The Optimal Paper Moebius Band by Richard Schwartz (Brown)

KIAS Mathematics Colloquium

March 12th (Wed) 2025, 4 pm

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

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.

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Le Retour de Pappus (The Return of Pappus) by Richard Schwartz (Brown)

Parts I & II : March 7th (Fri) 2025, 10 -  11:50 am, KIAS--Springer Lectures

Part III : March 14th (Fri) 2025, 11 -  11:50 am

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

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.

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March 20 (Th), 11 am, KIAS 1423 & zoom https://kimsh.kr/vz

Homin Lee (Northwestern, KIAS)

Random dynamics on surfaces

In this talk, we will discuss about smooth random dynamical systems and group actions on surfaces. Random dynamical systems, especially understanding stationary measures, can play an important role when we consider a group action. For instance, when a group action on torus is given by toral automorphisms, using random dynamics, Benoist-Quint classified all orbit closures. 

In this talk, we will study on non-linear actions on surfaces using random dynamics. We will discuss about absolutely continuity of stationary measures, classification of orbit closure, and exact dimensionality of stationary measures. This talk will be mostly about the joint work with Aaron Brown, Davi Obata, and Yuping Ruan.

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