1:30 최영필 (인하대)

Global existence of weak solutions for Navier-Stokes-BGK system

2:30 문상혁 (카이스트)

A pattern formation from an elliptic Neumann system with a large mixed interaction

3:30 곽철광 (Pontificia Universidad Católica de Chile)

Well-posedness issues of some dispersive equations under the periodic boundary condition 

4:30 황경하 (영남대)

Existence and symmetric properties of solutions to the Neumann problem of Hardy-Sobolev equation with Hardy potential

15 November(Thursday)

14:00           Opening address

14:20-15:10 Lee, Ji-Oon : Weak detection of signal in the spiked Wigner model

15:20-16:10 Jin, Tianling : On the isoperimetric ratio over scalar-flat conformal classes

16:20-17:10 Sun, Rongfeng : Moment Asymptotics for the (2+1)-dimensional Directed Polymer in the Critical Window

16 November(Friday)

09:30-10:20 Li, Dong : Existence of nontrivial steady states for nonlocal models

10:30-11:20 An, Xinliang : Emergence of Black Holes in General Relativity

11:30-12:20 Jung, Paul : Levy-Khintchine Random Matrices

17 November(Saturday)

09:30-10:20 Yu, Shih-Hsien : Green's functions and Well-posedness of Compressible Navier-Stokes equation

10:30-11:20 Kwon, Soonsik : Scattering of the defocusing generalized Benjamin-Ono equations.

11:30-12:20 Bao, Zhigang : Local single ring theorem on optimal scale

 You can find the program with abstracts via the following link: 

Intensive Lecures on Semi-orthogonal decomposition of a derived category of an algebraic variety

Prof. Yujiro Kawamata (University of Tokyo)

16:00-17:15 in Jan. 16, 18, 22, 24,   Room 1401 

Abstarct.

I will start with the definition of a derived category of an algebraic variety. The derived category contains much essential information of the algebraic variety.

Then I consider a decomposition of the derived category into simpler components called a semi-orthogonal decomposition (SOD) and explain examples.

I will explain SOD’s related to the minimal model program in birational geometry. Some SOD’s are obtained by looking at so-called exceptional objects

or their deformed variants called relative exceptional objects. I will explain examples of SOD’s for some singular surfaces.

References

Schedule
14:00-14:50 Vitaly Moroz (Swansea University)
Ground-states of a Schrödinger-Poisson-Slater type equation Abstract: Schrödinger-Poisson-Slater equation is a nonlinear modification of Schrödinger equation with a repulsive nonlocal Coulomb potential and a local nonlinearity. We develop a variational framework for a class of Schrödinger-Poisson-Slater type equations and discuss existence, positivity and radial symmetry of ground state solutions

15:00-15:50 Jongmin Han (Kyung Hee University)
On the self-dual Einstein-Maxwell-Higgs equation on compact surfaces
Abstract: In this talk, we discuss recent progress on the study of the self-dual Einstein-Maxwell-Higgs equation on compact surfaces. We give a brief background on the equation and known results on the plane. The main topics are two theorems on the existence of topological and nontopological type solutions as the coupling parameter tends to be zero.

16:00-16:50 Jinmyoung Seok (Kyonggi University)
Existence criterion for standing waves to pseudo-relativistic nonlinear Schrodinger equations

Abstract : The pseudo-relativistic Schrodinger operator is defined by the square root of the elliptic operator , that arises when we consider a relativistic versions of quantum mechanics. Especially, it is used for describing spin zero particles as is Klein-Gordon operator. In this talk, I will present an almost complete existence criterion for standing waves to the pseudo-relativistic nonlinear Schrodinger equations, which exhibit an intermediate features between nonrelativistic nonlinear Schrodinger equations and nonlinear half wave equations.
We will see that this criterion depends on the quantity , not only on n and nonlinear exponent p, where  denotes the frequency of standing wave . Due to the supercriticality of the equation, the standard variational method does not seem to work although the equation enjoys a variational structure. Instead, we approach by adopting the contraction mapping principle. It turns out that a uniform L^p estimate for the pseudo-relativistic operator plays a crucial role for obtaining the existence of solutions in the full range of supercritical exponent p. This shall be obtained by the Hörmander-Mikhlin Theorem based on a symbol analysis of the pseudo-relativistic operator.

Invited Speakers

Schedule

Feb. 11, 2019, Monday

1:30pm-2:20pm Jeong Han Kim: Entropy and sorting
2:20pm-3:10pm Cory T. Palmer: Generalized Turán problems – Berge hypergraphs
Coffee Break
4:00pm-4:50pm Martin Balko: Ramsey numbers of edge-ordered graphs
4:50pm-5:40pm Dong Yeap Kang: T.B.A.
Banquet

Feb. 12, 2019, Tuesday

9:30am-10:20am Boram Park: Sum-free set problem on integers
Coffee Break
11:00am-11:50am Dániel Gerbner: Generalized Turán problems – counting subgraphs
Lunch

We plan to provide meals to all participants and provide a room at a near-by hotel for invited speakers and selected participants. Please register in the following form below by January 28, Monday; please register early if you want to receive the support for the accommodation.

March 7

15:00  Conserved   energies  for NLS, KdV and Gross-     

           Pitaevskii (Herbert Koch)

16:10 TBA (Yonggeun Cho)

March 8

9:30 Conserved   energies  for NLS, KdV and Gross-    

        Pitaevskii (Herbert Koch)

11:00 Scattering of the  defocusing generalized

          Benjamin-Ono equations (Kiyhun Kim)

14:00 Conserved   energies  for NLS, KdV and Gross-

          Pitaevskii. (Herbert Koch)
15:30 Ill-posedness of the Hall-MHD equations without

          resistivity (In-Jee Jung)

16:40 Well-posedness of the Hall-MHD equations

          without resistivity (Sung-Jin Oh)

14:00 ~ 14:30 최우성 박사 (한국전력공사)

PHM(Prognostics and Health Management) 분야에서의 베이지안 및 딥러닝 활용 사례

14:45 ~ 15:15 김재덕 박사 (삼성전자)

Towards Practicality: Theorems should not limit practicality

15:15 ~ 16:00 자유토론 및 티타임

16:00 ~ 16:30 유용균 박사 (한국원자력연구원)

최적설계 분야의 딥러닝 응용

16:45 ~ 17:15 조현제 박사 (삼성전자)

기업 관점에서의 자동화된 데이터 분석 시스템

17:15 ~ 18:00 자유토론 및 티타임

시간 : 2019년 6월 24일 -28일 오후 3-5시

강연 내용 :

1. 평균 곡률 흐름의 소개 : 역사와 의의 소개, 특이점에 관한 주요 연구의 흐름 논의.기하학적 측도 이론/미분기하/조화 해석/함수 해석/편미분방정식/최소-최대 이론/동역학계 등이 어떻게 활용되는지 간략하게 소개.

2. 평균 곡률 흐름의 편미분방정식 : 평균 곡률 흐름이 편미분방정식 유도. 평균 곡률 흐름의 닫힌 자기동형해의 미분방정식 소개

3. 볼록하고 닫힌 평균 곡률 흐름의 특이점 : Huisken density 소개, 제 1형 특이점을 분석. Stampacchia(de Giorgi) iteration과 제 2형 특이점의 분석 소개.

4. 기울기 흐름으로서의 평균 곡률 흐름 : 평균 곡률 흐름이 Huisken density의 기울기 흐름임을 설명. 최소 곡면의 고립된 특이점과 기울기 흐름의 관계를 소개, 관련 특이점 연구들에 대해 논의. Huisken density를 이용한 엔트로피를 정의하고, 닫힌 곡면의 최소 엔트로피에 대해 논의.

5. 평균 곡률 흐름의 고대 해 : 고대 해, 접촉 해, 극한 해 등을 정의하고, 특이점 연구에의 응용을 소개. 닫힌 리찌 흐름과 평균 곡률 흐름의 붕괴를 정의하고, 붕괴하는 않는 해의 특이점에 대해 논의. 비붕괴성이나 작은 엔트로피가 극한 해의 점근 해를 결정함을 보이고, 기울기 흐름으로서 점근 해가 고정 됨을 논의. 결정된 점근 해 위에서 간단한 조화 해석학과 동역학계를 이용하여 극한 해를 분석하여 분류.

References

0. Xi-Ping Zhu, Lecture Notes on Mean Curvature Flows, AMS/IP

1. T. Colding and W. Minicozzi. Generic mean curvature flow I; generic singularities. Ann. of Math. (2), 175(2):755{833, 2012.

2. T. Colding and W. Minicozzi. Uniqueness of blowups and Lojasiewicz inequalities.

Ann. of Math. (2), 182(1):221{285, 2015.

3. J. Bernstein and L. Wang. A topological property of asymptotically conical

self-shrinkers of small entropy. Duke Math. J 166(3):403{435, 2017.

4. B. White. The size of the singular set in mean curvature flow of mean convex sets. J. Amer. Math. Soc. 13(3):665{695, 2000.

5. B. White. A local regularity theorem for mean curvature flow. Ann. of Math. (2), 161(3):1487-1519, 2005

6. X. Wang. Convex solutions to the mean curvature flow. Ann. of Math. (2), 173(3):1185{1239, 2011

7. S. Angenent, P. Daskalopoulos, and N. Sesum. Unique asymptotics of ancient convex mean curvature flow solutions. arXiv:1503.01178, 2015

8. S. Brendle and K. Choi. Uniqueness of convex ancient solutions to mean curvature flow in R3. arXiv:1711.00823v2, 2017

9. K. Choi, R. Haslhofer, and O. Hershkovits, Ancient low entropy flows, mean convex neighborhoods, and uniqueness, arXiv:1810.08467, 2018.

10. O. Chodosh and F. Schulze, Uniqueness of asymptotically conical tangent flows, arXiv:1901.06369, 2019.

11. J. Bernstein and L. Wang, A sharp lower bound for the entropy of closed hypersurfaces up to dimension 6, Invent. Math. 206

12. S. Brendle, Embedded self-similar shrinkers of genus 0, Ann. of Math. (2) 183 (2016), no. 2, 715–728.

13. L. Wang, Uniqueness of self-similar shrinkers with asymptotically conical ends, J. Amer. Math. Soc. 27 (2014), 613-638.

14. L. Wang, Asymptotic structure of self-shrinkers, https://arxiv.org/abs/1610.04904 (2016).

Schedule

July 22 Monday

10:00-11:00 Introduction

11:00-12:00 Open Problems

July 23 Tuesday

11:00-10:30 Stefan Kratsch, Humboldt-Universität zu Berlin, Germany
Elimination Distances, Blocking Sets, and Kernels for Vertex Cover

10:45-11:15 Benjamin Bergougnoux, University Clermont Auvergne, France
More applications of the d-neighbor equivalence

11:30-12:00 Yixin Cao, Hong Kong Polytechnic University, China
Enumerating Maximal Induced Subgraphs

July 24 Wednesday

July 25 Thursday

10:00-11:00 Nick Brettell, Eindhoven University of Technology, Netherlands
Recent work on characterising matroids representable over finite fields

11:30-12:00 Mamadou M. Kanté, University Clermont Auvergne, France
On recognising k-letter graphs

July 26 Friday

10:00-11:00 O-joung Kwon (권오정), Incheon National University, Korea
The grid theorem for vertex-minors

11:00-12:00 Progress Report

July 29 Monday

10:00-11:00 Archontia Giannopoulou, National and Kapodistrian University of Athens, Greece
The directed flat wall theorem

11:30-12:00 Eunjung Kim (김은정), LAMSADE-CNRS, France
Subcubic even-hole-free graphs have a constant treewidth

July 30 Tuesday

10:00-11:00 Pierre Aboulker, ENS Ulm, France
Generalizations of the geometric de Bruijn Erdős Theorem

11:30-12:00 Michael Dobbins, Binghamton University, USA
Barycenters of points in polytope skeleta

July 31 Wednesday

10:00-11:00 Magnus Wahlström, Royal Holloway, University of London, UK
T.B.A.

11:30-12:00 Édouard Bonnet, ENS Lyon, France
The FPT/W[1]-hard dichotomy of Max Independent Set in H-free graphs

August 1 Thursday

10:00-11:00 Euiwoong Lee (이의웅), NYU, USA
 Losing treewidth by separating subsets

11:30-12:00 Sang-il Oum (엄상일), IBS Discrete Mathematics Group and KAIST, Korea
Branch-depth: Generalizing tree-depth of graphs

August 2 Friday

10:00-11:00 Dabeen Lee (이다빈), IBS Discrete Mathematics Group, Korea
t-perfect graphs and the stable set problem

11:00-12:00 Progress Report

August 5-9: Free Discussions / Research Collaborations / Progress Report
Tea time: Every weekday 3:30pm

Abstracts

July 23 Tuesday

Stefan Kratsch, Elimination Distances, Blocking Sets, and Kernels for Vertex Cover

The Vertex Cover problem plays an essential role in the study of polynomial kernelization in parameterized complexity, i.e., the study of provable and efficient preprocessing for NP-hard problems. Motivated by the great variety of positive and negative results for kernelization for Vertex Cover subject to different parameters and graph classes, we seek to unify and generalize them using so-called blocking sets, which have played implicit and explicit roles in many results. We show that in the most-studied setting, parameterized by the size of a deletion set to a specified graph class C, bounded minimal blocking set size is necessary but not sufficient to get a polynomial kernelization. Under mild technical assumptions, bounded minimal blocking set size is showed to allow an essentially tight efficient reduction in the number of connected components. We then determine the exact maximum size of minimal blocking sets for graphs of bounded elimination distance to any hereditary class C, including the case of graphs of bounded treedepth. We get similar but not tight bounds for certain non-hereditary classes C, including the class CLP of graphs where integral and fractional vertex cover size coincide. These bounds allow us to derive polynomial kernels for Vertex Cover parameterized by the size of a deletion set to graphs of bounded elimination distance to, e.g., forest, bipartite, or CLP graphs.

Benjamin Bergougnoux, More applications of the d-neighbor equivalence

In this talk, I will present a framework which gives efficient algorithms for several connectivity problems such as Connected Dominating Set, Node Weighted Steiner Tree, Maximum Induced Tree, Longest Induced Path, and Feedback Vertex Set. For all these problems, we obtain efficient algorithms parameterized respectively by tree-width, clique-width, Q-rank-width, rank-width and maximum induced matching width. Our approach simplifies and unifies the known algorithms for each of the parameters and match asymptotically also the running time of the best algorithms for Vertex Cover and Dominating Set. Our framework is based on the d-neighbor equivalence defined in [Bui-Xuan, Telle and Vatshelle, TCS 2013]. The results we obtain highlight the importance and the generalizing power of this equivalence relation on width measures. We also prove that this equivalence relation could be useful for Max Cut: a W[1]-hard problem parameterized by clique-width.

Paper available on HAL : https://hal.archives-ouvertes.fr/hal-01799573

Yixin Cao, Enumerating Maximal Induced Subgraphs

We study efficient algorithms for the maximal induced subgraphs problem: Given a graph on nvertices, enumerate all its maximal induced subgraphs that belong to a particular hereditary graph class. While its optimization version, known as the vertex deletion problem in literature, has been intensively studied, algorithms for the enumeration version exist only for few simple graph classes, e.g., independent sets and cliques. Enumeration algorithms are mainly categorized in three complexity classes, polynomial total time (polynomial on n and the total number of solutions), incremental polynomial time (for all s, the time to output the first s solutions is polynomial on n and s), and polynomial delay (for all s, the time to output the first s solutions is polynomial on n and linear on s). We first show that the maximal induced subgraphs problem can be solved in polynomial total time if and only if it can be solved in incremental polynomial time. We then propose general approaches to develop polynomial-delay algorithms and incremental-polynomial-time algorithms for the problem. They enable us to develop simple algorithms to solve the problem with polynomial delay for a large number of graph classes, and in incremental polynomial time for interval graphs, chordal graphs as well as two of its well-studied subclasses, and all graph classes with finite forbidden induced subgraphs.

July 25 Thursday

Nick Brettell, Recent work on characterising matroids representable over finite fields

Characterising when a matroid is representable over a certain field or set of fields is one of the oldest problems in matroid theory, dating back to Whitney’s 1935 paper. In this talk, I will discuss some of the more recent work in this area, with a focus on work I have been involved with towards characterising matroids representable over all fields of size at least four.

Mamadou M. Kanté, On recognising k-letter graphs

k-letter graphs are a subclass of graphs of linear clique-width k, but are well-quasi-ordered by the induced subgraph ordering. I present a simple FPT algorithm for recognising k-letter graphs and also an upper bound on the size of minimal obstructions. The characterisation is based on a simple observation allowing an MSOL-definability. (joint work with V. Lozin)

July 26 Friday

O-joung Kwon (권오정), The grid theorem for vertex-minors

We prove that, for a circle graph H, every graph with sufficiently large rank-width contains a vertex-minor isomorphic to H. This is joint work with Jim Geelen, Rose McCarty, and Paul Wollan.

July 29 Monday

Archontia Giannopoulou, The directed flat wall theorem

At the core of the Robertson-Seymour theory of Graph Minors lies a powerful structure theorem which captures, for any fixed graph H, the common structural features of all the graphs not containing Has a minor [Neil Robertson, Paul D. Seymour: Graph Minors. XVI. Excluding a non-planar graph. J. Comb. Theory, Ser. B 89(1): 43-76 (2003)]. An important step towards this structure theorem is the Flat Wall Theorem [Neil Robertson, Paul D. Seymour: Graph Minors .XIII. The Disjoint Paths Problem. J. Comb. Theory, Ser. B 63(1): 65-110 (1995)], which has a lot of algorithmic applications (for example, the minor-testing and the disjoint paths problem with fixed number terminals).
In this paper, we prove the directed analogue of this Flat Wall Theorem. Our result builds on the recent Directed Grid Theorem by two of the authors (Kawarabayashi and Kreutzer), and we hope that this is an important and significant step toward the directed structure theorem, as with the case for the undirected graph for the graph minor project.
Joint work with Ken-ichi Kawarabayashi, Stephan Kreutzer, and O-joung Kwon.

Eunjung Kim (김은정), Subcubic even-hole-free graphs have a constant treewidth

It is known that even-hole-free graphs can have arbitrarily large rankwidth, but all known constructions have many high-degree vertices. It has been believed in the structural graph theory community that the rankwidth shall be bounded if the maximum degree is bounded. We prove that there exists a universal constant c such that every even-hole-free graph of degree at most three has treewidth at most c. As a by-product of the proof, we also show that there exists a function f such that for any r, Kr-minor-free and even-hole-free graph has treewidth at most f(r); this extends the result of Silva et. al. (Discrete Applied Mathematics 2010) addressing the case of planar graphs.
This is a joint work with Pierre Aboulker and Isolde Adler.

July 30 Tuesday

Pierre Aboulker, Generalizations of the geometric de Bruijn Erdős Theorem

A classic Theorem of de Bruijn and Erdős states that every noncollinear set of n points in the plane determines at least n distinct lines. The line L(u,v)determined by two points u, v in the plane consists of all points p such that

With this definition of line L(uv) in an arbitrary metric space (V,dist), Chen and Chvátal conjectured that every metric space on n points, where n is at least 2, has at least n distinct lines or a line that consists of all n points. The talk will survey results on and around this conjecture.

Michael Dobbins, Barycenters of points in polytope skeleta

In this talk I will classify the n-tuples of dimensions such that any target point in any d-polytope is the barycenter of points in faces of the prescribed dimensions. Specifically, for a (nk+r)-polytope and target point, we can always find r points in faces of dimension k+1, and n−r points in faces of dimension k, that have their barycenter at the given target. This is tight in the sense that we cannot require even one of the points to be in a face of dimension less than k, and we cannot require more than n−r of the points to be in faces of dimension k. This is joint work with Florian Frick.

July 31 Wednesday

Magnus Wahlström, T.B.A.

Édouard Bonnet, The FPT/W[1]-hard dichotomy of Max Independent Set in H-free graphs

Maximum Independent Set (MIS) is in general graphs the paradigmatic W[1]-hard problem. In stark contrast, polynomial-time algorithms are known when the inputs are restricted to structured graph classes such as, for instance, perfect graphs (which includes bipartite graphs, chordal graphs, co-graphs, etc.) or claw-free graphs. In this talk, we introduce some variants of co-graphs with “parameterized noise”, that is, graphs that can be turned into disjoint unions or complete sums by the removal of a certain number of vertices and the edition of a certain number of edges per incident vertex, both controlled by the parameter. We give a series of FPT Turing-reductions on these classes and use them to make some progress on the parameterized complexity of MIS in H-free graphs. We present the current state of the (randomized) FPT vs W[1]-hard dichotomy of MIS in H-free graphs. We then show that for every fixed t≥1, MIS is FPT in P(1,t,t,t)-free graphs, where P(1,t,t,t) is the graph obtained by substituting all the vertices of a four-vertex path but one end of the path by cliques of size t. In particular, this helped finishing the classification when H has at most five vertices.
This follows joint works with Nicolas Bousquet, Pierre Charbit, Stéphan Thomassé, and Rémi Watrigant.

August 1 Thursday

Euiwoong Lee (이의웅), Losing treewidth by separating subsets

We study the problem of deleting the smallest set S of vertices (resp. edges) from a given graph G such that the induced subgraph (resp. subgraph) G∖Sbelongs to some class of graphs H. When graphs in H have treewidth bounded by t, we construct a framework for both vertex and edge deletion versions where approximation algorithms for these problems can be obtained from approximation algorithms for natural graph partitioning problems called k-Subset Vertex Separator and k-Subset Edge Separator.
For the vertex deletion, our framework, combined with the previous best result for k-Subset Vertex Separator, yields improved approximation ratios for fundamental problems such as k-Treewidth Vertex Deletion and Planar-F Vertex Deletion. For the edge deletion, we give improved approximation algorithms for k-Subset Edge Separator and their applications to various problems in bounded-degree graphs.
Joint work with Anupam Gupta, Jason Li, Pasin Manurangsi, and Michal Wlodarczyk.

Sang-il Oum (엄상일), Branch-depth: Generalizing tree-depth of graphs

We present a concept called the branch-depth of a connectivity function, that generalizes the tree-depth of graphs. Then we prove two theorems showing that this concept aligns closely with the notions of tree-depth and shrub-depth of graphs as follows. For a graph G=(V,E) and a subset A of E we let λG(A)be the number of vertices incident with an edge in Aand an edge in E∖A. For a subset X of V, let ρG(X)be the rank of the adjacency matrix between  https://dimag.ibs.re.kr/event/2019-ibs-summer-research-program/

    (http://www.hbaik.org/gt-fair-2019)

    (http://www.hbaik.org/kaix-summer-school-2019) 

    첨부된 파일 참고 바랍니다. (Please refer to the file attached.)

일시: 7월 30일 오후 2시~5시30분

장소: 자연과학동(E6-1) 1410호

Session A (Chair: Prof. Ganguk Hwang)

14:00 ~ 14:20  - Optimal sampling and clustering in the stochastic block model
                          Prof. Se Young Yun (KAIST)

14:20 ~ 14:40  - Local stability problem for mu-Wasserstein GAN
                          with simple gradient penalty
                          Prof. Hyung Ju Hwang (POSTECH)

14:40 ~ 15:00  - Accelerated First-order Methods for Large-scale Optimization
                          Prof. Donghwan Kim (KAIST)

15:00 ~ 15:40 Coffee Break

Session B (Chair: Prof. Hyung Ju Hwang)

15:40 ~ 16:00  - Solving partial differential equations with
                          many parameters using deep learning
                          Prof. Minseok Choi (POSTECH)

16:00 ~ 16:20  - Gaussian Process Regression and Its Applications
                          Prof. Ganguk Hwang (KAIST)

16:20 ~ 17:00  - Discussion

17:30 ~ 19:30 Dinner 

Invited Speakers

Schedule

August 12, Monday

11:00am-12:00pm Jaehoon Kim (김재훈): Tree decompositions of graphs without large bipartite holes

12:00pm-1:30pm Lunch

1:30pm-2:30pm Abhishek Methuku: Bipartite Turán problems for ordered graphs

3:00pm-4:00pm Péter Pál Pach: On some applications of graph theory to number theoretic problems

4:30pm-5:30pm Hong Liu: Recent advance in Ramsey-Turán theory

6:00pm-8:00pm Banquet

Invited Speakers

Sunday, August 25, 2019

Monday, August 26, 2019 

Tuesday, August 27, 2019 

Wednesday, August 28, 2019 

Thursday, August 29, 2019 

Friday, August 30, 2019