Research
I don’t currently work in research but from time to time I get interested in a project and write a paper about it. Those papers will appear below. You can also check out my Google scholar page.
Numerical Optimization, Control and Statistics
I currently work in numerical optimization and real-time control, so one of the things I am very interested in is how to ensure/verify/certify that a control algorithm is safe to deploy. I have been thinking a lot about this topic and recently put the following paper on the arXiv:
- (joint with L. Hewing and A. Domahidi). A risk analysis framework for real-time control systems. arXiv preprint
Pure mathematics
In a previous life I worked in symplectic topology. That’s a field within pure mathematics which studies the geometry of Hamiltonian systems (think of celestial mechanics). I loved the work but eventually lost interest in the topic. During my PhD I wrote the following papers.
- Mather theory and symplectic rigidity. Journal of Modern Dynamics 15 (2019), 165-207
- Topology of (small) Lagrangian cobordisms. Algebraic & Geometric Topology 19-2 (2019), 701-742
- A distance expanding flow on exact Lagrangian cobordism classes. arXiv preprint
- Invariants of Lagrangian cobordisms via spectral numbers. Journal of Topology and Analysis Vol 11, No. 01, 2019
For this work I was awarded the ETH medal in 2019. Preprints of all of these papers are also available through the arXiv. If you are interested in this kind of stuff you can watch a talk on an introduction to Aubry Mather theory as well as one on symplectic Mather theory which I gave at an MSRI summer school.