일시: 03월 26일 금요일 오후 2시 ~ 6시

장소: 129동 101호

제목: A survey on symplectic fillings and Milnor fibers of a normal complex surface singularity

연사: 박종일 (2시)

초록:

One of active research areas in symplectic 4-manifolds is to classify symplectic fillings of certain 3-manifolds equipped with a contact structure. Among them, people have long studied symplectic fillings of the link of a normal surface singularity. Note that the link of a normal surface singularity carries a canonical contact structure which is also known as the Milnor fillable contact structure. In this talk, I briefly review some basics on complex surface singularities, symplectic fillings and Milnor fibers of a normal surface singularity. Then I will explain some known results for minimal symplectic fillings of the link of quotient surface singularities and weighted homogeneous surface singularities with a canonical contact structure.

제목: The category $\mathcal{O}$ and the prefundamental representations

연사: 장일승 (4시)

초록:

Let $U_q(\mathfrak{g})$ be the quantum affine algebra of untwisted type. In this talk, I will briefly introduce the category $\mathcal{O}$ of representations of the Borel subalgebra of $U_q(\mathfrak{g})$ and the prefundamental representations in $\mathcal{O}$, which can be viewed as building blocks of $\mathcal{O}$. This talk may give a brief overview of the paper ``{\em Asymptotic representations and Drinfeld rational fractions}" by D. Hernandez and M. Jimbo (Compositio Math. {\bf 148} (2012), 1593--1623, doi:10.1112/S0010437X12000267)