My talk "What is... a condition number?" in the BMS student's seminar was recorded on video and you can watch it here.


List of my research articles

The average condition number of most tensor rank decomposition problems is infinite
with C. Beltran and N. Vannieuwenhoven. Preprint 2019; arXiv1903.05527.

3264 Conics in a Second
with B. Sturmfels and S. Timme. Preprint 2019; arXiv1902.05518.

Sampling from the uniform distribution on an algebraic manifold
with O. Marigliano. Preprint 2018; arXiv1810.06271.

Pencil-based algorithms for tensor rank decomposition are not stable
with C. Beltran and N. Vannieuwenhoven. SIAM J. Matrix Anal. and Appl. (accepted).

On the geometry of the set of symmetric matrices with repeated eigenvalues
with K. Kozhasov and A. Lerario. Arnold Mathematical Journal (2019).

Learning Algebraic Varieties from Samples
with B. Sturmfels, S. Kališnik Verovšek and M. Weinstein. Rev. Mat. Compl. 31 (2018), 545-593.

On the average condition number of tensor rank decompositions
with N. Vannieuwenhoven. Preprint, 2018; arXiv1801.01673.

Random Spectrahedra
with K. Kozhasov and A. Lerario. Preprint, 2017; arXiv1711.08253.

A Riemannian trust region method for the canonical tensor rank approximation problem
with N. Vannieuwenhoven. SIAM Journal of Optimization 28(3) (2018), 2435-2465.

Convergence analysis of RGN methods and its connection with the geometric condition number
with N. Vannieuwenhoven. Applied Mathematics Letters 78 , 42-50.

How Many Eigenvalues of a Random Symmetric Tensor are Real?
Preprint, 29 pages, 2019; arXiv1701.07312.

The condition number of join decompositions
with N. Vannieuwenhoven. SIAM J. Matrix Anal. and Appl. 39(1), 287–309.

The expected number of eigenvalues of a real gaussian tensor
SIAM J. Appl. Algebra Geometry 1(1), 254–271.

An efficient randomized homotopy method to approximate eigenpairs of tensors
Preprint, 2018; arXiv1512.03284.

Distribution of the eigenvalues of a random system of homogeneous polynomials
with P. Bürgisser. Linear Algebra and its Applications 497, (2016), 88-107 .

Kronecker's Jugendtraum
with D. Samart. Student project for the International Summer School on Number Theory.


Theses

Numerical and Statistical Aspects of Tensor Decompositions
PhD thesis, TU Berlin, 2017.
First supervisor: P. Bürgisser. Second supervisor: F. Cucker.

On a p-adic Newton method.
Master's, Georg-August Universität Göttingen, 2013.
First supervisor: P. Mihailescu. Second supervisor: P. Bürgisser.