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
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".
2018
MFO Workshop: Convex Geometry and its Applications,
Oberwolfach, December 9th–15th, 2018.
TU Dresden, December 7th–8th, 2018.
Title: "Spherical floating bodies".
Ruhr-Universität Bochum, Bochum, November, 20th, 2018.
Titel: "Weighted floating bodies of polytopes".
CSASC 2018, Workshop on Functional Analysis and Geometry
Slovak University of Technology, Bratislava, September 11th–14th, 2018.
Title: "Weighted floating bodies of polytopes"
Recent Advances in Convex Geometry and Geometric Functional Analysis
TSIMF, Sanya, May 14th–18th, 2018.
Title: "Spherical floating bodies and floating area measures"
Workshop on Emerging Trends in Geometric Functional Analysis
BIRS, Banff, March 25th–30th, 2018.
Title: "Floating bodies and random approximation" (Video)
Ohio State University, March 16th–18th, 2018.
Title: "Floating bodies and random approximation"
2017
Université de Fribourg, December 13th, 2017.
Title: " Floating bodies in spherical and hyperbolic geometry".
Otto-von-Guericke-Universität Mageburg, December 8th–9th, 2017.
Title: "Floating bodies of polytopes".
Convex and Integral Geometry 2017,
Goethe University Frankfurt, September 25th–29th, 2017.
Title: "Weighted floating bodies of polytopes".
19th ÖMG Congress and Annual DMV Meeting,
Paris-Lodron University of Salzburg, September 11th–15th, 2017.
Title: "Weighted floating bodies of polytopes".
Convex, Discrete and Integral Geometry,
Banach Center Będlewo, June 4th–9th, 2017.
Title: "Weighted Floating Bodies".
Analysis and Probability Seminar,
Case Western Reserve University, Cleveland, March 7th, 2017.
Title: "The affine surface area in Euclidean convex geometry and beyond".
Mini-Workshop: Perspectives in high-dimensional probability and convexity,
Mathematisches Forschungsinstitut Oberwolfach, February 5th–11th, 2017.