학술회의 및 워크샵

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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

1. Gelfand-Manin: Methods of Homological Algebra, Springer, 2003.
2. Kawamata: Birational geometry and derived categories.  Surveys in Differential Geometry, Vol. 22, No. 1 (2017), pp. 291--317.  ArXiv:1710.07370.
3. Karmazyn-Kuznetsov-Shinder: Derived categories of singular surfaces. ArXiv:1809.10628.
2018-12-24 15:38:56

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
2018-07-31 10:41:13

Organizers

Dohoon Choi (Korea University)
Bo-Hae Im (KAIST) 

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/
2018-06-20 21:18:50

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)

2018-08-08 12:32:45

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

2018-10-15 10:58:21

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

 

2018-11-12 08:39:36

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.

2019-01-14 12:44:19