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자연과학동(E6) Room 1401
1월 16일(수)-1월 24일(목), Intensive Lectures on Algebraic Geometry by Prof. Y. Kawamata

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

The purpose of the conference is to help promoting the academic exchange and the friendship among researchers of three East Asian countries in the area of knot theory and related topics and encouraging graduate students of the three countries to study in this fascinating area of mathematics.

*https://sites.google.com/site/knotschool2018/index*

KSIAM 2018 Spring Conference

SCHEDULE

▶ Opening Ceremony : May 25, 13:00-13:20 [E11 203]

- Jung, Eunok (President of KSIAM)

- Kim, Sang Kyu (Dean, College of Natural Sciences, KAIST)

▶ Invited Talks

○ Sung, Hyung Jin (KAIST)

- Title : Logarithmic Behavior of Wall-attached Structures in a Turbulent Boundary Layer

- May 25, 13:20-14:10 [E11 203]

○ Hiroshi Kokubu (Kyoto University)

- Title : Computer-assisted approach to the global dynamics of multi-parameter systems

- May 25, 16:00-16:50 [E11 203]

○ Ha, Seung Yeal (Seoul National University)

- Title : A panoramic view of the collective dynamics

- May 26, 9:00-9:50 [E11 203]

▶ Poster Session : May 26, 10:00-10:40 [E11 1st floor]

▶ KSIAM Young Researcher Paper Award： May 25, 17:00-17:25 [E11 203]

▶ KSIAM Journal Excellent Article Award： May 25, 17:25-17:50 [E11 203]

▶ Special Sessions

○ Applications of Computational Structures

○ CJK-SIAM Joint Special Session: Mathematical Material Science I

○ CJK-SIAM Joint Special Session: Cryptology

○ Mathematical Biology I: Data analysis

○ MathWorks Special Session

○ Engineering Optimization Using CFD

○ CJK-SIAM Joint Special Session: Mathematical Material Science II

○ Applied Algebra and Geometry

○ Mathematical Biology II: Population dynamics

○ Stochastic Modeling and Analysis

○ Mathematical Modeling and Algorithms in Finance

- May 25, 14:20-15:40 [E11 203]

- May 25, 14:20-15:40 [E11 206]

- May 25, 14:20-15:40 [E11 207]

- May 25, 14:20-15:40 [E11 208]

- May 25, 14:20-15:40 [E11 209]

- May 26, 10:40-12:00 [E11 203]

- May 26, 10:40-12:00 [E11 206]

- May 26, 10:40-12:00 [E11 207]

- May 26, 10:40-12:00 [E11 208]

- May 26, 13:00-14:20 [E11 207]

- May 26, 13:00-14:20 [E11 209]

▶ General Sessions

○ General Session Ⅰ

○ General Session Ⅱ

○ General Session Ⅲ

○ General Session Ⅳ

- May 26, 10:40-12:00 [E11 209]

- May 26, 13:00-14:20 [E11 203]

- May 26, 13:00-14:20 [E11 206]

- May 26, 13:00-14:20 [E11 208]

▶ Welcome Reception : May 25, 18:00-21:00 [Faculty Club]

주 관 : 한국산업응용수학회, 이화여자대학교 수리과학연구소

후 원 : KAIST 자연과학대학, MathWorks, 연세대학교 응용해석 및 계산센터

*https://www.ksiam.org/conference/30558827-2b97-4be3-872e-873ee263c85b/welcome*

### Organizers

Sang-il Oum

***** Intensive lecture series *****

DATE: June 25 - 29

TIME: 10:30AM-12PM, 2:30PM-4PM

PLACE: E6-1, ROOM 3434

SPEAKER: Jaehoon Kim (김재훈), School of Mathematics, Birmingham

University, Birmingham, UK

TITLE: A course in graph embedding

http://mathsci.kaist.ac.kr/~sangil/seminar/2018-06-25/

In this lecture, we aim to learn several techniques to find sufficient

conditions on a dense graph G to contain a sparse graph H as a

subgraph.

Tentative plan for the course (June 25, 26, 27, 28, 29)

Lecture 1 : Basic probabilistic methods

Lecture 2 : Extremal number of graphs

Lecture 3 : Extremal number of even cycles

Lecture 4 : Dependent random choice

Lecture 5 : The regularity lemma and its applications

Lecture 6 : Embedding large graphs

Lecture 7 : The blow-up lemma and its applications I

Lecture 8 : The blow-up lemma and its applications II

Lecture 9 : The absorbing method I

Lecture 10 : The absorbing method II

Other upcoming events:

1. June 26: Jinyoung Park, "Coloring hypercube"

2. July 18-20: Ron Aharoni, "Lectures on topological methods in combinatorics"

*http://mathsci.kaist.ac.kr/~sangil/seminar/2018-06-25/*

*http://www.hbaik.org/kaix-summer-school-2018*

Main lecturers (3 hours)

Vera Mikyoung Hur (UIUC)

Juhi Jang (Univ. Southern California)

Kenji Nakanishi (RIMS)

1 hour lecturers

Myeongju Chae (Hankyong National Univ.)

Yonggeun Cho (Chun Buk National Univ.)

Tatsuo Iguchi (Keio Univ.)

Donghyun Lee (Postech)

*http://mathsci.kaist.ac.kr/~soonsikk/participating-school/2018-kaix-summer-school-in-pde/*

‣ Speaker (강연자 성명): 김순영(서강대), 김호성(KIAS), 이광우(GIST), 이철규(KIAS), 정기룡(경북대), 정승조(KIAS)

‣ Organizers: 김인균(SNU), 신용주(KAIST), 윤영호(SNU)

‣ 학회 Homepage: https://sites.google.com/view/agin1n2d

*https://sites.google.com/view/agin1n2d*

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자연과학동(E6-1) Room 4415
7/10(화) ~7/12(목) Intensive Lectures on Moduli of differentials

************Intensive Lectures****************

15:00-16:00 in July 10 (Tue)

16:30-17:30 in July 10 (Tue)

15:00-16:00 in July 11 (Wed)

16:30-17:30 in July 11 (Wed)

10:30-11:30 in July 12 (Thur)

PLACE: E6-1, ROOM 4415

SPEAKER: Dawei Chen (Boston College)

TITLE: Moduli of differentials

Abstract:

An Abelian differential defines a flat metric such that the underlying Riemann surface can be realized as a polygon whose edges are pairwise identified via translation. Varying the shape of such polygons induces a GL(2,R)-action on the moduli space of Abelian differentials, called Teichmueller dynamics, whose study has provided fascinating results and opened new avenues to many fields in mathematics. In the first lecture I will give an accessible introduction to this subject, with a focus on its connections to billiard dynamics, enumerative geometry, and arithmetic geometry. In the remaining lectures I will explain how to use techniques in algebraic geometry to study various problems in Teichmueller dynamics, including compactification, birational geometry, cycle class computation, etc. A number of recent developments and open problems will be mentioned.

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Room 3434, Bldg. E6-1
(Intensive Lecture Series) Ron Aharoni, Lectures on topological methods in combinatorics

### Organizers

Andreas Holmsen

Department of Mathematics, Technion, Israel

The lectures will give an introduction to the application of topological methods in matching theory, graph theory, and combinatorics.

Topics that will be covered:

– A topological extension of Hall’s theorem

– combinatorial applications of the nerve theorem

– d-Leray complexes and rainbow matchings

– Matroid complexes and applications

– Open problems

*http://mathsci.kaist.ac.kr/~sangil/seminar/2018-07-18/*

### Organizers

Paul Jung, Ji Oon Lee

KAIST Summer School in Probability 2018 will be held as follows:

Dates: July 31-Aug 3

Place: Industrial Engineering and Management Building (E2) Room 1225,

KAIST, Daejeon, Korea

Registration is now closed

Principal lecturers and lecture topics

Oren Louidor (Technion)

Topic: Extreme and large values of the discrete Gaussian free field

Tadahisa Funaki (U. of Tokyo and Waseda Univ.).

Topic: Hydrodynamic limit for exclusion processes

*https://sites.google.com/view/kaistsummerschoolinprobability/2018*

### Organizers

Refer to

https://sites.google.com/site/llc2018kk/

Speakers:Kwangho Choiy (Southern Illinois University), Yeansu Kim (Chonnam National University)

*https://sites.google.com/site/llc2018kk/*

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산업경영학동(E2) Room 3221
The 6 th KAIST-Fudan Workshop on Analysis and Applied Mathematics

### Organizers

Prof. Yongnam Lee (KAIST), Prof. Ganguk Hwang (KAIST)

Variational Shape Prior Segmentation With an Initial Curve Based on Image Registration Technique Prof. Chang-Ock Lee (KAIST) |

The constructive role of randomly temporal connections in complex dynamical networks Prof. Wei Lin (Fudan Univ.) |

Stochastic Modeling and Analysis of Energy Trading System in Microgrids with Future Forecasting and Forecasting Errors Prof. Ganguk Hwang (KAIST) |

Aubry-Mather and weak KAM theories for contact Hamiltonian systems Prof. Jun Yan (Fudan Univ.) |

Series solution method to the conductivity interface problem based on the geometric function theory and its applications to the composite material properties Prof. Mikyoung LIm (KAIST) |

Jacobi-Like Algorithm for Bethe-Salpeter Eigenvalue Problem Prof. Weiguo Gao (Fudan Univ.) |

Scattering of the defocusing generalized Benjamin-Ono equations Prof. Soonsik Kwon(KAIST) |

Nonparametric Bayesian multivariate meta-regression with functional meta-predictors: an application in environmental epidemiology Prof. Yeonseung Chung (KAIST) |

The Mathematical Modeling Activities for High School Students in China Dr. Liqiang Lu (Fudan Univ.) |

Beyond the century of the Michales-Menten equation for the accurate estimation of drug clearance Prof. Jaekyoung Kim (KAIST) |

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E6, Rm 2411
PDE WORKSHOP

### Organizers

권순식

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

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E6-1, 1401(Choi, Seok-Jeong Lecture Room), KAIST
2018 KAIST-HKUST-NUS Joint Workshop in Mathematics : Analysis, PDE and Probability

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

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1401 (E6-1)
Number Theory/Topology Mini Workshop

### Organizers

Bo-Hae Im, Hyungryul Baik

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

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E6-1, seminar room 4415
Mini-workshop on Variational Methods for Elliptic PDE.

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.