부산대학교 기하학, 위상수학 세미나
(PNU Geometry and Topology seminar)

세미나 시간 및 장소

General information.

5월 10일 (May 10th)

Speaker. 박상우
Title. Rigidity of minimal hypersurfaces with free boundary in a ball
Abstract. We give two rigidity results of free boundary hypersurfaces in a ball. First, we prove that any minimal hypersurface with free boundary in a closed geodesic ball in a round open hemisphere $\mathbb{S}^{{n+1}_+}$ which is Killing-graphical is a geodesic disk. We note that we do not assume any topological condition on the hypersurface. We consider analogous result for self-shrinkers of the mean curvature flow. More precisely, we secondly proved that any graphical self-shrinker with free boundary in a ball in $\mathbb{R}^{n+1}$ is a flat disk passing through the center of the ball.

5월 17일 (May 17th)

Speaker. 김유식
Title. Disc superpotential of projective spaces
Abstract. Disc superpotentials have played a pivotal role in Lagrangian Floer theory and Mirror symmetry. The goal of this talk is to explain what disc superpotentials are in specific examples. After reviewing the construction of projective spaces, I will discuss how to compute the disc superpotential of projective spaces explicitly.

5월 24일 (May 24th)

Speaker. 박태원
Title. Uniformization theorem for Riemann surfaces
Abstract. In this talk, we will discuss the Uniformization theorem for Riemann surfaces and its applications

5월 31일 (May 31st)

Speaker. 박지윤
Title. Circle actions on 4-dimensional almost complex manifolds with at most 5 fixed points
Abstract. Let the circle act on a compact almost complex manifold $M$ with a discrete fixed point set. At each fixed point, there are well-defined integers, called weights. Let us call the fixed point data of $M$ by a collection of multisets of weights at the fixed points. The fixed point data encodes information of the manifold such as the Chern numbers, the Euler number, the Hirzebruch $\chi_y$-genus, the signature, the Todd genus, etc. In this talk, we classify the fixed point data of $M$ if the dimension of $M$ is 4 and there are at most 5 fixed points, and construct an $S^1$-manifold that has the fixed point data, proving the existence of such a manifold. Using the fixed point data, we determine the Chern numbers, the Euler number, the Hirzebruch $\chi_y$-genus, and the signature of $M$.

6월 7일 (June 7th)

Speaker. 서민주
Title. Quandle coloring quivers of surface-links via marked graph diagrams
Abstract. In 2018, K. Cho and S. Nelson introduced the quandle coloring quiver of an oriented knot or link diagram, which is a quiver structure on the set of quandle colorings of a knot or link diagram. Also, they gave a new invariant, called the in-degree quandle quiver polynomial, from the quiver structure.

A surface-link is a smooth embedding of a surface in the 4-space $\Bbb R^4$ or $S^4$. A surface-link can be presented by a marked graph diagram with specific condition, and a marked graph diagram is a generalization of a knot or link diagram. In this talk, we consider quandle coloring quiver invariants for oriented surface-links, represented by marked graph diagrams. We provide example computations for all oriented surface-links with ch-index up to 10 for choices of quandles and endomorphisms.

부산대학교 기하학, 위상수학 세미나(PNU Geometry and Topology seminar)