Organizers

Hyungryul Baik (KAIST), 

Inhyeok Choi, Sang-hyun Kim, Javier de la Nuez-González, Carl-Fredrik Nyberg-Brodda, David Xu (KIAS),

Sanghoon Kwak (SNU)

How to join

Zoom https://kimsh.kr/vz

Meeting ID: 824 9598 1373

Passcode: 7998

Time Generally, Tuesdays or Thursdays 11 am KST

Length is typically for one-hour unless noted otherwise, although it's often extended by questions etc.

Mailing list Please contact one of the organizers to subscribe.

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Feb 23 (Mon) 2 pm - 3 pm

KIAS (Room 1423) | Zoom https://kimsh.kr/vz

Sangrok Oh (Pusan National University) 

Title: Right-angled Artin groups in hierarchically hyperbolic groups

Abstract: Hierarchically hyperbolic groups form a broad class of groups characterized by axioms inspired by mapping class groups. In this talk, we will first show that any finite collection of elements in a mapping class group generates a right-angled Artin subgroup once taken to sufficiently large powers. We will then discuss how this phenomenon extends, under suitable assumptions, to the setting of hierarchically hyperbolic groups.

Mar 26 (Thu) 11 am - 12 pm

KIAS (Room 8101) | Zoom https://kimsh.kr/vz

Tengren Zhang (National University of Singapore) 

Title: A rigidity theorem for complex Kleinian groups

Abstract: The notion of hyperconvexity for representations into PGL(d,R) plays a central role in the study of positive representations in Higher Teichmüller theory; for instance, this property is responsible for ensuring good regularity properties of the limit sets of positive representations. On the other hand, hyperconvex representations into PGL(d,C) are much more rigid. In this talk, I will explain a  rigidity results about hyperconvex representations into PGL(d,C). This is joint work with Richard Canary and Andrew Zimmer.

April 16 (Thu) 11 am - 12 pm

KIAS (Room 8101) | Zoom https://kimsh.kr/vz

Christine Vespa (Aix-Marseille University) 

Title: Homology: homological stability and stable values

Abstract: Homology is a fundamental tool in algebra and topology, used to study mathematical objects through algebraic invariants. These invariants are often difficult to compute directly. A common strategy for computing the homology of objects that arise naturally in families is to analyze their behavior in a stable range.

One speaks of homological stability when, in a family indexed by a parameter n, the homology groups in degree d become independent of n once n is sufficiently large relative to d. The part of the homology that stabilizes is called stable homology. This stable part is often more accessible than the unstable one. By combining computations of stable homology with homological stability results, one can obtain explicit descriptions, of homology for large objects in the family.

Such phenomena occur in many natural settings.

In this talk, I will discuss the homology of groups. Classical examples of families exhibiting homological stability include the symmetric groups and the braid groups, which illustrate the strength and ubiquity of this phenomenon. I will first introduce the general notions of homological stability and stable homology, and then turn to the case of twisted coefficients, where stable homology is closely related to functor homology. I will then focus on the family of groups Aut(Fn​) and present recent computations of functor homology obtained in joint work with Minkyu Kim.