2020 SNU-SSWU Joint Topology Workshop

Schedule

시간	01.30.(Thu)	01.31.(Fri)	02.01.(Sat)
07:30~09:00		Breakfast	Breakfast
09:30~10:30		Talk Prof. Yunhyung Cho	Talk Prof. YoungRock Kim
10:30~10:50		Coffee Break	Coffee Break
10:50~11:50		Talk Prof. Kyungbae Park	Talk Prof. JongHae Keum
12:00~13:30	Check in/Lunch	Lunch	Lunch
14:00~15:00	Talk Prof. Jongil Park	Talk Dr. Dongheon Choe
15:00~15:20	Coffee Break	Coffee Break
15:20~16:20	Talk Prof. YoungRock Kim	Talk Dr. Hakho Choi
16:20~16:40	Coffee Break	Coffee Break
16:40~17:40	Talk Prof. Jinseok Cho	Talk Dr. Ju A Lee
18:00~19:30	Dinner	Dinner

2020.01.30(Thu)~2020.02.01.(Sat)

발표제목: A rational blowdown surgery revisited
발표자: Prof. Jongil Park(SNU)
발표내용: Since gauge theory was introduced in 1982, people working on 4manifolds have developed various techniques and surgeries and they have obtained many fruitful and remarkable results on 4-manifolds in last 35 years. Among them, a rational blowdown surgery technique initially introduced by R. Fintushel and R. Stern and later generalized by J. Park turned out to be one of the simple but powerful techniques to construct a new family of 4-manifolds. In this talk, ﬁrst I’d like to brieﬂy review what we have obtained in 4-manifolds topology by using a rational blowdown surgery. And then I’ll also explain how to generalize a rational blowdown surgery technique in more general setting.

발표제목: Asymptotic expansion of the colored Jones polynomial and the twisted torsion
발표자: Prof. Jinseok Cho (BNUE)
발표내용: The generalized volume conjecture suggests that an asymptotic expansion of the colored Jones polynomial gives many interesting invariants of knots including the complex volume and the Ray-Singer torsion. The optimistic limit of the colored Jones polynomial, a mathematical formulation of the physicist's method to find the the complex volume in the asymptotic expansion, suggested sort of twisted version of the volume conjecture. It means the optimitic limit determines not only the complex volume of a knot but also the volumes of the representations of the knot group. On the other hand, Dr. Byungmin Kang, a young physicist now in KIAS, suggested a physicial method to detect the twisted torsion in the asymptotic expansion when he was undergraduate student in SNU. In this talk, we will explain Dr. Kang's method and the importance of formulating his method mathematically.

발표제목: Hamiltonian circle actions and symplectic rigidity
발표자: Prof. Yunhyung Cho(SKKU)
발표내용: It is known that symplectic rigidity of reduced spaces of a Hamiltonian \(S^1\)-manifold guarantees that the fixed point data is a complete invariant for the action. In this talk, we explain the notion of symplectic rigidity and some results in dimension four. Using this, we classify all six-dimensional closed monotone semifree Hamiltonian \(S^1\)-manifolds.

발표제목: On generalizations of the knot surgery on 4-manifolds
발표자: Prof. Kyungbae Park(SNU)
발표내용: The Fintushel-Stern knot surgery is a useful cut-and-paste operation to produce an infinite family of smooth 4-manifolds that are homeomorphic each other but mutually non-diffeomorphic. In this talk, we introduce some generalizations of the knot surgery by using knots in homology spheres and self-concordances of knots. We also discuss some applications of them.

발표제목: Adaptive Basis Function Models
발표자: Dr. Dongheon Choe(NIMS)
발표내용: In this talk, we introduce adaptive basis function model to solve regression and classification problems in machine learning. Specifically, we will talk about decision tree algorithm. To improve performance and make up for the cons of single tree model, we also consider some of ensemble models(Bagging, Boosting). If time allows, we also explain some of results of applying the algorithms.

발표제목: A Lefschetz fibration on rational homology disk smoothings of weighted homogeneous singularities
발표자: Dr. Hakho Choi (KIAS)
발표내용: In this talk, we consider a genus-\(1\) Lefschetz fibration on rational homology disk smoothing of weighted homogeneous surface singularities whose dual graph of the minimal resolution have a bad vertex. The global monodromy of the Lefschetz fibration is obtained by applying lantern substitutions from the global monodromy of the minimal resolution after introducing appropriate cancelling pair so that induced contact structure on the boundary is the Milnor fillable contact structure.

발표제목: The Geography problem of fibered 4 manifolds
발표자: Dr. Ju A Lee(SNU)
발표내용: The geography problem of fibered 4 manifolds asks the possible signatureand the Euler characteristic of a smooth closed oriented 4 manifold in order to support a preassigned additional fibration structure such as a surface bundle over a surface, a Kodaira fibration, of a Lefschetz fibration. For the last case, it is closely related to the minimal number of singular fibers of Lefschetz fibrations. In this talk, some known results and open problems around this field will be discussed.

발표제목: The Cartwright-Steger surface
발표자: Prof. JongHae Keum (KIAS)
발표내용: The Cartwright-Steger surface is a surface of general type with \(p_g=q=1\) which is a complex ball-quotient by an arithmetic subgroup of \(PU(2,1)\). We prove that the bicanonical map of the Cartwright-Steger surface is an embedding. We also discuss two minimal surfaces of general type, both covered by the Cartwright-Steger surface. One has \(K^2=2, p_g=1, \pi_1=\{1\}\) and the other has \(K^2=1, p_g=0, \pi_1=\mathbb{Z}/2\mathbb{Z}\).