<Plenary Lecture>

ShuiNee Chow
Professor of Mathematics, Georgia Institute of Technology (USA)
Dynamical Systems and Nonlinear Studies
B.S. 1965, University of Singapore, Mathematics
Ph.D. 1970, University of Maryland, Mathematics 
[Plenary Lecture]  17:20~18:10, April 30(Sat), 2011
FokkerPlanck Equations for a Free Energy Functional or Markov Process on a graph
The classical FokkerPlanck equation is a linear parabolic equation which describes the time evolution of probability distribution of a stochastic process defined on an Euclidean space. Corresponding to a stochastic process, there often exists a free energy functional which is defined on the space of probability distributions and is a linear combination of a potential and an entropy. In recent years, it has been shown that FokkerPlanck equation is the gradient flow of the free energy functional defined on the Riemannian manifold of probability distributions whose inner product is generated by a 2Wasserstein distance. In this paper, we consider analogous matters for a free energy functional or Markov process defined on a graph with a finite number of vertices and edges. If $N\ge 2$ is the number of vertices of the graph, we show that the corresponding FokkerPlanck equation is a system of $N$ nonlinear ordinary differential equations defined on a Riemannian manifold of probability distributions. However, in contrast to stochastic processes defined on Euclidean spaces, situation is more subtle for discrete spaces. We have different choices for inner products on the space of probability distributions resulting in different FokkerPlanck equations for the same process. It is shown that there is a strong connection but also substantial discrepancies between the systems of ordinary differential equations and the classical FokkerPlanck equation on Euclidean spaces. Furthermore, both systems of ordinary differential equations are gradient flows for the same free energy functional defined on the Riemannian manifolds of probability distributions with different metrics. Some examples will also be discussed. 
<Special Lecture>
¿À¼¼Á¤ SeJung Oh
ÇÑ±¹¿¬±¸Àç´Ü ÀÌ»çÀå / President of National Research Foundation of Korea
[Special Lecture]  16:30~17:20, April 30(Sat), 2011
ÇÑ±¹¿¬±¸Àç´ÜÀÇ ±âÃÊ¿¬±¸ Áö¿øÁ¤Ã¥ ÀÌ °¿¬¿¡¼´Â ¸ÕÀú ¿ì¸®³ª¶ó R&DÀÇ ¼º°ú¿Í ´ç¸é¹®Á¦, Æ¯È÷ ±âÃÊ¿¬±¸ÀÇ ÇöÁÖ¼Ò¸¦ »ìÆìº» ÈÄ, ÀÌ¿¡ ´ëÀÀÇÏ´Â Á¤ºÎÀÇ ±âÃÊ ¹× ¿øÃµ¿¬±¸ Áö¿øÁ¤Ã¥ ¹æÇâÀ» °£´ÜÈ÷ Á¤¸®ÇØ º¼ °ÍÀÌ´Ù. ±×¸®°í ÀÌ¿¡ µû¶ó ÇÑ±¹¿¬±¸Àç´Ü¿¡¼ ¾ÕÀ¸·Î ´ëÇÐÀÇ ±âÃÊ¿¬±¸¸¦ Áö¿øÇÏ±â À§ÇØ¼ ÆîÄ¥ Á¤Ã¥À» ³íÀÇÇÏ·Á ÇÑ´Ù. 
<Invited Lectures>
±Ý»óÈ£ Sangho Kum
ÃæºÏ´ëÇÐ±³ ±³¼ö / Professor of Chungbuk National University
[Invited Lecture] Applied Mathematics  10:10~10:50, April 30(Sat), 2011
Resolvent average on symmetric cones Recently Bauschke et al. introduced a very interesting and new notion of proximal average in the context of convex analysis, and studied this subject systemically from various viewpoints. In addition, this new concept was applied to positive semidefinite matrices under the name of resolvent average, and basic properties of the resolvent average are successfully established by themselves from a totally different view and techniques of convex analysis rather than the classical matrix analysis. Inspired by their works and the wellknown fact that the convex cone of positive definite matrices is a typical example of a symmetric cone (selfdual homogeneous convex cone), we study the resolvent average on symmetric cones, and derive corresponding results in a different manner based on a purely Jordan algebraic technique. Some average for general convex functions is also introduced.

±Ç¼ø½Ä Soonsik Kwon
KAIST ±³¼ö / Professor of Mathematical Science, KAIST
2010³âµµ »ó»êÀþÀº¼öÇÐÀÚ»ó ¼ö»ó / The winner of 2010 Sangsan Prize for young mathematicians
[Invited Lecture] Analysis  15:20~16:00, April 30(Sat), 2011
PoincareDulac normal form reduction for unconditional wellposedness of the periodic cubic
We implement an infinite iteration scheme of PoincareDulac normal form reductions to establish an energy estimate on the onedimensional cubic nonlinear Schrodinger equation. As a result, we prove its unconditional wellposedness in L^2. In the talk we explain how to adopt PoincareDulac normal form technique to PDE setting with multilinear estimates. 
¹Ú¼ºÈ£ Sung Ho Park
ÇÑ±¹¿Ü±¹¾î´ëÇÐ±³ ±³¼ö / Professor of Hankuk University of Foreign Studies
[Invited Lecture] Geometry  11:00~11:40, April 30(Sat), 2011
Symmetry of planar curves and capillary surface in a wedge in $\mathbb H^3$
We give several conditions for a planar curve to be a circle in $\mathbb R^2$ and $\mathbb H^2$, and apply the result to derive a necessary condition for capillary surfaces in a wedge in $\mthbb H^3$. 
½É°æ¾Æ KyungAH Shim
±¹°¡¼ö¸®°úÇÐ¿¬±¸¼Ò ¼±ÀÓ¿¬±¸¿ø / Senior researcher of National Institute for Mathematical Sciences of Korea
[Invited Lecture] Cryptography  15:20~16:00, April 30(Sat), 2011
Efficient IDbased signatures and multisignatures based on the qSDH problem Paterson and Schuldt proposed an IDbased signature scheme based on Waters' signature scheme, secure in the standard model under the Computational DiffieHellman assumption. They claimed that the scheme allows secure IDbased aggregate signature (multisignature) scheme. We show that the IDbased aggregate (multisignature) scheme based on Paterson and Schuldt's signature scheme is insecure against forgery attacks. We then propose a new IDbased signature scheme based on the qSDH assumption which allows us to construct an efficient multisignature scheme secure in the standard model.

¾çÂù¿ì Chan Woo Yang
°í·Á´ëÇÐ±³ ±³¼ö / Professor of Korea University
[Invited Lecture] Analysis 
Nonlocalization phenomena of oscillatory integral operators In this talk we consider oscillatory integral operators $T_{\lambda}$ of the form $$T_{\lambda}f(x)=\int_{\mathbb{R}} e^{i \lambda S(x,y)} f(y) dy,$$ where $S$ is a polynomial with two real variables $x$ and $y$. We call these operators nonlocalized oscillatory integral operators. Usually oscillatory integral operators are operators of the form $$T_{\lambda}f(x)=\int_{\mathbb{R}} e^{i \lambda S(x,y)} \chi (x,y) f(y) dy,$$ where $\chi$ is a smooth cutoff function supported in a small neighborhood of the origin in $\mathbb{R}^2$. Because of the presence of the cutoff function $\chi$ we call these operators localized oscillatory integral operators. Almost full picture of decay rate of operator norm of localized oscillatory integral operators have been drawn in terms of Newton polygon of the phase function $S$ in numerous articles. However nonlocalized oscillatory integral operators have not been fully understood. The aim of this talk is to discuss interesting phenomena of mapping properties of nonlocalized oscillatory integral operators due to the absense of the cutoff function $\chi$ in terms of `nonlocalized' Newton polygon in adapted coordinate system.

¿À¿µÅ¹ Young Tak Oh
¼°´ëÇÐ±³ ±³¼ö / Professor of Sogang University
[Invited Lecture] Algebra  13:10~13:50, April 30(Sat), 2011
Witt vectors and WittBurnside rings The WittBurnside ring of a profinite group is a grouptheoretical generalization of big Witt vectors. For instance, the classical $p$typical Witt vectors of Teichmuller and Witt correspond to the WittBurnside ring of the profinite $p$completion of the infinite cyclic group $C$ and the universal Witt vectors of Lang and Witt to that of the profinite completion of $C$. In this talk, we explain recent results on the structure of WittBurnside rings. A special emphasis will be put on the classification and decomposition. Connection to representation theory will be also discussed.

ÀÓ¼±Èñ Seonhee Lim
¼¿ï´ëÇÐ±³ ±³¼ö / Professor of Seoul National University
[Invited Lecture] Topology  10:10~10:50, April 30(Sat), 2011
Dynamics of group action on nonpositively curved spaces and its application
We introduce several dynamical properties of group action on nonpositively curved spaces, and relate them with topological and geometrical properties of the spaces. We will also show some examples of its applications to problems in number theory. 
ÇÑÁ¾¹Î Jongmin Han
°æÈñ´ëÇÐ±³ ±³¼ö / Professor of Mathematics, Kyung Hee University
[Invited Lecture] Analysis  13:10~13:50, April 30(Sat), 2011
Existence of topological solutions in the selfdual gauge field theories via super and subsolution method In this talk, we discuss how to find topological solutions in the selfdual gauge field theories via the method of super and subsolutions. In particluar, we propose a new method to find an explicit subsolution. As an application, we provide a new proof of the existence of topological solutions in two Higgs model. We also prove the existence of topological solutions in the Maxwell gauged $O(3)$ sigma model and the ChernSimons gauged $O(3)$ sigma model. 
È²¼±¿í Sunwook Hwang
¼þ½Ç´ëÇÐ±³ ±³¼ö / Professor of Soongsil University
[Invited Lecture] Mathematical Education  13:10~13:50, April 30(Sat), 2011
Ã¢ÀÇ Áß½ÉÀÇ ¹Ì·¡Çü ¼öÇÐ°ú ±³À°°úÁ¤ ½Ã¾È °³¹ßÀÇ ¹æÇâ°ú ³»¿ë Ã¼°è

Lucian Beznea
Institute of Mathematics of the Romanian Academy, Romania
[Invited Lecture] Probability and Statistics  11:00~11:40, April 30(Sat), 2011
On the quasiregularity of nonsectorial Dirichlet forms by processes having the same polar sets
We obtain a criterion for the quasiregularity of generalized (non sectorial) Dirichlet forms, which extends the result of P.J. Fitzsimmons on the quasiregularity of (sectorial) semiDirichlet forms. Given the right (Markov) process associated to a semiDirichlet form, we present sufficient conditions for a second right process to be a standard one, having the same state space. The above mentioned quasiregularity criterion is then an application. The conditions are expressed in terms of the associated capacities, nests of compacts, polar sets, and quasicontinuity. A second application is on the quasiregularity of the generalized Dirichlet forms obtained by perturbing a semiDirichlet form with kernels. The talk is based on a joint work with Gerald Trutnau. 
Xuding Zhu
Professor of Zhejiang Normal University, China
[Invited Lecture] Mathematics for Information Sciences  14:00~14:40, April 30(Sat), 2011
Thue choice number of graphs
A sequence of even length is a repetition if the first half is identical to the second half. A sequence is said to contain a repetition if it has a subsequence which is a repetition. A classical result of Thue says that there is an infinite sequence on $3$ symbols which contains no repetition. This result motivated many deep research and challenging problems. One graph concept related to this result is Thuecolouring. A Thuecolouring of a graph $G$ is a mapping which assigns to each vertex of $G$ a colour (a symbol) in such a way that the colour sequence of any path of $G$ contains no repetition. The Thuechromatic number of a graph is the minimum number of colours needed in a Thuecolouring of $G$. Thue's result is equivalent to say that the infinite path has Thuechromatic number $3$. It is also known that the Thuechromatic number of any tree is at most $4$. Thuechoice number of a graph $G$ is the list version of its Thuechromatic number, which is the minimum integer $k$ such that if each vertex of $G$ is given $k$permissible colours, then there is a Thuecolouring of $G$ using a permissible colour for each vertex. This talk will survey some research related to Thue Theorem and will show that Thuechoice number of paths is at most $4$ and Thue choice number of trees are unbounded. 
