김대환 (고등과학원)

- Title: Rigidity of weighted minimal space-like hypersurfaces in the n-dimensional Minkowski space

- Abstract: The prescribed mean curvature submanifolds have great physical importance both in the Riemannian geometry and in the Lorentzian geometry. We first focus on the translating soliton that is a special solution of the mean curvature flow and provide several examples of rotationally symmetric translating solitons in the 3-dimensional Minkowski space. To be specific, there are three types of rotations according to the directions of the rotation axes: time-like, space-like and light-like. Secondly, we show a particular inequality related to the mean curvature of a space-like hypersurface in the Minkowski space. Finally, we consider the result of Cheng and Yau, namely, the only complete maximal hypersurface is a hyperplane in the n-dimensional Minkowski space, to extend to the weighted minimal space-like hypersurface.

김준태 (고등과학원)

- Title: Points and lines in symplectic geometry

- Abstact: This is an ongoing study with Urs Frauenfelder. In 1973, Bachmann considered reflections as geometric entitles, namely as new concepts of points and lines. Based on his idea, we explore points and lines in symplectic geometry in terms of involutions. We explain why these interesting objects may help us imagine a symplectic K3 surface. 

신진우 (고등과학원)

- Title: Evolution of eigenvalues along curvature flows

- Abstract: Studying the eigenvalues of geometric operators is a very powerful tool for the understanding of Riemannian manifold. In this talk we introduce a method for studying these eigenvalues using curvature flows. In more detail, we discuss monotonicity formula of eigenvalues of various geometric operators under the Ricci flow and the Yamabe flow.

우창화 (부경대학교)     PDF file ↓

- Title: ON THE Q⊥-PARALLELISM OF RICCI TENSORS IN REAL HYPERSURFACES EMBEDDED IN COMPLEX GRASSMANNIANS OF RANK TWO

- Abstact: In this talk, the notions of Q⊥-parallel Ricci tensor is introduced on a real hypersurface M in complex Grassmannians of rank two. Moreover, by using classification theory, we can give a complete classification for real hypersurfaces M in complex Grassmannians of rank two.

윤석범 (고등과학원)

- Title: Adjoint Reidemeister torsions of hyperbolic 3-manifolds

- Abstract: For a compact 3-manifold with a torus boundary, Porti defined the adjoint Reidemeister torsion as a function on the character variety depending on a choice of a boundary curve. In this talk, I would like to introduce a conjectural identity of the adjoint torsion which is motivated by the 3d-3d correspondence. Also, we prove that the conjecture holds for all hyperbolic twist knots by using Jacobi's residue theorem.

장동훈 (부산대학교)

- Title: Fixed points of symplectic/Hamiltonian circle actions

- Abstract: In this talk, we study symplectic/Hamiltonian circle actions on compact symplectic manifolds, which have fixed points. First, we discuss the classification when the number of fixed points is small. Second, we discuss the classification in low dimensions. Third, we discuss when a symplectic circle action is Hamiltonian.

조윤형 (성균관대학교)

- Title: Hamiltonian action and symplectic rigidity

- Abstract: It is known that Hamiltonian circle actions can be classified in terms of fixed point data when the symplectic rigidity of reduced spaces is guaranteed. In this talk, we introduce the notion of symplectic rigidity of symplectic manifolds (of dimension two and four), and classify all monotone symplectic manifolds admitting semifree Hamitlonian circle actions in dimension six.

팽성훈 (건국대학교)

- Title: Total mass, isoperimetric inequality and integral norm of Ricci curvature

- Abstract: We obtain a relative volume comparison estimate with a bounded integral norm of Ricci curvature. From this comparison estimate, we obtain an upper bound of total mass for an asymptotically flat manifold. Also we obtain a global isoperimetric inequality for a manifolds with boundary.

홍한솔 (연세대학교)

- Title: Noncommutative resolutions via Lagrangian deformation

- Abstract: Given a Lagrangian in a symplectic manifold, one can consider its Maurer-Cartan deformation which produces a local chart of the mirror that encodes mirror geometry near this Lagrangian. Construction applies to the union of Lagrangian spheres in a certain open symplectic manifold, and produces noncommutative resolutions of well-known algebraic singularities, which are in the form of quivers with potentials. In this talk, I will examine such a construction in different dimensions, and explain how quivers can be used to effectively compare mirror geometries.