@article{helmer_tsigaridas_2024, title={Segre-driven radicality testing}, volume={122}, ISSN={["1095-855X"]}, DOI={10.1016/j.jsc.2023.102262}, abstractNote={We present a probabilistic algorithm to test if a homogeneous polynomial ideal I defining a scheme X in Pn is radical using Segre classes and other geometric notions from intersection theory which is applicable for certain classes of ideals. If all isolated primary components of the scheme X are reduced and it has no embedded components outside of the singular locus of Xred=V(I), then the algorithm is not applicable and will return that it is unable to decide radically; in all the other cases it will terminate successfully and in either case its complexity is singly exponential in n. The realm of the ideals for which our radical testing procedure is applicable and for which it requires only single exponential time includes examples which are often considered pathological, such as the ones drawn from the famous Mayr-Meyer set of ideals which exhibit doubly exponential complexity for the ideal membership problem.}, journal={JOURNAL OF SYMBOLIC COMPUTATION}, author={Helmer, Martin and Tsigaridas, Elias}, year={2024} }
 @article{helmer_nanda_2023, title={Complex Links and Hilbert-Samuel Multiplicities}, volume={7}, ISSN={["2470-6566"]}, DOI={10.1137/22M1475533}, abstractNote={We describe a framework for estimating Hilbert-Samuel multiplicities $e_XY$ for pairs of projective varieties $X \subset Y$ from finite point samples rather than defining equations. The first step involves proving that this multiplicity remains invariant under certain hyperplane sections which reduce $X$ to a point $p$ and $Y$ to a curve $C$. Next, we establish that $e_pC$ equals the Euler characteristic (and hence, the cardinality) of the complex link of $p$ in $C$. Finally, we provide explicit bounds on the number of uniform point samples needed (in an annular neighborhood of $p$ in $C$) to determine this Euler characteristic with high confidence.}, number={1}, journal={SIAM JOURNAL ON APPLIED ALGEBRA AND GEOMETRY}, author={Helmer, Martin and Nanda, Vidit}, year={2023}, pages={29–48} }
 @article{helmer_nanda_2023, title={Conormal Spaces and Whitney Stratifications (Jun, 10.1007/ s10208-022-09574- 8, 2022)}, ISSN={["1615-3383"]}, DOI={10.1007/s10208-022-09602-7}, abstractNote={Abstract}, journal={FOUNDATIONS OF COMPUTATIONAL MATHEMATICS}, author={Helmer, Martin and Nanda, Vidit}, year={2023}, month={Feb} }
 @article{helmer_nanda_2022, title={Conormal Spaces and Whitney Stratifications}, ISSN={["1615-3383"]}, DOI={10.1007/s10208-022-09574-8}, abstractNote={Abstract}, journal={FOUNDATIONS OF COMPUTATIONAL MATHEMATICS}, author={Helmer, Martin and Nanda, Vidit}, year={2022}, month={Jun} }