Max-Planck-Institute for Mathematics in the Sciences Leipzig
|Phone: ||+49 (0) 341 - 9959 - 769|
|Room: ||F3 07|
I'm a Postdoc in the group Nonlinear Algebra
at the Max-Planck-Institute for Mathematics in the Sciences in Leipzig.
Here is my CV
In the winter semester 2018/2019 I teach the course Condition: the geometry of numerical algorithms
. It follows the book with the same name
by Bürgisser and Cucker. Here are hand-written lecture notes
Minisymposia at SIAM AG 2019
For SIAM AG 2019
I co-organize a minisymposium on Numerical Methods in Algebraic Geometry
and a minisymposium on Random Geometry and Topology
Together with Sascha Timme I am developing HomotopyContinuation.jl, a polynomial equation solver for Julia. The current release is v.0.3.3.
Our website is available at
If you want to know what the gif on the right is about, you should read the post on computing the maximal curvature of a hypersurface.
Looking at data through the lens of algebraic geometry
Algebraic methods yield insight into the geometry of datasets: in a world where huge amounts of information are released and collected every day, it has become essential to be able to give meaning to data sets and to recognise any underlying pattern in the collected data.
Read more about this in our press release in the MPG News.
is a MATLAB package for tensor computations. I wrote a tutorial as Jupyter Notebook
, which you can download here
. Alternatively, you can view a HTML version
A brief history of mathematics
"A brief history of mathematics"
is a podcast by Prof. Marcus du Sautoy for BBC Radio. It is also available on Spotify
You can find my dissertation
Here is an overview of articles I wrote.
- Critical curvature degree of an algebraic variety. (with D. Agostini and E. Sertoz). 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). Preprint 2018; arXiv1807.04530.
- 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
My recent and near future travels are
- Low-rank Optimization and Applications, April 1-5, 2019, Leipzig, Germany. Invited talk.
- Complexity Reduction in Algebraic Statistics, November 26-27, 2018, Magdeburg, Germany. Invited talk.
- Workshop on Random Real Geometry, October 29-30, 2018, Triest, Italy. Organizer.
- ISMP 2018, July 1-6, 2018, Bordeaux, France. Invited talk.
- Einstein Workshop Discrete Geometry and Topology, March 13-16, 2018, Berlin, Germany. Contributed Poster.
- Numerical Methods for Curves, February 19-23, 2018, Rennes, France. Invited talk.
- Algebra meets Numerics: Condition and Complexity, November 6-7, 2017, Berlin, Germany. Invited talk.
- SIAM Conference on Applied Algebraic Geometry, July 31- August 4, 2017, Atlanta, Georgia, USA. Invited talk.
- FOCM 2017, July 10-19, 2017, Barcelona, Spain. Invited talk.
- Tensors: Algebra meets numerics, December 12-14, 2016, Leipzig, Germany. Participant.
- 7ECM, July 18-22, 2016, Berlin, Germany. Constributed Talk.
- Workshop on Software and Applications of Numerical Algebraic Geometry, May 23-25, 2016, Notre Dame, IN, USA. Participant.
- TDA 2016, January 18-22, 2016, Leuven, Belgium. Contributed poster.
- Algorithms and Complexity in Algebraic Geometry Reunion, December 14-16, 2015, Berkeley, CA, USA. Invited talk.