January 16th (Thu) 2025, 11 am 

KIAS 1424 & 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. 

KIAS--Springer Lectures

March 6th (Thu) 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.