Research
Publications
1. Random inscribed polytopes in projective geometries (arXiv)
accepted Mathematische Annalen (2021), jointly with Daniel Rosen and Christoph Thäle.
2. Asymptotic normality for random polytopes in non-Euclidean geometries (arXiv)
Transactions of the American Mathematical Society 373 (2020), jointly with Christoph Thäle.
3. Asymptotic normality for random simplices and convex bodies in high dimensions (arXiv)
Proceedings of the American Mathematical Society 149 (2021), jointly with David Alonso-Gutiérrez, Julian Grote, Zakhar Kabluchko, Matthias Reitzner, Christoph Thäle, Beatrice-Helen Vritsiou, Elisabeth M. Werner.
4. Intrinsic and dual volume deviations of convex bodies and polytopes (arXiv)
Int. Math. Res. Not. IMRN (2019), rnz277, jointly with Steven Hoehner and Gil Kur.
5. Spherical centroid bodies (arXiv)
submitted (2019), jointly with Thomas Hack, Peter Pivovarov and Franz Schuster.
6. Flag numbers and floating bodies (arXiv)
Advances in Mathematics 338 (2018), jointly with Carsten Schütt and Elisabeth Werner.
7. Weighted floating bodies and polytopal approximation (arXiv)
Transactions of the American Mathematical Society 370 (2018), jointly with Monika Ludwig and Elisabeth Werner.
8. The floating body in real space forms (arXiv)
Journal of Differential Geometry 110 (2018), jointly with Elisabeth Werner.
9. The spherical convex floating body (arXiv)
Advances in Mathematics 301 (2016), jointly with Elisabeth Werner.
10. Binary operations in spherical convex geometry (arXiv)
Indiana University Mathematics Journal 65 (2016), jointly with Franz Schuster.
Conferences and Workshops
2021
Interaction Between Partial Differential Equations and Convex Geometry (21w5139) (online conference),
Hangzhou, China, October 17th–22nd, 2021.
Title: "On the asymptotic normality of random polytopes in spherical geometry".
DMV-ÖMG Annual Conference 2021: Sektion Geometrie und Topologie (hybrid conference),
Universität Passau, September 27th–October 1st.
Conference on Convex, Integral and Stochastic Geometry,
Bad Herrenalb (Black Forest), Germany, September 5th–10th, 2021.
Title: "Asymptotic normality for the volume of random polytopes in non-Euclidean geometries".
Workshop: High dimensional measures: geometric and probabilistic aspects (online conference),
Universität Bonn, Germany, March 22nd–26th, 2021.
Winter School on "The Interplay between High-Dimensional Geometry and Probability"(online conference),
Universität Bonn, Germany, January 11th–15th, 2021.
The Interplay between High-Dimensional Geometry and Probability (online semester program),
Universität Bonn, Germany, January 5th–April 23th, 2021.
Problem Group on "Random polytopes in spherical geometries".
2020
Bernoulli-IMS One World Symposium 2020 (online conference),
Section: "Limit theorems, large deviations and extremes", August 24th-28th, 2020.
prerecorded presentation on "Random convex hulls in non-Euclidean geometries" jointly with Daniel Rosen and Christoph Thäle (YouTube).
Research Seminar on Probability and Geometry (online lecture via Zoom),
Ruhr-Universität Bochum, Bochum, June 2nd, 2020.
Titel: "Best and random approximation in the dual Brunn–Minkowski theory".
MFO Wokshop: New Perspectives and Computational Challenges in High Dimensions,
Oberwolfach, February 2nd–8th, 2020.
Title: "Polytopal Approximation in Non-Euclidean Geometries".
2019
Conference on Convex, Discrete and Integral Geometry,
Friedrich-Schiller-Universität Jena, September 16th–20th, 2019.
Title: "Polytopal Approximation in the dual Brunn–Minkowski Theory".
Differential Geometry and its Applications
Hradec Králové, Czech Republic, September 1st–7th, 2019.
Title: "Polytopal Approximation in Hilbert Geometries".
Asymptotic Geometric Analysis IV,
Euler International Mathematical Institute, St. Petersburg, July 1st–6th, 2019.
Title: "Polytopal Approximation in the dual Brunn–Minkowski Theory".
Bolyai Institute, Szeged, April 5th–6th, 2019.
Title: "Spherical Centroid Bodies".
Spring School and Workshop on Polytopes,
RUB, Bochum, March 11th–15th, 2019.
Title: "Random polytopes and spherical centroid bodies".
Analysis and Probability Seminar,
Case Western Reserve University, Cleveland, February 19th, 2019.
Title: "Spherical Centroid Bodies".