You can find my dissertation
Here is an overview of articles I wrote.
- Critical curvature degree of an algebraic variety. In preparation.
- The average condition number of tensor rank decompositions is infinite (with C. Beltran and N. Vannieuwenhoven). In preparation.
- 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). Preprint 2018; arXiv1807.04159.
- On the geometry of the set of symmetric matrices with repeated eigenvalues (with K. Kozhasov and A. Lerario). Arnold Mathematical Journal (2019).
- Convex Geometry of Ricardian Trade Theory. This is a poster which shows the connection between convex geometry min-plus geometry and Ricardian trade theory.
- Learning Algebraic Varieties from Samples (with B. Sturmfels, S. Kališnik Verovšek and M. Weinstein). Revista Matemática Complutense 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) pp. 2435-2465.
- Convergence analysis of Riemannian Gauss-Newton methods and its connection with the geometric condition number (with N. Vannieuwenhoven). Applied Mathematics Letters, 78 , pp. 42-50.
- The average number of critical rank-one-approximations to a symmetric tensor. Preprint, 27 pages, 2017; arXiv1701.07312.
- The condition number of join decompositions (with N. Vannieuwenhoven). SIAM J. Matrix Anal. and Appl., 39(1), 287–309. (The picture below is from this article.)
- The expected number of eigenvalues of a real gaussian tensor. SIAM J. Appl. Algebra Geometry, 1(1), 254–271. (18 pages).
- 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, Vol. 497, p.88-107 (2016).
- On a p-adic Newton method. Master's thesis. Submitted to the Institute of Mathematics, Georg-August Universität Göttingen, 09/2013. Under the supervision of P. Mihailescu and P. Bürgisser.
- Kronecker's Jugendtraum (with D. Samart). Student project for the International Summer School on Number Theory, July 29 - August 18, 2012, Göttingen, Germany.
My talk "What is... a condition number?" in the BMS student's seminar was recorded on video and you can watch it here