Academic interests
Determinantal varieties. Spectrahedra. Real and complex geometry.
Preprints
 Helsø, M. Maximality of quartic symmetroids with a double quadric of codimension 1. 2019. [arXiv]
 Helsø, M and Ranestad, K. Rational quartic spectrahedra. 2018. [arXiv]
Courses taught
Spring 2020: MAT2000, MEK3200, STKMAT2011
Autumn 2019: MAT2500
Background
2016: Master of Science in Mathematics, UiO
2014: Bachelor of Science in Computational Science and Mathematics, UiO
Tags:
Mathematics,
Algebra and algebraic geometry,
LaTeX
Publications

Helsø, Martin (2019). Rational quartic spectrahedra.
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A spectrahedron is called rational if its boundary admits a rational parametrisation. The Zariski closure in complex projective space of the boundary is a symmetroid. Rational quartic symmetroids in 3space have been classified in previous work; they have a triple point, an elliptic double point or are singular along a curve. In this talk, I will give bounds on the number of real singularities on the algebraic and topological boundary of rational quartic spectrahedra in 3space. This is joint work with Kristian Ranestad.

Helsø, Martin (2018). Rational quartic spectrahedra.

Helsø, Martin (2017). Parametrising spectrahedra.
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A matrix is a table of numbers, with rules for adding and multiplying such tables with each other. To a matrix, we can associate a set of important numbers called eigenvalues. These reflect the underlying geometric action of the matrix. In our work, we study convex bodies of symmetric matrices where all the eigenvalues are nonnegative. These bodies are called spectrahedra. Spectrahedra appear naturally in applied fields such as optimisation and statistics. We consider only matrices with four rows and four columns. In this case, we describe the subset of spectrahedra that have a boundary that can be parametrised by a class of simple functions. This is joint work with Kristian Ranestad.

Helsø, Martin (2016). Parametrising spectrahedra.

Helsø, Martin (2016). Rational quartic spectrahedra.
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Published Aug. 22, 2016 4:18 PM
 Last modified Sep. 15, 2020 9:05 PM