Martin Helmer

I am currently a Postdoctoral Fellow in the Department of Mathematical Sciences at the University of Copenhagen mentored by Elisenda Feliu. From 2015--2017 I was an NSERC Postdoctoral Fellow in the Department of Mathematics at the University of California, Berkeley mentored by Bernd Sturmfels. To view my updated webpage click here.

Contact

Email: m.helmer at math.ku.dk

Research Interests

My primary interest is to construct computational and theoretic tools to aid in understanding algebraic geometry and its applications. Broadly I am interested in algebraic geometry (theoretical, computational, and applied) and in related topics in computer algebra. I am particularly interested in practical methods in intersection theory, polynomial system solving and combinatorial algebraic geometry.

Publications

Martin Helmer and Bernd Sturmfels. Nearest Points on Toric Varieties. To appear in Mathematica Scandinavica, 2017. Software page. arxiv link.
Martin Helmer. Computing characteristic classes of subschemes of smooth toric varieties. Journal of Algebra, Volume 476, 2017, Pages 548-582, ISSN 0021-8693. arxiv link.
Martin Helmer (with Appendix by Martin Helmer and Éric Schost). A Direct Algorithm to Compute the Topological Euler Characteristic and Chern-Schwartz-MacPherson Class of Projective Complete Intersection Varieties. Theoretical Computer Science, Volume 681, 2017, Pages 54-74, ISSN 0304-3975. arxiv link.
Martin Helmer. Computing the Chern-Schwartz-MacPherson Class of Complete Simplical Toric Varieties. Springer Proceedings in Mathematics & Statistics book series (PROMS), volume 198 (ACA 2015), pp 207-217, July 2017. arxiv link.
Martin Helmer. Algorithms to compute the topological Euler characteristic, Chern-Schwartz-Macpherson class and Segre class of projective varieties. Journal of Symbolic Computation, 73, page 120-138, 2016. arxiv link.
Martin Helmer. An algorithm to compute certain Euler characteristics and Chern-Schwartz-MacPherson classes. In Proceedings of the 2014 Symposium on Symbolic-Numeric Computation, pp. 130-131. ACM, 2014.
PL Buono, Martin Helmer, and Jeroen SW Lamb. On the zero set of G-equivariant maps. In Mathematical Proceedings of the Cambridge Philosophical Society, volume 147, page 735. Cambridge Univ. Press, 2009. arxiv link.
Ramiro Liscano, John Khalil Jacoub, Anand Dersingh, Jinfu Zheng, Martin Helmer, Charles Elliott, and Ali Najafizadeh. Network performance of a wireless sensor network for temperature monitoring in vineyards. In Proceedings of the 8th ACM Symposium on Performance evaluation of wireless ad hoc, sensor, and ubiquitous networks, pp. 125-130. ACM, 2011.

Preprints

Michael F Adamer, Martin Helmer. Euclidean Distance Degree for Chemical Reaction Networks (2017). arXiv preprint arXiv:1707.07650.
Carlos Améndola, Nathan Bliss, Isaac Burke, Courtney R. Gibbons, Martin Helmer, Serkan Hoşten, Evan D. Nash, Jose Israel Rodriguez, Daniel Smolkin. The Maximum Likelihood Degree of Toric Varieties. (2017). arXiv preprint arXiv:1703.02251.
James Fullwood and Martin Helmer. On a projective bundle formula. (2016). arXiv preprint arXiv:1603.03553.

Software

EDPolytope: A Macaulay2 software package to compute the Euclidean Distance Degree, the polar degrees, and the Chern-Mather class of a projective toric variety using combinatorial methods.
CharacteristicClasses: A Macaulay2 built-in software package coauthored with Christine Jost. The package computes the Segre class, Chern-Schwartz-MacPherson class and Euler characteristic of a given subscheme of certain smooth toric varieties.
char-class-calc: A Sage program to compute the Segre class, Chern-Schwartz-MacPherson class and Euler characteristic of a projective variety.

These and other software projects can also be found on my github page https://github.com/Martin-Helmer.

Conference Talks

Fields Institute Thematic Program on Computer Algebra. Workshop on Algebra, Geometry and Proofs in Symbolic Computation. December 7, 2015. Fields Institute, Toronto, Canada. Algorithms to Compute Characteristic Classes of Subschemes of Certain Toric Varieties. Slides. Video of the talk.
SIAM Conference on Applied Algebraic Geometry. August 3-7, 2015. National Institute of Mathematical Sciences, Daejeon, Korea. Talk Slides (Titled "Algorithms to Compute Chern-Schwartz-Macpherson and Segre Classes and the Euler Characteristic") . Conference webpage.
ACA 2015 Conference (Applications of Computer Algebra). July 20-23, 2015 Kalamata, Greece. Talk Slides (Titled "Computing the Chern-Schwartz-MacPherson Class of a Complete Simplicial Toric Variety") . Conference webpage.
SNC 2014 Conference (Symbolic-Numeric Computation Conference). July 28-31, 2014 East China Normal University. Shanghai, China. Talk Slides (Titled "An Algorithm to Compute Certain Euler Characteristics and Chern-Schwartz-MacPherson Classes") . Conference webpage.
ACA 2014 Conference (Applications of Computer Algebra). July 9-12, 2014 Fordham University. New York, New York. Talk Slides (Titled "Algorithms to Compute Chern-Schwartz-Macpherson and Segre Classes and the Euler Characteristic") . Conference webpage.
ECCAD 2014, (April 26, 2014, Duke University, Durham, NC). Poster .

Education

Ph.D Applied Mathematics, University of Western Ontario, Canada. (2011-2015)
- Advisor: Éric Schost
- Thesis: Algorithms to Compute Characteristic Classes
M.Sc Mathematics, Queen's University, Canada. (2009-2011)
B.Sc Applied Mathematics, University of Ontario Institute of Technology, Canada. (2005-2009)