Registration

Chun-Chi Lin 林俊吉

Title: The $p$-elastic flows of inextensible planar closed curves for $p\in(1,\infty)$

Abstract: Building on the work of Blatt, Hopper, and Vorderobermeier (2022) on the existence of geometric flows for the p-elastic energy with $p\in[2,\infty)$, we investigate how to extend their results to the case  $p\in (1,2)$. In this talk, we focus on the class of inextensible planar closed curves.

We establish the existence of global weak solutions to the $L^2$-gradient flow of the p-elastic energy for all $p\in(1,\infty)$. Further directions, including extensions to open curves and applications to sub-Riemannian geodesics will also be addressed.

The results presented in this talk are based on the joint work with Ying-Hsiang Tsai.

 Lunch break

Yi-Sheng Wang 王以晟

Title: Meet the extended family of the Hopf link

Abstract: The Hopf link is assuredly one of the most studied links in knot theory. In this talk, we generalize the notion of the Hopf link to the context of spatial graphs and linked handlebodies, and discuss the symmetry and classification problems of these cousins of the Hopf link.

Tea break

Chao-Ming Lin 林朝明

Title: Intermediate Ricci curvature and functional convexity

Abstract: One of the most profound developments in optimal transport theory is the discovery of deep connections between the geometry of a space and the behavior of natural functionals on the associated Wasserstein space. More precisely, let $(M,g)$ be a smooth complete Riemannian manifold without boundary, and let $\mathcal P_2(M)$ denote the Wasserstein space consisting of probability measures on $M$ with finite second moment. The Boltzmann entropy defines a natural functional on $\mathcal P_2(M)$. Fundamental works of Otto--Villani, Cordero-Erausquin--McCann--Schmuckenschläger, and von Renesse--Sturm established that $(M,g)$ has nonnegative Ricci curvature if and only if the Boltzmann entropy is displacement convex along Wasserstein geodesics.

In this work, we generalize this result to intermediate Ricci curvature and discuss several applications. This is joint work with Kai-Hsiang Wang.

Break

forum

Symposium Banquet (The expense will be covered by NCTS)

Place: 客庄生活館/甘家伙房 (near Taipower Building metro station)