# 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****,**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".