


ÃÊÃ»¿¬»ç (Invited Speakers)
±âÁ¶°¿¬ (Plenary Lecture)
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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, 1971present University of Wisconsin, Associate Professor, 19691971 Stanford University, Assistant Professor, 19661969 Stanford University, Instructor, JanuarySeptember 1966 
¡¡ Plenary Lecture  11:2012:10, 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.  ÇÑ±¹°úÇÐ»ó ¼ö»ó±â³ä °¿¬ (Special Lecture by the Korean Science Award Winner)
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°Çö¹è Hyeonbae Kang
ÀÎÇÏ´ëÇÐ±³ Á¤¼®¼®ÁÂ±³¼ö / Jungseok Chair Professor of Inha University, Korea 2010³â ÇÑ±¹°úÇÐ»ó ¼ö»ó / 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, 2008.9present Seoul Nat'l University, Assistant/Associate/Full Professor, 1997.92008.8 
¡¡ Special Lecture by the Korean Science Award Winner  10:3011:20, 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, KangMilton's solution to the PolyaSzego conjecture, and connection to the DirichlettoNeumann 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.  ÃÊÃ»°¿¬ (Invited Lectures)
¡¡Carsten Carstensen Professor of Humboldt University, Germany Invited Lecture_Applied Mathematics  15:3016:10, October 22(Fri), 2010 A posteriori error estimator competition for 2ndorder Partial Differential Equations Five classes of up to 13 a posteriori error estimators compete in three secondorder model cases, namely the conforming and nonconforming firstorder approximation of the PoissonProblem 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 LuceWohlmuth and the leastsquare 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 CrouzeixRaviart 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 meshrefinement is sufficiently pleasant as accurate when based on explicit residualbased 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  15:3016:10, 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 SturmLiouville 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_  15:3016:10, 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. 
¡¡±è¿µÈÆ YoungHoon Kiem ¼¿ï´ëÇÐ±³ ±³¼ö / Professor of Seoul National University, Korea
Invited Lecture_Algebra  15:3016:10, 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 GromovWitten 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 KatzKlemmVafa conjecture (generalization of YauZaslow formula) by MaulikPandharipandeThomas, (2) a calculation of GW invariants for surfaces of general type, (3) a theory of spin curve counting by ChangLi, (4) a wall crossing formula without ChernSimons functional and (5) a theory of g eneralized DT invariants via Kirwan blowups. 
¡¡Miyuki Koiso Professor of Kyushu University, Japan
Invited Lecture_Geometry  15:3016:10, 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 symmetrybreaking 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. 
¡¡ÀÌÇö´ë Hyun Dae Lee ÀÎÇÏ´ëÇÐ±³ ±³¼ö / Professor of Inha University, Korea 2009³âµµ »ó»ê ÀþÀº¼öÇÐÀÚ»ó ¼ö»ó / The winner of 2009 Sangsan Prize for young Mathematicians
Invited Lecture_Applied Mathematics  15:3016:10, 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. 
¡¡ÀÌ°Çõ KangHyurk Lee °íµî°úÇÐ¿ø ±³¼ö / Professor of KIAS, Korea
Invited Lecture_Analysis  15:3016:10, October 22(Fri), 2010
On the bounded realization of unbounded models in Several Complex Variables As the Riemann mapping theorem fails on multidimensional 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 noncompact automorphism group. Many theories said that most of model domains can be realized as a socalled Siegel type domain, a generalization of the halfplane 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 realanalytic boundary. 

