# Research

## Publications

**1. Random inscribed polytopes in projective geometries **(arXiv)

submitted (2020), 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.