The seminar usually takes place in Astro-Math 202 at 4-5PM every Tuesday, unless noted otherwise.
Organizers: Yng-Ing Lee 李瑩英, Chung-Jun Tsai 蔡忠潤, Mao-Pei Tsui 崔茂培
Video watching: lecture of A. Neves
https://www.youtube.com/watch?v=1HWeTqHr7kE
Ser-Wei Fu 傅斯緯 (NCTS): Deformations of Flat Surfaces
A flat surface can be easily obtained by gluing Euclidean polygons together. Local deformation of flat surfaces via deforming polygons is classical and well-understood. In this talk the focus will be placed on a family of flat surfaces called half-translation surfaces. The space of quadratic differentials, interpreted as a cotangent space of the moduli space of hyperbolic surfaces, can be used to describe optimal quasiconformal maps between hyperbolic surfaces. The goal of the talk is to introduce deformations of half-translation surfaces called flat grafting to develop a better geometric understanding of the space of quadratic differentials. Every fixed topological surface admits a large family of flat structures and deformations of flat surfaces are useful in proving local and boundary properties. One particularly interesting aspect of deformations is the geodesic length spectrum.
Kuan-Hui Lee 李冠輝 (NTU): Some examples of hyper-Kähler 4-manifolds
It is well known that hyper-Kähler condition in 4 manifold is equivalent to the self-dual equation. We will use this result on the Bianchi type IX metric. By solving the ODE, we will derive two examples of hyper-Kähler 4-manifolds. Also, we will see the local behavior of these examples.
2PM Friday
in #440
Peng Lu 呂鵬 (Oregon): Evolution of relative Yamabe constant under Ricci Flow
In a joint work with S.C. Chang in 2007 we derive, under a crucial technical assumption, a formula for the derivative of Yamabe constant $Y(g(t))$, where $g(t)$ is a solution of Ricci flow on closed manifolds.
In this talk we will present a joint work with B. Botvinnik to study the evolution of the relative Yamabe constants under Ricci flow on compact manifolds with boundary $M$. In particular, we show that if the initial metric $\bar{g}_0$ is a Yamabe metric, then, for Ricci flow $\bar{g}(t)$ with boundary conditions that mean curvature $H_{\bar{g}_t} =0$ and conformal class $\bar{g}_t|_M \in [\bar{g}_0|_M]$, we prove that, under some natural assumptions, the time derivative of relative Yamabe constant is nonnegative and is equal to zero if and only the metric $\bar{g}_0$ is Einstein.
Jih-Hsin Cheng 鄭日新 (Academia Sinica): On the Sobolev quotient of three dimensional CR manifold
We exhibit examples of compact three-dimensional CR manifolds of positive Webster class, Rossi spheres, for which the pseudo-hermitian mass is negative, and for which the infimum of the CR-Sobolev quotient is not attained. To our knowledge, this is the first geometric context on smooth closed manifolds where this phenomenon arises, in striking contrast to the Riemannian case. This is joint work with Andrea Malchiodi and Paul Yang.
11AM, 3PM
Wednesday
NCTS Distinguished Lectures link
Yakov Eliashberg (Stanford): Recent Advances in Symplectic Flexibility
Two sides of symplectic topology, rigid and flexible, coexist in constant competition. The rigid side concerns with developing new invariants and constraints, while the flexible side attempts to make constructions which are not yet prohibited. Many outstanding results on both sides of symplectic topology were proven over 30 years ago, mostly by M. Gromov, when the subject of symplectic topology was created. While in the following years most successes were on the rigid side the situation changed in the last 5 years when many unexpected new results on the flexible side were discovered. In two lectures I will introduce the subject of symplectic flexibility and review its most recent development.
Chien-Hao Liu 劉劍豪 (CMSA/Harvard): Action functional for D-branes
D-brane stands for Dirichlet boundary condition on open string world-sheet. In this talk, we will discuss action functionals for D-branes from physics, and related mathematical issues.
in #201
Yohsuke Imagi 今城洋亮 (ShanghaiTech): Example of Compact Singular Special Lagrangians
There is an important class of compact singular special Lagrangians whose singularities are all isolated and modelled upon Harvey-Lawson's T^2-cone. I will explain an example and some general properties of these special Lagrangians (including the contributions by Joyce, Haskins and myself).
