Research

Machine learning

Published papers:

• Training and Evaluating Norwegian Sentence Embedding Models At NoDaLiDa 2023.
• Generating Reflexive Polytopes via Sequence Modeling At 2nd MATH-AI Workshop at NeurIPS 22.

Preprints:

-Measuring global properties of neural generative model outputs via generating mathematical objects.

Algebraic geometry

My research in algebraic geometry is within the field of toric geometry. It is a subfield were one studies algebraic varieties with a praticular kind of group action by an algebraic torus. Using this group action one establishes links between algebraic geometry and combinatorics, thus enabling one to study algebraic varieties via studying combinatorial objects such as lattice polytopes and rational polyhedral fans.

My PhD thesis.

My Master thesis.

My arXiv preprints with publication details where relevant:

• Some positivity results for toric vector bundles.
• Murphy’s law for toric vector bundles on smooth projective toric varieties.
• Chow groups and pseudoeffective cones of complexity one T-varieties.
• Polar degrees and closest points in codimension two, with Martin Helmer. In Journal of Algebra and Its Applications, Volume 18, Number 5, 2019.
• Secants, bitangents, and their congruences, with Kathlen Kohn and Paolo Tripoli. In Combinatorial Algebraic Geometry, Selected Papers From the 2016 Apprenticeship Program, Springer 2017.
• The Hilbert scheme of 11 points in A^3 is irreducible, with Theodosios Douvropoulos, Joachim Jelisiejew and Zach Teitler. In Combinatorial Algebraic Geometry, Selected Papers From the 2016 Apprenticeship Program Springer 2017.
• Local Euler obstructions of toric varieties, Journal of Pure and Applied Algebra, Volume 222, Issue 3, March 2018, Pages 508-533.
• A toric proof of Bezout’s theorem for weighted projective spaces.

Macaulay2 code

Here is some Macaulay2 code I wrote for various algebraic geometry projects. The code is not well written, and some of it may even be incompatible with current versions of Macaulay2.

Toric Vector Bundles

Macaulay2 code I wrote for computing parliaments of polytopes of toric vector bundles:

A package Parliament.m2 and Examples from Di Rocco-Jabbusch-Smith’s article illustrating its use.

Local Euler obstructions of WPS

Macaulay2 code I wrote for computing local Euler obstructions and degrees of dual varieties for weighted projective surfaces and threefolds: A package EulerObstructionWPS.m2 and the examples appearing in my article “Local Euler obstructions of toric varieties”.