Research Interests
Parametrised Complexity in Post-Quantum-Cryptography
Currently I am working on the following problems:
- identifying suitable parameters for cryptographic problems
- finding proofs of hardness or FPT containment
Algorithmical aspects of certificates for non-negativity of polynomials
This area is the continuation of my PhD.
See also my software POEM.
It uses methods from the following fields:
- Polynomial Optimisation,
- Geometric Programming, Relative Entropy Programming, Semidefinite Programming
- Discrete Geometry,
- Parametrised Complexity
There is a video, where I present parts of my research.
Feel free to contact me, if you happen to know something about
- computing extremal points of an integer point set,
- solving LPs on the GPU
- solving many LPs with the same coefficient matrix, with small entries: complexity/preprocessing/implementations
- complexity of deciding nonnegativity of polynomials
- Parametrised running time for: Tarski's quantifier elimination, existential theory over the Reals
Publications
You can find my math articles on ArXiv.
-
Mechanical verification of a constructive proof for FLP,
with Bisping, B., Brodmann, P.D., Jungnickel, T., Rickmann, C., Stüber, A., Wilhelm-Weidner, A., Peters, K., Nestmann, U.,
International Conference on Interactive Theorem Proving 2016, also see Archive of Formal Proofs -
The minimum shared edges problem on grid-like graphs,
with Fluschnik, T., Hatzel, M., Härtlein, S., Molter, H.,
WG 2017, see ArXiv -
An Experimental Comparison of SONC and SOS Certificates for Unconstrained Optimization,
with Timo de Wolff,
accepted for MEGA 2019, see ArXiv -
Exact Optimization via Sums of Nonnegative Circuits and Sums of AM/GM Exponentials,
with Victor Magron and Timo de Wolff,
accepted for ISSAC 2019, see ArXiv -
Improved Lower Bounds for Global Polynomial Optimisation,
2021, see ArXiv -
Computational and Algebraic Aspects of Sums of Nonnegative Circuit Polynomials,
PhD thesis, 2022, see Link
Last Update: September 14, 2023