D. Hauenstein, Martin Helmer
Alt's problem, formulated in 1923, is to count the number of four-bar linkages whose coupler curve interpolates nine general points in the plane. This problem can be phrased as cou…
Families of Toric Chemical Reaction Networks
Michael F. Adamer, Martin Helmer
We study families of chemical reaction networks whose positive steady states are toric, and therefore can be parameterized by monomials. Families are constructed algorithmically fr…
Multistationarity and Bistability for Fewnomial Chemical Reaction Networks
Elisenda Feliu, Martin Helmer
Bistability and multistationarity are properties of reaction networks linked to switch-like responses and connected to cell memory and cell decision making. Determining whether and…
Segre Class Computation and Practical Applications
Corey Harris, Martin Helmer
Let be closed (possibly singular) subschemes of a smooth projective toric variety . We show how to compute the Segre class as a class in the Chow group of…
Polar degrees and closest points in codimension two
Martin Helmer, Bernt Ivar Utstøl Nødland
Suppose that is a toric variety of codimension two defined by an integer matrix , and let be a Gale dual of . In this paper…
Complexity of Model Testing for Dynamical Systems with Toric Steady States
Michael F Adamer, Martin Helmer
In this paper we investigate the complexity of model selection and model testing for dynamical systems with toric steady states. Such systems frequently arise in the study of chemi…
The Maximum Likelihood Degree of Toric Varieties
Carlos Améndola, Nathan Bliss, Isaac Burke +6
We study the maximum likelihood degree (ML degree) of toric varieties, known as discrete exponential models in statistics. By introducing scaling coefficients to the monomial param…
Nearest Points on Toric Varieties
Martin Helmer, Bernd Sturmfels
We determine the Euclidean distance degree of a projective toric variety. This extends the formula of Matsui and Takeuchi for the degree of the -discriminant in terms of Euler o…
On the Euler characteristic of a relative hypersurface
James Fullwood, Martin Helmer
We derive a general formula for the Euler characteristic of a fibration of projective hypersurfaces in terms of invariants of an arbitrary base variety. When the general fiber is a…
Computing the Chern-Schwartz-MacPherson Class of Complete Simplical Toric Varieties
Martin Helmer
Topological invariants such as characteristic classes are an important tool to aid in understanding and categorizing the structure and properties of algebraic varieties. In this no…
Computing characteristic classes of subschemes of smooth toric varieties
Martin Helmer
Let be a smooth complete toric variety defined by a fan and let be a subscheme of defined by an ideal homogeneous with respect to the grading on the to…
A Direct Algorithm to Compute the Topological Euler Characteristic and Chern-Schwartz-MacPherson Class of Projective Complete Intersection Varieties
Martin Helmer
Let be a possibly singular scheme-theoretic complete intersection subscheme of over an algebraically closed field of characteristic zero. Using a recent result o…
An Algorithm to Compute the Topological Euler Characteristic, Chern-Schwartz-MacPherson Class and Segre Class of Projective Varieties
Martin Helmer
Let be a closed subscheme of a projective space . We give an algorithm to compute the Chern-Schwartz-MacPherson class, Euler characteristic and Segre class of $ V…
On the zero set of G-equivariant maps
P-L. Buono, M. Helmer, J. S. W. Lamb
Let be a finite group acting on vector spaces and and consider a smooth -equivariant mapping . This paper addresses the question of the zero set near a zer…