January 17th (Fri) 2025, 11 am 

KIAS 1423 & Zoom https://kimsh.kr/vz

Inhyeok Choi (KIAS / Cornell)

Free discrete subgroups of Homeo(S) and the fine curve graph.

Recently, Bowden-Hensel-Webb proposed the notion of the fine curve graph for the study of Homeo(S) as an analogue of the curve graph for the mapping class group Mod(S). In the case of Mod(S), the orbit map from a subgroup of Mod(S) to the curve graph may be seriously distorted. In this talk, I will describe an analogous example for Homeo(S) acting on the fine curve graph, namely, a free discrete subgroup of Homeo(S) without global fixed points, whose one free factor is a loxodromic and the other one free factor fixes the basepoint on the fine curve graph. If time allows, I will explain why the (metric) WPD of point-pushing pseudo-Anosov maps help understand this subgroup. This project is in progress. 

February 13 (Th), 11 am, KIAS 1423 & zoom https://kimsh.kr/vz

Jineon Baek (Yonsei)

Optimality of Gerver's Sofa

We resolve the \textit{moving sofa problem}, posed by Moser in 1966, which asks for the maximum area of a connected planar shape that can move around the right-angled corner of a \textit{L}-shaped hallway with unit width. We confirm the conjecture made by Gerver in 1994 that his construction, known as Gerver's sofa, with 18 curve sections attains the maximum area 2.2195...

February 18 (Tu), 11 am, KIAS 1423 & zoom https://kimsh.kr/vz

David Xu

TBA

February 24, 25 (Mon, Tue), 11 am, KIAS 1423 & zoom https://kimsh.kr/vz

Maximiliano Escayola (USACH)

Critical regularities of nilpotent groups acting on one-manifolds (Parts 1 & 2)

In the context of group actions, there is a general setting of a critical regularity: some actions are possible in class C^\alpha for \alpha<r and impossible for \alpha>r. For instance, the classical Denjoy theorem and Denjoy/Herman examples state that an action of Z on the circle with a Cantor minimal set is impossible in C^2, but possible for all smaller C^{1+\alpha}’s. Meanwhile, if one replaces Z by Z^d, the critical regularity is (1+1/d): there are such action for all C^{1+(1/d - \eps)}, and it is impossible for C^{1+ (1/d +\eps)}   (a result of Bertrand Deroin, Victor Kleptsyn, and Andres Navas, obtained in 2009).

The joint work with Victor Kleptsyn, that I will speak on, concerns critical regularities for actions of general nilpotent groups on one-dimensional manifolds: closed interval, circle, half-open interval. For all these groups and manifolds, we obtain the exact value of the critical regularity, describing it in purely algebraic terms (relative growth of some special subgroups).

KIAS--Springer Lectures

March 7th (Fri) 2025, Part 1, 10 - 10:50 am, Part 2, 11 -  11:50 am

KIAS 1503 & Zoom https://kimsh.kr/vz

Richard Schwartz (Brown)

Le Retour de Pappus (The Return of Pappus)

Pappus's Theorem is a classic theorem in projective geometry, going back to antiquity. In this talk I will explain how Pappus's Theorem is related to Farey addition, representations of the modular group, and pleated surfaces contained in the rank 2 symmetric space associated to SL_3(R).    Some of these ideas go back to my 1993 paper, "Pappus's Theorem and the Modular Group", and some of the ideas are things I discovered when I returned to the topic this year.  I hope to explain  everything from scratch in the talk.

KIAS Mathematics Colloquium

March 12th (Wed) 2025, 4 pm

KIAS 1503 & Zoom https://kimsh.kr/vz

Richard Schwartz (Brown)

The Optimal Paper Moebius Band

A paper Moebius band is made  by twisting a 1 x L rectangular strip of paper in space and gluing together the length-1 sides. If L is large, this is easy to do. If L is small this is impossible. What is the cutoff value?  This question goes back at least to Wunderlich in 1962 and is most likely much older.  In 1977 B. Halpern and C. Weaver conjectured that L>sqrt(3) is a necessary and sufficient condition. In this talk I will explain my proof of the Halpern-Weaver Conjecture and I will also prove that a minimizing sequence of examples converges to a unique limiting shape, the equilateral triangle.

March 10 (Th), 11 am, KIAS 1423 & zoom https://kimsh.kr/vz

Homin Lee (Northwestern, KIAS)

TBA