Suname / Given Name	Position	Title	Abstract
KIM / PANKI	prof.	Heat Kernel Estimates for Truncated Stable-like Processes and Weighted Poincare Inequality.	In this talk, we discuss pure jump symmetric processes whose jumping kernel is comparable to the one for truncated rotationally symmetric stable process where jumps of size larger than a fixed number is removed. We discuss how to get sharp two-sided heat kernel estimate and parabolic Harnack principle for such jump-type processes. We also present a new form of weighted Poincare inequality of fractional order which played a crucial role in obtaining the lower bound heat kernel estimate. This is a joint work with Zhen-Qing Chen and Takashi Kumagai.
Lee / IN SOK	prof.
KIEM / YOUNG HOON	prof.	Gromov-Witten invariants of varieties with holomorphic 2-forms	This is a joint work with Jun Li (Stanford). We show that a holomorphic 2-form on a smooth algebraic variety X localizes the virtual fundamental class of the moduli of stable maps to the locus where the 2-form degenerates; this localization phenomenon enables us to define the localized GW-invariant, an algebro-geometric analogue of the local invariant of Lee and Parker in symplectic geometry, which coincides with the ordinary GW-invariant when X is proper. It is deformation invariant. Using this, we prove formulas for low degree GW-invariants of minimal general type surfaces with p_g>0, conjectured by Maulik and Pandharipande.
CHI / DONG PYO	prof.
CHO / CHEOL HYUN	prof.
KIM / MYUNG HWAN	prof.
KANG / SEOK JIN	prof.
KIM / MYUNGHO	graduate student	LEVEL l ADJOINT CRYSTALS AND YOUNG WALL REALIZATIONS OF CRYSTAL GRAPHS FOR A(1) 1	There is a unform construction of level 1 perfect crystals for all quantum affine algebras, called the adjoint crystals. Focusing on the quantum affine algebra of A(1) 1 type, Uq(bsl2), we construct the adjoint crystals of level l, for all l 2 N. Using these adjoint crystals, we also construct the Young walls for irreducible highest weight modules over Uq(bsl2).
PARK / EUIYONG	graduate student	CALCULATIONS OF TOR AND EXT FOR REPRESENTATIONS USING GRÄOBNER BASES TECHNIQUES	We study GrÄobner bases techniques for left modules over a noncommutative algebra, including methods to ¯nd the intersection of submodules and the kernel of a given homomorphism between left modules over a noncommutative algebra. Using the techniques, we calculate Tor and Ext for representations.
KIM / JAEWOONG	graduate student	THE OPERATOR VALUED POISSON KERNEL AND THE OPERATOR CLASS C½	If T is a bounded linear operator on a separable, infinite-dimensional, complex Hilbert space H such that ¾(T) ½ clD, then the operator-valued Poisson kernel Kreit (T) for every reit 2 D is defined by Kreit (T) = (1 ¡ reitT¤)¡1 + (1 ¡ re¡itT)¡1 ¡ 1: It is clear that Kreit (T) is a self adjoint operator for each reit 2 D. Also from the Cauchy’s formula we get f(rT) = 1 2¼ Z 2¼ 0 f(eit)Kreitdt for any function f 2 A(D) and 0 · r < 1. Write C½ for the class of all operators having a unitary ½- dilation and ACPB(H) for the class of absolutely continuous polynomially bounded operators. Using the operator-valued Poisson kernel we show that if T 2 L(H) is an operator whose spectrum is contained in the closed unit disk and if T 2 C½ \ACPB(H) then for every x; y 2 H the radial limit limr!1¡hKreit (T)x; yi exists almost everywhere and is a L1 function.
YOO / SANG-BUM	graduate student	The intersection betti numbers of the moduli space of Higgs pairs with trivial determinant.	Let $\mathcal{M}_{Higgs}$ be the moduli space of semistable rank 2 holomorphic Higgs pairs with trivial determinant over a compact Riemann surface $X$ of genus $g\geq 2$. We provide a closed formula for the intersection betti numbers of $\mathcal{M}_{Higgs}$.
KIM / HYESEON	graduate student	ON THE INFINITESIMAL AUTOMORPHISM ON A REAL FOUR DIMENSIONAL ALMOST COMPLEX MANIFOLD	Abstract. For an almost complex manifold (M; J), an in¯nitesimal automorphism of J is a vector ¯eld V satisfying that LV J ´ 0. Then V generates a local 1-parameter group of local J-invariant transformations. In case of an integrable J, an in¯nitesimal automorphism is holomorphic vector ¯eld and vice versa. So the algebra of in¯nitesimal automorphism is of in¯nite dimensional. But for generic almost complex structure J, there is a few in¯n- itesimal automorphism. In this talk, we describe the in¯nitesimal automorphisms of real 4-dimensional almost complex manifolds. At ¯rst we consider the existence of a model in C2 which is locally homogeneous. And this question is equivalent to the existence of a model in C2 whose in¯nitesimal automorphisms at a point span the whole tangent space. Secondly, we consider the maximal dimension of the space of all in¯nitesimal automorphism. Let us denote that V = Im NJ which is the image of the Nijenhuis tensor of a real dimension 2 as a J- invariant subspace of TJR4: Then for involutive V; we give a locally homogeneous example whose in¯nitesimal automorphisms are of the in¯nite dimension as an answer of the above two questions. It is known fact that the Engel structure is a generic case and the dimension of Engel CR automorphisms is at most 5: For non-involutive V; we prove that the ini¯nitesimal automorphism algebra constitutes a complete system of a ¯rst order and the dimension is at most 4:
SUH / UHI RINN	graduate student
KIM / SUNGWOOK	graduate student	A Parameterized Splitting System and its Application to the Discrete Logarithm Problem with Low Hamming Weight Product Exponents	A low Hamming weight product (LHWP) exponent is used to increase the efficiency of cryptosystems based on the discrete logarithm problem (DLP). In this paper, we introduce a new tool,  called a Parameterized Splitting System, to analyze the security of the DLP with LHWP exponents. We apply a parameterized splitting system to attack the GPS identification scheme modified by Coron, Lefranc and Poupard in CHES'05. Also a parameterized splitting system can be used to solve the DLP with a LHWP exponent proposed by Hoffstein and Silverman.
JEONG / KYUNG CHUL	graduate student	A New Time-Memory Tradeoff Method Using a Variant of Distinguished Points	In 1980 Hellman described a cryptanalytic time-memory tradeoff (TMTO) algorithm that makes it possible to invert a one-way function f : {0, 1, . . . ,N−1} → {0, 1, . . . ,N-1} in O(N23 ) time with O(N23 ) memory. The distinguished point (DP) suggested by Rivest can be used to reduce the number of table search in Hellman algorithm. We propose a new TMTO algorithm. It is a variant of DP, but with very different properties. We can store the result of precomputation as a hash table in order to reduce the size and search it efficiently. Our method makes the Hellman table to be a minimal perfect hash table. So it can maximize the reduced size by using hash table and the efficiency of searching. The main advantage of our method is that the starting points of Hellman chain need not be stored.
CHOI / JEONG WOON	graduate student	Three party d-level quantum secret sharing	We develop a three-party Quantum Secret Sharing(QSS) protocol which is based on arbitrary dimensional quantum states. Unlike previous QSS protocols, the sender can always control the state, just using local operations, for adjusting the correlation of measurement directions of three parties and thus there is no waste of resource due to the discord between the directions. Moreover, our protocol contains the hidden value which enables the sender to leak no information of secret key to the dishonest receiver until the last steps of the procedure.
KIM / HYOUNG JOON	graduate student	Hyperinvariant Subspace Problem for Quasinilpotent Operators (II)	In this paper we consider the hyperinvariant subspace problem for quasinilpotent operators in a separable complex Hilbert space. Let T 2 L(H) be a quasinilpotent quasiaffinity. It is shown that if for each n, xn is a c-eigenvector of TnT¤n with c > 0, that is, hTnT¤nxn; xni ¸ c kTnT¤nxnk and if every subsequence of fxng contains a norm convergent subsequence then T has a nontrivial hyperinvariant subspace.
HAN / KYUNG HOON	Post-Doc.	EXACT ASSOCIATE OF C¤-TENSOR NORM	The maximal tensor norm satis¯es the following three conditions with ® = max. (1) For C¤-algebras A1;A2;B1;B2 and completely positive maps T1 : A1 ! B1 and T2 : A2 ! B2, their tensor product T1 ­ T2 is continuous with respect to C¤-tensor norm ® with kT1 ­ T2 : A1 ­® A2 ! B1 ­® B2k 5 kT1kkT2k; and its continuous extension T1 ­ T2 is completely positive. (2) For C¤-algebras A;B and an element z in their algebraic tensor product A ¯ B, we have kzkA­®B = inffkzkC­®D : z 2 C ¯ Dg where the in¯mum runs over a separable C¤-subalgebra C of A and a separable C¤-subalgebra D of B. (3) For C¤-algebras A;B and a norm closed ideal I of A, two sequences 0 ! I ­® B ! A ­® B ! A=I ­® B ! 0 and 0 ! B ­® I ! B ­® A ! B ­® A=I ! 0 are exact. The C¤-tensor norm satisfying condition (1) need not satisfy condition (3). The tensor product of completely positive maps between C¤-algebras is continuous with respect to the minimal tensor norm, and its continuous extension is completely positive. Wasserman has proved that the sequence 0 ! I ­min C¤(F2) ! C¤(F2) ­min C¤(F2) ! C¤r (F2)  min C¤(F2) ! 0 is not exact for the free group F2. Hence, the minimal tensor norm does not satisfy condition (3) with ® = min. The maximal tensor norm is the largest C¤-tensor norm. For a C¤-tensor norm ® satisfying condition (1), there exists at least one C¤-tensor norm larger than ® that satis¯es conditions (1),(2), and (3), for example the maximal tensor norm. It is natural to search for the smallest C¤-tensor norm among them and to determine its uniqueness. We will answer this question in the a±rmative. It is a C¤-algebraic analogue of a projective associate in Banach space theory.