Contacts
Contact email:martin.helmer@anu.edu.au
Contact phone:+61 2 6125 3146
Location:Room 4.70, Hanna Neumann Building 145
MSI Fellow
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, combinatorial algebraic geometry and real algebraic geometry.
Groups
- Researcher, Computational mathematics
- Researcher, Algebra & topology
Projects
A current list including preprints and software can be found here.
- Corey Harris and Martin Helmer. Segre Class Computation and Practical Applications. Mathematics of Computation, DOI: 10.1090/mcom/3448, 2019. arxiv link.
- James Fullwood and Martin Helmer. On the Euler characteristic of a relative hypersurface. Journal of Mathematical Physics, 60, 052302, 2019. arxiv link.
- Elisenda Feliu and Martin Helmer. Multistationarity and Bistability for Fewnomial Chemical Reaction Networks. Bulletin of Mathematical Biology, DOI: 10.1007/s11538-018-00555-z, 2018. arxiv link.
- Michael F Adamer, Martin Helmer. Complexity of Model Testing for Dynamical Systems with Toric Steady States. Advances in Applied Mathematics Volume 110, September 2019, Pages 42-75. arxiv link.
- Martin Helmer, Bernt Ivar Utstøl Nødland. Polar degrees and closest points in codimension two. Journal of Algebra and Its Applications (2017): 1950095 Software page. arxiv link.
- Martin Helmer and Bernd Sturmfels. Nearest Points on Toric Varieties. Mathematica Scandinavica, Volume 122.2, page 213-238, 2018. Software page. arxiv link.
- 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. Journal of Symbolic Computation, 2018. 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.
