# Research

## Publications

1. Floating bodies and duality in spaces of constant curvature (arXiv)

submitted (2023),

jointly with Elisabeth M. Werner.

2. An intrinsic volume metric for the class of convex bodies in R^n (arXiv)

Communications in Contemporary Mathematics (2023), https://doi.org/10.1142/S0219199723500062

jointly with Steven Hoehner.

3. Spherical convex hull of random points on a wedge (arXiv)

Mathematische Annalen (2023), https://doi.org/10.1007/s00208-023-02704-9

jointly with Anna Gusakova, Matthias Reitzner, Carsten Schütt, Christoph Thäle and Elisabeth M. Werner.

4. Random inscribed polytopes in projective geometries (arXiv)

Mathematische Annalen 381 (2021),

jointly with Daniel Rosen and Christoph Thäle.

5. Asymptotic normality for random polytopes in non-Euclidean geometries (arXiv)

Transactions of the American Mathematical Society 373 (2020),

jointly with Christoph Thäle.

6. 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.

7. Intrinsic and dual volume deviations of convex bodies and polytopes (arXiv)

Int. Math. Res. Not. IMRN 22 (2021),

jointly with Steven Hoehner and Gil Kur.

8. Spherical centroid bodies (arXiv)

American Journal of Mathematics 145 (2023),

jointly with Thomas Hack, Peter Pivovarov and Franz Schuster.

9. Flag numbers and floating bodies (arXiv)

Advances in Mathematics 338 (2018),

jointly with Carsten Schütt and Elisabeth Werner.

10. Weighted floating bodies and polytopal approximation (arXiv)

Transactions of the American Mathematical Society 370 (2018),

jointly with Monika Ludwig and Elisabeth Werner.

11. The floating body in real space forms (arXiv)

Journal of Differential Geometry 110 (2018),

jointly with Elisabeth Werner.

12. The spherical convex floating body (arXiv)

Advances in Mathematics 301 (2016),

jointly with Elisabeth Werner.

13. Binary operations in spherical convex geometry (arXiv)

Indiana University Mathematics Journal 65 (2016),

jointly with Franz Schuster.

## Conference Organization

Mini-Symposium on Geometric Probability and Valuation Theory (jointly with Fabian Mussnig)

TU Wien, Austria, April 20th–22nd, 2022.

## Conferences and Workshops

## 2024

Bernoulli-ims 11th World Congress in Probability and Statistics

Ruhr-Universität Bochum, August 11th–16th, 2024.

Title: "The intrinsic volume metric and new upper bounds for optimal polytopal approximation".

Research visit at CWRU,

Case Western Reserve University, Cleveland, July 13th–26th, 2024.

Workshop: High dimensional phenomena: geometric and probabilistic aspects

Hausdorff Center for Mathematics, Universität Bonn, Bonn, March 11th–15th, 2024.

Title: "Floating bodies and duality in spaces of constant curvature". (video)

Workshop: Asymptotics of (random) convex sets: fluctuations and large deviations

Hausdorff Center for Mathematics, Universität Bonn, Bonn, February 19th–23rd, 2024.

Winter School on Geometry and Probability

Hausdorff Center for Mathematics, Universität Bonn, Bonn, January 22nd–26th, 2024.

Title: "The floating body construction and its applications". (video)

Hausdorff Center for Mathematics, Universität Bonn, Bonn, January 21st–April 19th, 2024.

## 2023

Conference on Convex Geometry and Geometric Probability

Paris Lodron University Salzburg (PLUS), Salzburg, September 25th–29th, 2023.

Title: "Floating Bodies and Polarity in Non-Euclidean Geometries".

ÖMG Meeting 2023 Graz, Mini-Symposium: "Probabilistic Methods in Convexity"

Karl-Franzens-University (KFU) and Graz University of Technology (TUG), Graz, September 18th–22nd, 2023.

Title: "Spherical Centroid Bodies".

Research visit at CWRU,

Case Western Reserve University, Cleveland, August 15th–29th, 2023.

Workshop: Convex Geometry - Analytic aspects,

INdAM Meeting, Cortona, June 26th–30th, 2023

Title: "Weighted Floating Bodies and Polarity".

CIEM, Castro Urdiales, June 5th–9th, 2023.

Title: "Floating Bodies and Polarity on the Unit Sphere".

Research visit at CWRU with talk in the MAMS Colloquium,

Case Western Reserve University, Cleveland, February 20th–28th, 2023.

Title: "Random Spherical Polytopes"

## 2022

Approximation and geometry in high dimensions,

Banach Center Będlewo, October 9th–15th, 2022.

Title: "An Intrinsic Volume Metric on Convex Bodies".

Research visit at RUB with talk in the research seminar,

Ruhr-Universität Bochum, July 8th–22th, 2022.

Title: "Weighted floating body of polytopes".

geOmetry, anaLysis & convExity,

Universidad de Sevilla, Spain, June 20th–24th, 2022.

Title: "Weighted floating body of polytopes".

University of Szeged, May 27th–28th, 2022.

Title: "Weighted floating body of polytopes".

Integral and metric geometry (22w5181) (online conference),

Casa Matemática Oaxaca (CMO), May 1st–6th, 2022.

Rubio de Francia Seminar (online talk, video),

Universidad de Zaragoza, Spain, March 31st, 2022.

Title: "Random spherical polytopes".

## 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".