Inselstr. 22

04103 Leipzig

Germany

Phone: | +49 (0) 341 - 9959 - 769 |

Email: | breiding-at-mis.mpg.de |

Room: | F3 07 |

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

https://www.juliahomotopycontinuation.org

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.

Read more about this in our press release in the MPG News.

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.

- 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.