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

David Xu

Convex-cocompact representations into the isometry group of the infinite-dimensional hyperbolic space

Similarly to Euclidean spaces, there is an infinite-dimensional analog for the (algebraic) hyperbolic spaces. This space enjoys all the "geometric" properties of its finite-dimensional siblings. However, the topological aspects of this space and its group of isometries are more involved than in finite dimension. In particular, even the notion of discrete isometry groups needs to be specified in this context. In this talk, I will present the infinite-dimensional hyperbolic space and describe some of its properties, emphasizing some differences with finite dimension. Then, I will discuss about a generalization of the classic stability result of convex-cocompact representations of finitely generated groups in hyperbolic spaces.

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