This is the main page for the Joint Seminar on Teichmüller theory and Related topics (JSTeichR), organized by:

- Yi HUANG 黄意 (Yau Mathematical Sciences Center, Tsinghua University)
- Qiongling LI 李琼玲 (Chern Institute of Mathematics, Nankai University)
- Yi LIU 刘毅 (Beijing International Center of Mathematical Research, Peking University)
- Yunhui WU 吴云辉 (Yau Mathematical Sciences Center, Tsinghua University)

Here's the attendance information for the seminar series:

- Time: Monday, 15:30 PM (Beijing time).
- Place: online.
- Zoom: 405 416 0815, pw: 111111

We're taking a break this week because of the October 1st national holidays!

The universality of Brownian motion underlies the appearance of SLE in conformally invariant 2D systems. The action functional of Brownian motion, namely the Dirichlet energy, corresponds to the Loewner energy for a Jordan curve. This energy, intuitively speaking, measures the roundness of a Jordan curve and the density of SLE around the curve. Furthermore, this energy is shown by Takhtajan and Teo to be a Kahler potential on the space of Weil-Petersson quasicircles, identified with the Weil-Petersson universal Teichmüller space. I will overview different geometric and probabilistic descriptions of the Loewner energy and Weil-Petersson Teichmüller space and discuss further development by exploring those links.

In this talk, I will survey what is known or conjectured about maps between configuration spaces and moduli spaces of surfaces. Among them, we consider two categories: continuous maps and also holomorphic maps. We will also talk about some results and conjectures about maps between finite covers of those spaces. Unlike the case of the whole spaces, much less is known about their finite covers.

I will talk about mapping class group action on the curve complex with the following conjecture in mind: an element with small stable translation length is a normal generator. This conjecture is motivated by a similar statement in the case of the action on the Teichmüller space proved by Lanier-Margalit. I will discuss various partial results (based on joint works with various subsets of \(\{\)Dongryul Kim, Hyunshik Shin, Philippe Tranchida, Chenxi Wu\(\}\)).

- Seminar notes.
- Watch.

Spacelike minimal surfaces in the pseudo-hyperbolic (2+q)-spacetime are actually maximal and are related to \(\mathrm{SO}\)(2,q+1)-representations of surface groups through the works of Bonsante-Schlenker and Collier-Tholozan-Toulisse. We investigate a type of minimal surface associated to \(\mathrm{SO}\)(n,n+1)-representations. They occur in pseudo-hyperbolic spacetimes with higher space dimensions, and hence are not maximal; but they are still infinitesimally rigid, hence can be used to prove Labourie's conjecture in rank \(2\).

- Seminar notes.
- Watch.

Let \(G\) be a Lie group acting transitively on a manifold \(X\). A *compact quotient of \(X\)* (also called *compact Clifford--Klein form*) is simply a quotient of \(X\) by a discrete subgroup of \(G\) acting properly discontinuously and cocompactly. In this talk, we will address the following questions:

- Does \(X\) admit compact quotients?
- If so, what is their topology?
- If so, do these compact quotients have deformations?

These questions are rooted in the mathematics of the late XIX^{th} century: Klein's *Erlangen program*, the uniformization of (closed) Riemann surfaces, Poincaré's *Analysis Situs*...

If there are any issues, please feel free to contact any of the organizers.