Mostly Teichmuller Spaces (MTS) Seminar is intended to feature seasoned and young researchers in the fields related to quasiconformal maps, Riemann surfaces, hyperbolic geometry, Teichmuller spaces, or any other related topic. The meetings will be on Zoom. We will meet on some Thursdays 11am-12pm during the semester.
Meeting ID: 813 0384 9091
- Anja Randecker, Heidelberg University, February 24, 11am (EST)
- Ferran Valdez, Centro de Ciencias Matematicas, March 3, 11am (EST)
- Bram Petri, Sorbonne Université, March 24, 11am (EST)
- Nhat Minh Doan, University of Luxembourg, March 31, 11am (EST)
- Hugo Parlier, University of Luxembourg, October 14, 11 am (EST)
- Title: Curves, surfaces and intersection
- Abstract: On closed surfaces of positive genus, through classical work of Dehn, simple closed curves can be described using intersection numbers. Now what if you want to describe curves with self-intersections in a similar way? This talk will be on joint work with Binbin Xu about this question, and where we end up constructing and studying so-called k-equivalent curves. These are distinct curves that intersect all curves with k self-intersections the same number of times.
- Alastair Fletcher, Northern Illinois University, October 21, 11 am (EST)
- Title: Cantor sets and Julia sets
- Abstract: One does not have to study complex dynamics much before coming across examples of Julia sets which are Cantor sets. It is then a natural question to ask which Cantor sets can be Julia sets? The rigidity of holomorphic maps precludes certain examples, and so we will ask this question in the context of uniformly quasiregular mappings with a focus on dimensions two and three. Based on joint work with D. Stoertz (Gustavus Adoplhus College) and V. Vellis (University of Tennessee – Knoxville).
- Nicholas Miller, Berkeley, November 4, 11 am (EST)
- Title: Big mapping class groups and loxodromic isometries on hyperbolic graphs
- Abstract: For finite-type surfaces, the Nielsen-Thurston classification tells us that every element of the mapping class group is either finite order, fixes a collection of simple closed curves, or is pseudo-Anosov. A coarser version of this classification is captured by the action of the mapping class group on the curve complex, namely the elements which act loxodromically are precisely the pseudo-Anosovs. For infinite type surfaces, much less is known about analogues of these two classifications. In fact, we currently do not even know many explicit examples of mapping classes acting loxodromically on hyperbolic graphs which do not come from the finite-type setting. In this talk, I will give a broad overview of the area and then present some new examples of “instrinsically infinite type” mapping classes acting loxodromically on an infinite-type analogue of the curve complex. This is joint work with Carolyn Abbott and Priyam Patel.
- Harry Baik, KAIST, December 2, 10am (EST)
- Title: Reducible normal generators for mapping class groups are abundant
- Abstract: There is this philosophy “small translation length means normal generation” for mapping class group actions. For instance, Lanier-Margalit showed that the pseudo-Anosov elements with small translation length on the Teichmüller space normally generate the mapping class group. We provide a similar criterion for reducible mapping classes. This is a joint work with Dongryul M. Kim and Chenxi Wu.
- Xinlong Dong, Graduate Center, CUNY, December 7, 10am (EST)
- Title: On complex extension of the Liouville map
- Abstract: This is a Colloquium style talk on the Liouville map.