Quasiworld


Welcome to the Quasiworld!

This is an international and virtual seminar organized by Mario Bonk and his post docs Annina Iseli, Mikhail Hlushchanka and Sylvester Eriksson-Bique. The seminar focuses on quasiconformal geometry, complex dynamics and analysis on metric spaces. We construe these broadly and invite anyone interested to participate, and to volunteer talks.

We are currently on a Winter break. We expect to resume in a format TBD around February 2022.

See below or join the email list for more information.

Schedule, Titles and Abstracts Fall 2021


  • October 6th

Wei Qian (CNRS and Université Paris-Saclay)

Uniqueness of the welding problem with fractal interfaces

Abstract: We give a simple set of geometric conditions on curves η, ῆ in H from 0 to infinity so that if φ : HH is a homeomorphism which is conformal off eta with φ(η) = ῆ then phi is a conformal automorphism of H. Our result applies to the setting where the interface eta is not the boundary of a Hölder domain or even a connected domain. Our motivation comes from the fact that it is possible to apply our result to random conformal welding problems related to the Schramm-Loewner evolution (SLE) and Liouville quantum gravity (LQG). This is based on a joint work with Jason Miller.


  • October 20th

Ryosuke Shimizu (Kyoto University)

Construction of a canonical p-energy on the Sierpinski carpet

Abstract: It is known that the Brownian motion on the Sierpinski carpet (abb. SC) has sub-Gaussian behavior (it is also called anomalous diffusion), and so we can not develop the upper gradient based analysis on SC. In this talk, we give a construction of a ``canonical'' p-energy (formally written as ∫|∇f |^p) on SC as a scaling limit of discrete energies on approximating graphs. A motivation of this work is related to the study of Ahlfors regular conformal dimension of fractals.


  • November 3rd

Damaris Meier (University of Fribourg)

Quasiconformal almost parametrizations of metric surface

Abstract: The uniformization problem for metric spaces asks to find conditions on a given metric space X, homeomorphic to some model space, under which there exists a homeomorphism from the model space to X with good geometric and analytic properties

 We consider the case where X is a two-dimensional metric surface of locally finite Hausdorff-2-measure. By only assuming that X is locally geodesic, we show that any Jordan domain in X of finite boundary length admits a quasiconformal almost parametrization. This generalizes the uniformization results of Bonk and Kleiner as well as Rajala. The proof makes use of the theory of energy and area minimizing Sobolev discs developed by Lytchak and Wenger. A large part of this talk is devoted to the existence of Sobolev discs spanning a given Jordan curve in X. This is joint work with Stefan Wenger.


Slides available here.


  • November 17th

Chenxi Wu (University of Wisconsin-Madison)

Galois conjugate for exponents of core entropy

Abstract: This is a collaboration with Kathryn Lindsey and Giulio Tiozzo. The Hubbard tree of a post-critically finite complex quadratic map is a finite simplicial tree that encodes the dynamics on its Julia set, and the core entropy is the topological entropy of the induced map on the Hubbard tree. Properties of core entropy have been extensively studied and they have important connections with the geometry of the Mandelbrot set. Using kneading theory and symbolic dynamics, we found new properties of the set of the Galois conjugates of the exponent of core entropy of superattracting points, which leads to a new necessary condition for an algebraic integer to be the exponent of core entropy of superattracting maps that lie in a specific vein. I will also discuss our ongoing work on generalizing these results to higher degree maps.



  • December 1st

Ursula Hamenstädt (Universität Bonn, Germany)

Title: Random walks and boundaries of groups

Abstract: We explain how random walks on a hyperbolic group can be used to construct a hyperbolic flow from the group whose invariant measures correspond precisely to quasi-invariant measures on the boundary of the group. This construction gives rise to families of Sobolev spaces in the spirit of Bonk and Saksman whose properties can be related to topological properties of the boundary of the group.



  • December 15th

Tatiana Smirnova-Nagnibeda (University of Geneva)

Title: Schreier graphs of self-similar groups as source of examples in spectral graph theory

Abstract: In this talk we will discuss some questions from spectral theory of infinite graphs and how to solve them by studying self-similar groups and their actions.



Seminar Logistics and Email List

The zoom invitation will be distributed through the email list. If you do not receive it, you can contact one organizer to give you the link and password. You may also share it within our community, but do not post it on a publicly viewable website. It is the same every week, so you do not need to receive a new one each week.


All participants will join automatically muted and with no video on entry. The format worked fine with lots of videos, so you can keep your video on, and if there is an issue we will address it. You may, and are encouraged, to unmute yourself to ask questions. Keep yourself muted otherwise. You may also post questions in the chat, that the organizers and/or speaker will follow. At the end the host may choose some of these questions to ask from the speaker. This is a friendly and conversational seminar, so many questions are encouraged. The chatwindow will be monitored by hosts, speaker and/or possibly collaborators, and will answer questions in a live feed format (you can answer too if you know the answer).


We are looking for volunteer speakers. Contact one of the organizers to be added to the schedule. If you want and choose to use slides, you can send your slides to be added to this website.


The easiest way you can join our email list is by sending a blank email to

quasiworld-seminar+subscribe@googlegroups.com.

If you wish to view past emails, and have a google account, you can access these at https://groups.google.com/d/forum/quasiworld-seminar (requires joining first with a google account).


Also, we may consider using the email list for announcements of more broad interest to our community. Contact the organizers if you wish to post such an announcement. We also may add other relevant events to our community to this calendar, and if you would like, we can add your seminar as well.

Picture by M.C. Escher