Organizer

Hyungryul Baik (KAIST), Sang-hyun Kim (KIAS)

How to join

Zoom Link http://cayley.kr/vz

Time Wed 4 pm or Thursday 9 am (or so) in KST (Korea Standard Time)

2022

November 21 (M), 10 am

Online http://shkim.org/vz

In person KIAS 1423

KyungRo Kim (SNU)

Laminar groups, veering triangulations, and Kleinian groups

In various circumstances, the fundamental groups of low-dimensional manifolds act on the circle preserving a number of laminations simultaneously. For instance, Thurston showed that every tautly foliated three manifold groups acts on the circle preserving pairs of laminations. In this talk, I will first introduce the veering pairs which is a special class of pairs of laminations. Then, I will explain how veering pairs produce veering triangulations via loom spaces. In the end, I will introduce the recent result that every group preserving a veering pair is the fundamental group of an irreducible 3-orbifold  which is obtained by Dehn-filling the veering triangulation induced from the veering pair. This work is joint with Hyungryul Baik and Hongtaek Jung.

November 30 (W), 10 am

Online Only http://shkim.org/vz

Jungin Lee (KIAS)

Mixed moments and the joint distribution of random groups

The moment problem is to determine whether a probability distribution is uniquely determined by its moments. Recently, the moment problem for random groups has been applied to the distribution of random groups, in particular the cokernels of random p-adic matrices. In this talk, we introduce the mixed moments of random groups and apply this to the joint distribution of random abelian and non-abelian groups. In the abelian case, we provide three universality results for the joint distribution of the multiple cokernels for random p-adic matrices. In the non-abelian case, we compute the joint distribution of random groups given by the quotients of the free profinite group by random relations. We will also briefly explain the work of Sawin and Wood on the distribution of the fundamental group of random 3-manifolds given by the Dunfield-Thurston model of random Heegaard splittings.