NSERC Postdoctoral Fellow at the University of California, Berkeley, beginning September 2015.My Current Webpage at the UC Berkeley Math Department
Formally a Ph.D student in the Department of Applied Mathematics at the University of Western Ontario (Ph.D completed July 3, 2015).
ContactEmail: martin.helmer2 at gmail.com or mhelmer at math.berkeley.edu
- Broadly I am interested in computer algebra and computational algebraic geometry. I am also interested in intersection theory and polynomial system solving. Currently my main research focus is developing algorithms to compute characteristic classes of projective varieties, specifically the Chern-Schwartz-MacPherson class and the Euler characteristic.
- Ph.D Applied Mathematics, University of Western Ontario, Canada. (2011-2015)
- Supervisor: Eric Schost
- Thesis: Algorithms to Compute Characteristic Classes
- Completed July 3, 2015
- M.Sc Mathematics, Queen's University, Canada. (2009-2011)
- Thesis: The Maslov Index and ω-Index Applied to Questions of Stability of Periodic Solutions to Hamiltonian Systems
- B.Sc Applied Mathematics, University of Ontario Institute of Technology, Canada. (2005-2009)
- Undergraduate Thesis: An Exploration of Lie Algebras and Their Representations with Applications in Biology
- Martin Helmer. Algorithms to compute the topological Euler characteris- tic, Chern-Schwartz-Macpherson class and Segre class of projective varieties. Journal of Symbolic Computation, 2015. Preprint on arXiv at arXiv:1402.2930.
- Martin Helmer. An algorithm to compute certain Euler characteristics and Chern- Schwartz-Macpherson classes. In Proceedings of the 2014 Symposium on Symbolic-Numeric Computation, pages 130-131. ACM, 2014.
- PL Buono, M 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.
- M Helmer. A Direct Algorithm to Compute the Topological Euler Characteristic and Chern-Schwartz-MacPherson Class of Projective Complete Intersection Varieties. (2014). arXiv preprint arXiv:1410.4113.
- A Sage program to compute the Segre class, Chern-Schwartz-MacPherson class and Euler characteristic of a projective variety, the plain text version can be found here characteristic_class and the Sage worksheet version can be found here CharacteristicClass.sws . To upload the .sws file to the Sage notebook the url http://publish.uwo.ca/~mhelmer2/CharacteristicClass.sws can be used. If you don't have your own installation of Sage you may run the notebook file supplied here online at http://www.sagenb.org/ .
- A Macaulay2 program to compute the Segre class, Chern-Schwartz-MacPherson class and Euler characteristic of a projective variety. The inclusion/exclusion algorithm (this is the default algorithm in the M2 package) is the one used for testing in the above arXiv preprint. This M2 package also includes a more recent algorithm to compute the Chern-Schwartz-MacPherson class and Euler characteristic for the special case of complete intersections, which offers speed improvements for many examples with a particular structure. This algorithm can be accessed via the option Alg=>Composite in the CSM and Euler methods of the M2 package. See the documentation in the package file for more details. The M2 package can be downloaded from github https://github.com/Martin-Helmer/char-class-calc.
- The Macaulay2 program to compute the Segre class, Chern-Schwartz-MacPherson class and Euler characteristic of a projective variety described in the arXiv preprint described above can also be accessed directly in Macaulay2 version 1.7 and above in the Characteristic Classes M2 Package using the option Algorithm=>ProjectiveDegree, see the package documentation Macaulay2 Characteristic Classes Package. The package can be veiwed here: CharacteristicClasses.m2 .
- 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 .
Teaching Assistant for AM2415, Applied Mathematical Methods for Electrical and Software Engineering (2014):
- Taught tutorials, created and maintained a tutorial blog: AM2415 tutorial blog
Teaching Assistant for AM2413, App. Math. and Numerical Methods for Mechanical Eng. (2013-2014)
- Taught tutorials, created and maintained a tutorial blog: AM2413 tutorial blog
Teaching Assistant for AM1413, Applied Mathematics for Engineers (2013)
- Taught tutorials, created and maintained a tutorial blog: AM1413 tutorial blog
Teaching Assistant for AM1411, Linear Algebra for Engineers (2013)
- Taught tutorials
- Created electronic learning resources in Sage for APSC 172, Calculus (2011)
- Taught tutorials
- A pdf of my C.V. can be found here.