2010 Global KMS International Conference

2010.10.22(금)~23(토), 포항공과대학교(POSTECH)
학술발표회 홈
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초청연사
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초록제출 및 확인
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후원 및 전시
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/Exhibition)
초청연사 (Invited Speakers)


 기조강연  (Plenary Lecture)

  

Paul H. Rabinowitz

Edward Burr Van Vleck Professor of Mathematics and a Vilas Research Professor
at the University of Wisconsin, Madison, USA
Distinguished Visiting Professor of Mathematics at POSTECH, Korea
 
PH.D. New York University, 1966
M.A. New York University, 1963
B.A. New York University, 1961
 
University of Wisconsin, Professor of Mathematics, 1971-present
University of Wisconsin, Associate Professor,         1969-1971
Stanford University, Assistant Professor,                 1966-1969
Stanford University, Instructor,                                January-September 1966
   
   
Plenary Lecture  ||  11:20-12:10, October 22(Fri), 2010 
   
   
It all started with Moser
    We survey work on a class of nonlinear elliptic partial differential equations that was initiated by Moser. Methods
    from the calculus of variations, dynamical systems, and geometry as well as PDE have been used to find a rich
    variety of solutions.

    
 
 
 한국과학상 수상기념 강연 (Special Lecture by  the Korean Science Award Winner) 
        

  

강현배  Hyeonbae Kang

인하대학교 정석석좌교수 / Jungseok Chair Professor of Inha University, Korea  
2010년 한국과학상 수상 / Korean Science Award Winner (Presidential Award)
 
PH.D. University of Wisconsin, Madison, 1989
M.S. Seoul Nat'l University, 1984
B.S. Seoul Nat'l University, 1982
 
Inha University, Jungseok Chair Professor,                          2008.9-present
Seoul Nat'l University, Assistant/Associate/Full Professor,   1997.9-2008.8
 

   
   
Special Lecture by the Korean Science Award Winner  ||  10:30-11:20, October 23(Sat), 2010 
        
    Generalized Polarization Tensors: Mathematics and Applications
    The generalized polarization tensors (GPT) are geometric and physical quantities associated with inclusions.
    They appear naturally in multipolar expansions of electric potentials near infinity in the presence of the inclusion.
    In this talk I will discuss about optimal bounds for GPTs, Kang-Milton's solution to the Polya-Szego conjecture, and
    connection to the Dirichlet-to-Neumann map. I then discuss their usage for reconstruction of fine details of the
    shape of the inclusion. I will also mention briefly on their connection to the cloaking (invisibility) which attracts much
    attention these years.

    
  
 
 초청강연 (Invited Lectures)
 
  
 
Carsten Carstensen
       
   Professor of Humboldt University, Germany
  
   Invited Lecture_Applied Mathematics  ||  15:30-16:10, October 22(Fri), 2010 
  
   A posteriori error estimator competition for 2nd-order Partial Differential Equations
   Five classes of up to 13 a posteriori error estimators compete in three second-order model cases, namely the
   conforming and non-conforming first-order approximation of the Poisson-Problem plus some conforming obstacle
   problem. Since it is the natural first step, the error is estimated in the energy norm exclusively -- hence the
   competition has limited relevance. The competition allows merely guaranteed error control and excludes the question
   of the best error guess. Even nonsmooth problems can be included. For a variational inequality, Braess considers
   Lagrange multipliers and some resulting auxiliary equation to view the a posteriori error control of the error in the
   obstacle problem as computable terms plus errors and residuals in the auxiliary equation. Hence all the former a
   posteriori error estimators apply to this nonlinear benchmark example as well and lead to surprisingly accurate
   guaranteed upper error bounds. This approach allows an extension to more general boundary conditions and a
   discussion of efficiency for the affine benchmark examples. The Luce-Wohlmuth and the least-square error estimators
   win the competition in several computational benchmark problems. Novel equilibration of nonconsistency residuals and
   novel conforming averaging error estimators win the competition for Crouzeix-Raviart nonconforming finite element
   methods. Our numerical results provide sufficient evidence that guaranteed error control in the energy norm is indeed
   possible with efficiency indices between one and two. Furthermore, accurate error control is slightly more expensive
   but pays off in all applications under consideration while adaptive mesh-refinement is sufficiently pleasant as accurate
   when based on explicit residual-based error estimates. Details of our theoretical and empirical ongoing investigations
   will be found in the papers quoted below.
   
  
  
 Youri Egorov
    
   Professor of Paul Sabatier University, Toulouse, France

   Invited Lecture_Analysis  ||  15:30-16:10, October 22(Fri), 2010 
  
   On the tallest column
   A new approach is proposed to the study of the classical problem about the highest column of given volume stated
   by L. Euler. The diculty of the problem is related to the presence of the continuous spectrum for the corresponding
   Sturm-Liouville operator. The existence and the uniqueness of the solution is proved for the rst time. The method is
   based on the study of critical points of a suitable nonlinear functional.
   
      
  
 Baohua Fu
     
   Professor of Chinese Academy of Science, China

   Invited Lecture_  ||  15:30-16:10, October 22(Fri), 2010 
   
   Geometry of nilpotent orbit closures 
   Nilpotent orbits play an important role in the study of representation theory of a reductive group. Their closures
   provide very nice examples of symplectic singularities. I'll give a survey on the study of birational geometry of
   nilpotent orbit closures, from the viewpoint of Minimal Model Program. A list of open problems will be discussed at
   the end.  
  
     
  
 김영훈  Young-Hoon Kiem
     
   서울대학교 교수 / Professor of Seoul National University, Korea

   Invited Lecture_Algebra  ||  15:30-16:10, October 22(Fri), 2010

   Curve counting invariants and wall crossing

   This talk is about joint work with Jun Li (Stanford).
   Curve counting invariants are defined as intersection numbers on moduli spaces of curves in a given projective variety
   when the moduli spaces are (1)compactified and (2)equipped with perfect obstruction theories. I will explain various
   compactifications which give rise to a variety of curve counting invariants such as Gromov-Witten and Donaldson-
   Thomas invariants. A prominent open problem is to compare these invariants and wall crossing for objects in the
   derived category has been playing a key role in recent progress. Also I will explain known techniques to handle
   virtual fundamental classes obtained from perfect obstruction theories. Special emphasis will be laid on our recent
   technique, called ``localization by cosection'' which tells us that if the obstruction sheaf admits a cosection, the
   virtual fundamental class localizes to the locus where the cosection is not surjective. This technique has found
   exciting applications in (1) a recent proof of the Katz-Klemm-Vafa conjecture (generalization of Yau-Zaslow formula)
   by Maulik-Pandharipande-Thomas, (2) a calculation of GW invariants for surfaces of general type, (3) a theory of spin
   curve counting by Chang-Li, (4) a wall crossing formula without Chern-Simons functional and (5) a theory of g
   eneralized DT invariants via Kirwan blow-ups.
  
   
  
 Miyuki Koiso
    
   Professor of Kyushu University, Japan

   Invited Lecture_Geometry  ||  15:30-16:10, October 22(Fri), 2010 
          
   Geometric variational problems and bifurcation theory 
   In the study of geometric variational problems, it is natural to ask whether each critical point is stable (that is, the
   considered critical point attains a local minimum of the energy) or not. Also it is important to determine the geometric
   properties of solutions and to study the structure of the set of solutions. In this talk, as one of the steps to investigate
   these problems, we discuss stability, existence of bifurcation, and symmetry-breaking for solutions of variational
   problems for hypersurfaces with constraint. Although our method is sufficiently general to apply various variational
   problems, we mainly concentrate on hypersurfaces with constant anisotropic mean curvature in the euclidean space,
   which are characterized as critical points of anisotropic surface energy with volume constraint. 
   Useful criteria for the stability and existence of bifurcation are given by the properties of eigenvalues and 
   eigenfunctions of the eigenvalue problem associated with the second variation of the energy. We will give general
   methods and their applications to several concrete examples which may be interesting from both mathematical and
   physical point of view.
  
   
  
 이현대  Hyun Dae Lee 
     
   인하대학교 교수 / Professor of Inha University, Korea
   2009년도 상산 젊은수학자상 수상 / The winner of 2009 Sangsan Prize for young Mathematicians

   Invited Lecture_Applied Mathematics  ||  15:30-16:10, October 22(Fri), 2010  

   Asymptotic imaging of cracks
   We consider cracks with Dirichlet boundary conditions. We first derive an asymptotic expansion of the boundary
   perturbations that are due to the presence of a small crack. Based on this formula, we design a noniterative
   approach for locating a collection of small cracks. In order to do so, we construct a response matrix from the
   boundary measurements. The location and the length of the crack are estimated, respectively, from the projection
   onto the noise space and the first significant singular value of the response matrix. Indeed, the direction of the crack
   is estimated from the second singular vector. We then consider an extended crack with Dirichlet boundary conditions.
   We rigorously derive an asymptotic expansion for the boundary perturbations that are due to a shape deformation of
   the crack. To reconstruct an extended crack from many boundary measurements, we develop two methods for
   obtaining a good guess. Several numerical experiments show how the proposed techniques for imaging small cracks
   as well as those for obtaining good initial guesses toward reconstructing an extended crack behave.
  
   
  
 이강혁  Kang-Hyurk Lee 
     
   고등과학원 교수 / Professor of KIAS, Korea

   Invited Lecture_Analysis ||  15:30-16:10, October 22(Fri), 2010

   On the bounded realization of unbounded models in Several Complex Variables 
   As the Riemann mapping theorem fails on multi-dimensional complex Euclidean spaces, it has been a fundamental
   problem in Several Complex Variables to classify domains which can play the same role of model objects as the unit
   disc. This is indeed the classification program for domains with non-compact automorphism group. Many theories
   said that most of model domains can be realized as a so-called Siegel type domain, a generalization of the
   half-plane representation of the unit disc. Although Siegel type domains are unbounded, they have many affine 
   automorphisms; hence this representation of models has been employed in wide area of Several Complex Variables.
   In this talk, I will introduce briefly theories on this topic and then discuss problems on the realization of a Siegel type
   domain as a bounded domain. Especially I will mention my current collaboration with Jisoo Byun on the smoothly
   bounded realization of a Siegel type domain with real-analytic boundary.
  
  

 

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