AS-NCTS One Day Topology Workshop
Date: July 23 (Tuesday) 2024
Venue: Seminar Room 638, 6F, Astro-Math. Building (NTU Campus)
Hung-Lin Chiu (National Tsing Hua University)
Title: A contact invariant of singular points of surfaces in contact 3-manifolds
Abstract: I will give a contact invariant of singular points of surfaces in contact 3-manifolds. It turns out, at least when manifolds are CR spherical, that this invariant can be expressed in terms of p-minimal curvature and α-function, which are two geometry invariants for surfaces in pseudo-hermitian 3-manifold. So far, we are trying to find out the applications of this contact invariant to some related subjects.
Chung-I Ho (National Kaohsiung Normal University)
Title: Non-orientable Lagrangian surfaces in symplectic rational 4-manifolds
Abstract: In this talk, I will introduce some methods in constructing Lagrangian surfaces in sympelctic 4-manifolds and how they affect topology of the symplectic 4-manifolds and Lagrangian surfaces. For rational 4-manifolds, we will give more precise description of symplectic structures admitting Lagrangian surfaces.
Jyh-Haur Teh (National Tsing Hua University)
Title: Absolute semi-topological Galois groups and infinite Galois correspondences
Abstract: The absolute semi-topological Galois groups of some topological spaces areshown to be free profinite groups of countable rank. An infinite Galois correspondence between their closed subgroups and Weierstrass series covering spaces will be briefly explained. A new notion of absolute Galois group of (t) with respect to a topological space will be introduced.
Yi-Sheng Wang (National Sun Yat-sen University)
Title: Decompositions of knotted objects
Abstract: The idea of decomposition is a common method in mathematics to break down complicated objects into simpler pieces; it is especially useful when the decomposition is unique. A fundamental result in knot theory by Schubert states that every knot can be factorized into prime knots in a unique way, a reminiscence of the prime factorization of positive integers. We first review some known factorization results that generalize Schubert’s idea. Then we discuss how one can uniquely decompose a handlebody-knot by 2-spheres meeting the handlebody in three disks and some implications of the result. It is a joint work with G. Bellettini and M. Paolini.