2월 27일
안병희 (IBS-CGP) - DGA invariant for Legendrian graphs
The Chekanov-Eliashberg DGA is an invariant of Legendrian knots consisting of a differential graded algebra(DGA) whose differential is determined by counting rigid, punctured holomorphic disks in the plane with exactly one positive puncture and with boundary on the Lagrangian projection of a knot $L$. We extend this invariant to Legendrian graphs. This is joint work with Youngjin Bae.
윤영호 (KIAS-CMC) - Hirzebruch-Milnor Class of hyperplane arrangements
The Hirzebruch class and the virtual one of varieties are global invariants. The difference, so called the Hirzebruch-Milnor Class of the varieties, gives information of singularities in the varieties. The Hirzebruch-Milnor Class can be calculated by using the Hodge spectra, which are important in the local study of singularities. I will introduce these concepts and calculate them for an important class of varieties, hyperplane arrangement, in this talk.
원준녕 (IBS-CGP) - Alpha, Beta, Gamma and Delta invariant for K-stability
I will introduce Alpha, Beta, Gamma and Delta invariant for K-stability and discuss about recent progresses on the invariants.
이재혁 (이화여대) - The symmetry groups of regular polyhedron as 4-polytopes
In this talks, we consider the symmetry groups of regular polyhedrons and their modelling in quaternions. We show the modellings are also 4-polytopes of D- and F-type reflections groups. For this purpose, we also introduce relations between Coxeter-Dynkin diagrams with multiple rings and multi laces and polytopes.
2월 28일
권명기 (서울대) - Contact structures on links of singularities
In this talk, we introduce contact structures on links of singularities. On the one hand, contact structures on the links serves as a strong constraint on singularities, and on the other hand, the links have provide interesting exotic contact structures. We discuss some recent results on this topic.
유화종 (IBS-CGP) - Rational torsion points on Jacobians of modular curves
We introduce the classification result of Mazur on the rational torsion points of elliptic curves over Q, which can be obtained by means of Eisenstein ideals. If time permits, we will discuss some generalization of Mazur's result on rational torsion points on Jacobians of modular curves.
신용주 (KIAS-CMC) - Minimal surfaces of general type with $p_{g}=0,\ K^{2}=7$ and nonbirational bicanonical map
Let $S$ be a minimal surface of general type with $p_{g}(S)=0,\ K_{S}^{2}=7$. Assume that the bicanonical map $\varphi$ of $S$ is nonbirational. Then we classify branch divisors of $\varphi$, and show that the surface $S$ is Inoue's surface when the branch divisor of $\varphi$ is $B_{1}+B_{2}$ such that $g(B_{1})=3,\ B_{1}^{2}=0$ and $g(B_{2})=2,\ B_{2}^{2}=-2$. This is a joint work with Yifan Chen.
김선화 (IBS-CGP) - Ideal triangulation of 3-manifolds and PSL(2,C)-representations.
We survey Ideal triangulations of a 3-manifold which are a kind of decomposition to simplices.
It is originated from hyperbolic geometry and nowadays play a central role to study representations of 3-manifolds and quantum invariants.
조용화 (KAIST) - Exceptional collections on algebraic surfaces
We introduce basic notions involving derived categories and exceptional collections, and discuss known examples for surfaces with $p_g=q=0$.