Publications (26)
Landau Singularities from Whitney Stratifications
Martin Helmer, Georgios Papathanasiou, Felix Tellander
We demonstrate that the complete and non-redundant set of Landau singularities of Feynman integrals may be explicitly obtained from the Whitney stratification of a certain map. As…
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…
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…
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…
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…
Stratification of Projection Maps From Toric Varieties
Boulos El Hilany, Martin Helmer, Elias Tsigaridas
We prove a combinatorial version of Thom's Isotopy Lemma for projection maps applied to any complex or real toric variety. Our results are constructive and give rise to a method fo…