Merlin Incerti-Medici

Universität Wien

Fakultät für Mathematik

1090 Wien

Austria

Mail: firstname.secondpartoflastname magic-a gmail.com

About me

I'm a PostDoc at Universität Wien. I did my PhD at Universität Zürich under the supervision of Viktor Schroeder. My mathematical interests, broadly speaking, include asymptotic geometry, CAT(0) cube complexes, expanders, and non-positively curved manifolds.

Some central themes of my current and recent work are the geometry of negatively curved manifolds, isometry groups of CAT(0) cube complexes, and expanders. The first topic concerns itself with the study of non-hyperbolic, negatively curved manifolds that contain well-behaved codimension one subspaces (for example Gromov-Thurston manifolds) and is interested in quasi-isometry invariants for such spaces. The second project is about a systematic understanding of the isometry groups of certain CAT(0) cube complexes as totally disconnected, locally compact groups. The last subject is an offspring of the second and aims at new constructions of expanders with a view towards applications in quantum error correction.

Publications and Preprints

13. Fundamentals of cubical isometry groups

2025

12. On a generalization of Cannon's conjecture for cubulated hyperbolic groups

with Corey Bregman

2024

11. Automorphism groups of cocompact CAT(0) cube complexes and simplicity

with Tobias Hartnick

2023

Automorphisms of cube complexes test.jpg

10. Automorphisms of self-similar trees

with Tobias Hartnick

2023

9. Hyperbolic projections and topological invariance of sublinearly Morse boundaries

with Carolyn Abbott

2022

8. The normal growth exponent of a codimension one hypersurface of a negatively curved manifold

with Corey Bregman

2021

7. Contractibility of boundaries of cocompact convex sets and embeddings of limit sets

with Corey Bregman

2024, Analysis and Geometry on Metric Spaces

6. Sublinearly Morse boundaries from the viewpoint of combinatorics

with Abdul Zalloum

2023, Forum Mathematicum

Sublinearly Morse boundaries combinatorics_1.jpg

5. Circumcenter extension maps for non-positively curved spaces

2024, Geometriae Dedicata

4. Comparing topologies on the Morse boundary and quasi-isometry invariance

2021, Geometriae Dedicata

3. CAT(0) cube complexes are determined by their boundary cross ratio

with Jonas Beyrer, Elia Fioravanti

2021, Groups, Geometry & Dynamics

2. The Hausdorff- and Nagata-dimension of Möbius spaces

2017

1. Möbius structures, quasi-metrics and completeness

2024, Algebraic & Geometric Topology

Alexander von Humboldt, der Weltvernetzer

In collaboration with Life Science Communication AG, I organised a mobile exhibition in honour of the 250. birthday of Alexander von Humboldt in 2019. Humboldt was one of the most influential and well-known scientists of his time and his work on people and nature is not only integrated into how we think about nature but also highly relevant for modern research (most notably for climate science).

Humboldt cared a lot about the accessibility of science to the general public. In this spirit, the exhibition aims to provide an entry point for curious explorers of all ages to see science in a way they may not have known before.

More information can be found here. The pictures belong to Life Science Communication AG.