Surveys

3264 Conics in a Second
with B. Sturmfels and S. Timme. Not. Amer. Math. Soc. 67 (2020), 30-37.

An algebraic geometry perspective on topological data analysis
SIAM News 53(1) (2020).


Computational Algebraic Geometry

Certifying zeros of polynomial systems using interval arithmetic
with K. Rose and S. Timme. arXiv:2011.05000.

Equations for GL invariant families of polynomials
with C. Ikenmeyer, R. Hodges and M. Michalek. Preprint.


Mathematics of Data

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

Random points on an algebraic manifold
with O. Marigliano. SIAM J. Mathematics of Data Science 2(2) (2020), 683-704.


Riemannian optimization

The condition number of Riemannian approximation problems
with N. Vannieuwenhoven. arXiv:1909.12186.

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

Convergence analysis of RGN methods and its connection with the geometric condition number
with N. Vannieuwenhoven. Appl. Math. Letters 78 (2018), 42-50.


Numerical analysis of tensor decompositions

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

Pencil-based algorithms for tensor rank decomposition are not stable
with C. Beltran and N. Vannieuwenhoven. SIAM J. Matrix Anal. and Appl. 40 (2) (2019), 739-773.

On the average condition number of tensor rank decompositions
with N. Vannieuwenhoven. IMA J. Num. Anal. (2019).

The condition number of join decompositions
with N. Vannieuwenhoven. SIAM J. Matrix Anal. and Appl. 39(1) (2018), 287–309.

An efficient randomized homotopy method to approximate eigenpairs of tensors
arXiv1512.03284.


Metric geometry

On the geometry of the set of symmetric matrices with repeated eigenvalues
with K. Kozhasov and A. Lerario. Arnold Mathematical Journal 1 (4) (2019), 423-443.


Random polynomials

Quantitative singularity theory for random polynomials
with H. Keneshlou and A. Lerario. IMRN (to appear).

Random Spectrahedra
with K. Kozhasov and A. Lerario. SIAM J. Optim. 29 (4) (2019), 2608-2624.

How Many Eigenvalues of a Random Symmetric Tensor are Real?
Trans. Amer. Math. Soc. 372 (2019), 7857-7887.

The expected number of eigenvalues of a real gaussian tensor
SIAM J. Appl. Algebra and Geometry 1(1) (2017), 254–271.

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


Number theory

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


Random Algebraic Geometry

Here is a link to my book project Lectures on Random Algebraic Geometry with Antonio Lerario.


Colleagues



Carlos, Nick and I in Kreuzberg.

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.