Title    name 년도선택 최근 50건20102009200820072006200520042003200220012000   전공선택 :: 전체Algebra & CombinationsAnalysisApplied MathematicsGeometry & TopologyETC     2010 International Workshop on Mathematical Cryptology Pairing-based Non-interactive Zero-Knowledge Proofs Jens Groth (University College London) 2010-08-28    Non-interactive zero-knowledge proofs enable a prover to convince a verifier of the truth of a statement without revealing any other information. They are useful in contexts where verifiability and privacy are needed at the same time and have many applications, for instance in the context of anonymous signatures. Pairing-based cryptography has provided new insights in the area of non-interactive zero-knowledge proofs. We will see how pairing-based non-interactive proofs can be constructed in a simple fashion and how to obtain perfect and everlasting privacy. We will also see how pairing-based techniques have improved the efficiency of non-interactive zero-knowledge proofs and made them useful in practical application.   2010 International Workshop on Mathematical Cryptology Sharing Sensitive Information with Privacy Gene Tsudik (University of California) 2010-08-28    Modern society is increasingly dependent on, and fearful of, the availability of electronic information. There are numerous realistic scenarios where sensitive data must be (sometimes reluctantly or suspiciously) shared between two or more entities without mutual trust. As often happens, the research community has foreseen the need for mechanisms to enable limited (privacy-preserving) sharing of sensitive information and a number of effective (if not always efficient) solutions have been proposed. Among them, Private Set Intersection techniques are particularly appealing whenever two parties wish to compute an intersection of their respective sets of items without revealing to each other any other information. This talk motivates the need for Private Set Intersection (PSI) techniques with various features and privacy properties and illustrates several concrete Private Set Intersection protocols that offer appreciably better efficiency than prior work. We show how to integrate these protocols into a real database system supporting privacy-preserving querying. We also demonstrate their practicality via experimental results obtained from a prototype implementation and discuss a number of systems issues encountered in developing a toolkit that provides various flavors of PSI.   2010 International Workshop on Mathematical Cryptology Effcient Verifiably Encrypted Signatures Without Random Oracles Lee, Juhee (Ewha Womans University) 2010-08-28   A verifiably encrypted signature can convince the verifier that a given ciphertext is the encryption of the signature on a given message, but only the party whose key was used to encrypt it can recover the signature. Recently, Yang et al. proposed a verifiably encrypted signature scheme and claimed that their scheme was secure without random oracle model. Although their verifiably encrypted signature scheme is more efficient and provably secure in standard model, their security proof of opacity is awed. To overcome this weakness, we revisited this scheme and as a result, our verifiably encrypted signature scheme is more efficient and provably secure in the standard model under the q-SDH assumption.   2010 International Workshop on Mathematical Cryptology Practical and Robust Multi-Party Private Set Intersection Seo, Jaehong (Seoul National University) 2010-08-28   One challenge in privacy-preserving multiparty set operations is to design a protocol with linear complexities for communication and computation. This paper describes a new approach that enables to gain quasi-linear complexities in the input size. We outline technical alternatives to represent user’s dataset using polynomial and to carry out polynomial arithmetics, and show how they help improving practical efficiency, especially, in polynomial arithmetics and zero-knowledge proof. The complexities of our protocols are O(n2k) transmission overhead and O((n+log k)2k+(n+(log k)2)k ) computation overhead for k size dataset, n players, and plaintext domain size of an encryption. Based on these building blocks, we construct a multiparty set intersection (MPSI) protocol and then prove that our construction is secure in the malicious model. Our protocol is robust even when corrupted players leave during the process of the protocol.   2010 International Workshop on Mathematical Cryptology On the Generic Group Model in Pairing-Based Cryptography Hovav Shacham (University of California) 2010-08-27    The so-called generic group model, due to Nechaev, to Shoup, and to Maurer, abstracts away the details of the group operation and of element representation. For many problems of cryptographic interest, it is possible to prove lower bounds in the generic group model on the number of operations performed by algorithm solving the problem; the implication is that any more-efficient algorithm must be non-generic, i.e., make use of the details of the group in which the problem is posed. Since Boneh and Boyen's 2004 paper, the generic group model has been extensively used to gain confidence in hardness assumptions for pairing-based cryptography by demonstrating lower bounds for the associated problems in a generic group equipped with a bilinear map. This use of the generic group model has coincided with growth in the number and baroqueness of hardness assumptions introduced and used in the literature. We recall the generic group model and survey its use in pairing-based cryptography. We then consider some limitations of the generic group model, the most important of which is that the groups used for pairing-based cryptography have substantial special structure that could be exploited by non-generic algorithms. We suggest that the following problem is worth studying: Give a (natural) algebraic problem that is hard in the generic group model but not in (one of) the groups used for pairing-based cryptography.   2010 International Workshop on Mathematical Cryptology A New Approach on Pairings and Functional Encryption Tatsuaki Okamoto (NTT) 2010-08-27    If a cryptographic system is highly functional, it is not easy to design the system and analyze its security. It is a natural strategy to design and analize such a complicated system in a modular way.This talk introduces a type of modular way of design and analysis, hierarchical design and security proof. In our approach, the underlying primitive is bilinear pairing groups, and a higher level of concept, dual pairing vector spaces (DPVS), is constructed on the primitive, where a highly functional crypto system is directly designed over the higher level of concept. In addition, the security proof can be executed in a hierarchical manner.   2010 International Workshop on Mathematical Cryptology A Provable-Security Treatment of Symmetric Encryption Phillip Rogaway (University of California) 2010-08-27    Once a tool only for making quite theoretical claims in cryptography, reductions have become the central tool for the design and analysis of practical, high-assurance cryptographic schemes for intermediate-level primitives. This talk will develop the reduction-based treatment of symmetric (that is, shared-key) encryption. We will explore formalizations for the problem and then means for provably achieving symmetric-encryption goals, assuming the existence of a secure blockcipher   Lecture series on L2-invariants of knots and manifolds L2-signatures and homology cobordism of 3-manifolds Cha, Jaechoon (POSTECH) 2010-08-13     Lecture series on L2-invariants of knots and manifolds Homological L2-invariants of knots and manifolds III Cha, Jaechoon (POSTECH) 2010-08-13     Lecture series on L2-invariants of knots and manifolds Alexander polynomial, L2-signatures, and concordance on knots Kim, Taehee (Konkuk University) 2010-08-12     Lecture series on L2-invariants of knots and manifolds Homological L2-invariants of knots and manifolds II Cha, Jaechoon (POSTECH) 2010-08-12     Lecture series on L2-invariants of knots and manifolds Splitting properties of knot concordance invariants Kim Segoo (Kyunghee University) 2010-08-11     Lecture series on L2-invariants of knots and manifolds Homological L2-invariants of knots and manifolds I Cha, Jaechoon (POSTECH) 2010-08-11     Moduli and Birational Geometry Quasi-admissible hyperelliptic covers with A and D singularities Maksym Fedorchuk (Columbia University) 2010-08-08   Quasi-admissible hyperelliptic covers is a blend of admissible covers of Harris-Mumford and of twisted covers of Abramovich-Corti-Vistoli. We construct moduli spaces of quasi-admissible hyperelliptic covers with at-worst A and D singularities, with dependence on two parameters. The variation of parameters allows to interpolate between moduli stacks of stable limits of A and D singularities and weighted projective spaces. We interpret this variation of stability in terms of the log minimal model program. Finally, we discuss applications to the understanding of birational geometry of the moduli space of DM-stable curves.   Moduli and Birational Geometry Compactified moduli spaces of curves in projective varieties. Kiem, Younghoon (Seoul National University) 2010-08-08   An algebraic curve C in a projective variety X can be viewed as (1) a map C → X, (2) an ideal sheaf Ic of Ox, (3) a coherent sheaf Oc, (4) a curve C together with a line bundle and sections, etc. Different points of view give rise to different compactifications and lead to a variety of compactified moduli spaces and curve counting invariants, via stable map space, Hilbert scheme, stable sheaf space, quasi-map space, stable quotient space, etc. In light of recent interesting conjectures comparing curve counting invariants, there seems to be a strong demand for a comparative study of known compactified moduli spaces.   Moduli and Birational Geometry On geometric interpretation of other toroidal compactifications of the moduli of abelian varieties Valery Alexeev (University of Georgia) 2010-08-08   We begin with the following two facts about toroidal compacti-fications of the moduli space Ag of principally polarized abelian varieties: (1) The second Voronoi compactification has a geometric description as the moduli of stable pairs. (2) The first Voronoi compactification, on the other hand, is the canonical model, assuming g ≥12. In this talk, I will discuss the possibility of giving a geometric interpretation to the first Voronoi compactification, and to other toroidal compactifications of Ag.   Moduli and Birational Geometry Computing alpha-invariants of Tian. Ivan Cheltsov (University of Edinburgh) 2010-08-07   We describe a new local inequality that relates singularities of divisors on surfaces and their multiplicities. We show how to use this inequality to compute an algebraic counterpart of the so-called alpha-invariant of Tian of many del Pezzo orbifolds. This is joint work with Dimitra Kosta.   Moduli and Birational Geometry Fano 3-folds and finite subgroups of the Cremona group of rank 3. Yuri Prokhorov (Moscow State University) 2010-08-07   I will discuss relations between classification of certain singular Fano 3-folds and classical problem of classification of finite subgroups in the space Cremona group.   Moduli and Birational Geometry Exceptional and semi-exceptional quotient singularities. Constantin Shramov (Steklov Institute) 2010-08-06   Exceptional and semi-exceptional quotient singularities are interesting classes of singularities arising from birational geometry. It is known that the most straightforward way to characterize them is via the alphainvariant of Tian. In particular, in the case of quotient singularities the problem boils down to computation of the equivariant alpha-invariant with respect to the corresponding group. These computations appear to be rather interesting on their own, in particular in connection with invariant theory for finite groups. The talk is based on the joint works with I.Cheltsov.   Moduli and Birational Geometry On multiplier ideal sheaves and test configurations on toric Fano manifolds Yuji Sano (Kyushu University) 2010-08-06   It is known that the non-existence of multiplier ideal sheaves (MIS) implies the existence of K¨ahler-Einstein (KE) metrics on Fano manifolds. On the other hand, it is conjectured that the existence of KE metrics would be equivalent to K-polystability introduced by Tian and reformulated by Donaldson. In this talk, I would like to study some properties of MIS on toric Fano manifolds and discuss its relation with test configurations.   Moduli and Birational Geometry Hypertrees and moduli spaces of stable rational curves Ana-Maria Castravet (University of Arizona) 2010-08-06   We construct new exceptional divisors on the Grothendieck-Knudsen moduli space M0,n, of stable rational curves with n marked points, from new combinatorial structures which we call hypertrees. We conjecture that these divisors, together with the boundary, generate the cone of effective divisors of M0,n. This is joint work with Jenia Tevelev.   Moduli and Birational Geometry The birational classification of the universal Jacobian. Gavril Farkas (Humboldt Universit¨at zu Berlin) 2010-08-06   I will discuss joint work with A. Verra in which a classification by Kodaira dimension of the universal Jacobian over the moduli space of curves of genus g is carried out. Thus the universal Jacobian is unirational when g < 10, has Kodaira dimension zero (resp. 19) when g = 10(resp. g = 11), and has Kodaira dimension 3g − 3 when g > 11.   KAIST Discrete Math Seminar Quasi-randomness of graph properties Lee, Choongbum (UCLA) 2010-08-06   Quasi-random graphs can be informally described as graphs whose edge distribution closely resembles that of a random graph. They have been a subject of intensive study during the last two decades and have seen numerous applications both in Combinatorics and Computer Science. Starting with the work of Thomason and Chung, Graham, and Wilson, there have been many works which established the equivalence of various properties of graphs to quasi-randomness. In this talk, I will give a survey on this topic, and provide a new condition which guarantees quasi-randomness. This result answers an open question raised independently by Janson, and Shapira and Yuster.   Moduli and Birational Geometry Vector bundles of conformal blocks on $bar M_{0,n}$ for sln, level 1 David Swinarski (University of Georgia) 2010-08-05   The WZW model of conformal field theory yields a vector bundle on the moduli space of pointed curves Mg,n depending on a choice of a Lie algebra, a level, and a set of n weights in the corresponding Weyl alcove. Recently Fakhruddin gave formulas for the Chern classes of these bundles when g = 0 and showed they are globally generated. I will discuss recent joint work with Arap, Giansiracusa, Gibney, and Stankewicz showing that some of these vector bundles are extremal in the nef cone, and identify the images of the linear systems corresponding to these divisors.   Moduli and Birational Geometry Detaching embedded points Dawei Chen (University of Illinois at Chicago) 2010-08-05   Let D consist of a lci subscheme C with an embedded point of multiplicity m. When can D be a flat limit of C union m isolated points? We discuss this question along with various examples. This is a joint work with Scott Nollet.   Moduli and Birational Geometry Conformal Blocks Divisors on M0,n from sl2 Angela Gibney (University of Georgia) 2010-08-05     Moduli and Birational Geometry Three dimensional Q-conic bundles and related topics. Shigefumi Mori (RIMS & Kyoto University) 2010-08-05   We survey our results on three dimensional extremal contractions,especially Q-conic bundle contractions f from threefold X with only terminal singularities to normal surface Y whose anti-canonical divisor −KX is fample. The core of our joint work is the on-going project to classify analytic structures of three dimensional Q-conic bundles. It has been proved that Y has only Du Val singularities (the solution to Iskovskikh’s conjecture), and the analytic structures of f over arbitrary singular points of Y have been explicitly classified.   2010 Summer Workshop for Young Mathematicians in Korea Introduction to finite element method Jin, Sangwon (KAIST) 2010-08-04     2010 Summer Workshop for Young Mathematicians in Korea Introduction to Knot theory Kim, Minhoon (POSTECH) 2010-08-04    We will discuss introductory knot theory. We will study about Reidemeister moves, Seifert surface, intersection form, Seifert form, Alexander polynomial and some detailed examples.   2010 Summer Workshop for Young Mathematicians in Korea Intoduction to moduli spaces Moon, Hanbom (Seoul National University) 2010-08-04    In algebraic geometry, a moduli space is a space whose points represent certain algebro-geometric objects. Frequently, a moduli space itself has a algebro-geometric space such as variety, scheme or stack. In this talk, we introduce the notion of moduli spaces, and discuss several reasons why many mathematicians study moduli spaces.   2010 Summer Workshop for Young Mathematicians in Korea Stochastic calculus, application of real analysis in finance Lee, Seungkyu (POSTECH) 2010-08-04    In various fields of pure or social science, including life science and finance, many mathematical tools are used to explain randomness in nature. The direction of movement of molecular particles and stock prices is unpredictable, or not deterministic. In 1905, Einstein firstly formulate the movement of molecules, Brownian movement or motion, which was qualitatively introduced by Brown in 1827, and Wiener made a great contribution in the field of stochastic calculus by finding many mathematical properties of Brownian motion. Since Bachelier found that the price movement in Paris stock market is similar to that of pollen suspended on water surface and Ito founded calculus for Brownian motion, stochastic calculus has been widely used in finance. In this presentation, I’ll explain how the mathematical system of stochastic calculus was established by those frontiers in the point of view of real analysis. My presentation won’t be so difficult to all graduate and even undergraduate students who took a real analysis course. At the end of my presentation, I’ll briefly introduce main results of my recent research which is about American option pricing.   제 3회 Topology Workshop Real Bott manifolds and acyclic digraphs Choi, Suyoung (Osaka City University) 2010-08-04   A real Bott manifold is a closed smooth manifold obtained as the total space of an iterated RP^1-bundles starting with a point, where each RP^1-bundle is the projectivization of the Whitney sum of two real line bundles. The diffeomorphism types of real Bott manifolds can be completely characterized in terms of three simple matrix operations on square binary matrices symmetrically permutable to strict upper triangular form. This characterization can be visualized combinatorially in terms of graph operations on directed acyclic graphs. Using this combinatorial interpretation, we prove that the decomposition of a real Bott manifold into a product of indecomposable real Bott manifolds is unique up to permutations of the indecomposable factors, and prove that the toral rank conjecture holds for almost free torus action on real Bott manifolds.   제 3회 Topology Workshop Quantum homotopy theory II Park, Jaesuk (Yonsei University) 2010-08-04   Physicists assume that the physical reality is governed by quantum principle such that any classical physical entity is just an approximated or derived notion. In this philosophy the essential properties of classical world should have quantum origin and, thus, be explained via quantum prospective. The similar viewpoint could be adapted, and may proved to be useful, to study certain mathematical structure, provided that it can be described by the mathematics of certain classical physics admitting certain mathematically well-defined quantization. In this lecture homotopy theory shall be such an example.   제 3회 Topology Workshop Quantum homotopy theory I Park, Jaesuk (Yonsei University) 2010-08-04   Physicists assume that the physical reality is governed by quantum principle such that any classical physical entity is just an approximated or derived notion. In this philosophy the essential properties of classical world should have quantum origin and, thus, be explained via quantum prospective. The similar viewpoint could be adapted, and may proved to be useful, to study certain mathematical structure, provided that it can be described by the mathematics of certain classical physics admitting certain mathematically well-defined quantization. In this lecture homotopy theory shall be such an example.   제 3회 Topology Workshop An Introduction to ASD instantons and holomorphic Structures. Byun, Yanghyun (Hanyang University) 2010-08-04   이 강의는 connection의 정의로부터 출발하여 ASD 인스탄톤을 소개하는 것으로부터 시작한다. 이어서 복소다양체 위의 complex 벡터 번들의 holomorphic 구조를 partial connection이라는 도구를 통해 소개하고, 2차원 Kahler 다양체 위에서 ASD 인스탄톤과 holomorphic 구조와의 관계를 소개함으로써 이 강의가 목표로 하는 기본지식의 소개를 마친다. 강의의 맺음말은 최근에 수학자들이 관심을 두고 있는 이 분야의 문제를 하나 소개하는 것으로 한다.   제 3회 Topology Workshop Introduction to the theory of bounded cohomology Park, Heesook (KAIST) 2010-08-04   We introduce the theory of bounded cohomology and compare it with ordinary cohomology. We also investigate some known facts on bounded cohomology.   제 3회 Topology Workshop Homotopy theoretic view point of based loop space and free loop space. Choi, Younggi (Seoul National University) 2010-08-04   The relationship between the closed geodesic of compact Riemannian manifold M and the homology of the loop spaces of ¬M was developed by Marston Morse around 1930. Ever since it has become the main topic in the algebraic topology. The purpose of this talk is to discuss the (co)homology and the homotopy type of based loop space and free loop space of compact Lie groups and homogeneous spaces.   제 3회 Topology Workshop Yokota theory on ideal triangulation and volume of hyperbolic knot. Kim, Sunhwa (Seoul National University) 2010-08-04     제 3회 Topology Workshop Maurer-Cartan equation Kim, Donghui (Yonsei University) 2010-08-04     제 3회 Topology Workshop Three-fold branched covering spaces over a disk Kim, Byungchun (Inha University) 2010-08-04     2010 Summer Workshop for Young Mathematicians in Korea Iwasawa theory for elliptic curves Kim, Dohyung (POSTECH) 2010-08-03   The Birch and Swinnerton-Dyer(BSD) conjecture is one of the central open problems in number theory. It asserts that the rank of an elliptic curve defined over rationals must be the same as the order of vanishing at s=1 of the L-function associated to the curve. The aim of my talk is to explain the Birch and Swinnerton-Dyer conjecture and its p-adic analogue.   2010 Summer Workshop for Young Mathematicians in Korea Model theory and o-minimal structures Lee, Junguk (Yonsei University) 2010-08-03    In this talk, we will introduce basic notions for model theory, 1st order language, formulas, and structures. And we will introduce o-minimal structures where any unary definable set is a union of finite intervals and points. At last, we study about the real number field with exponential function.   제 3회 Topology Workshop Non-positively curved groups I,II Kim, Sanghyun (KAIST) 2010-08-03    We will survey applications of non-positive curvature to group theory. The first lecture will deal with the geometry of non-positively curved spaces; this includes Cartan--Hadamard theorem, π1-injectivity and Gromov's criteria for non-positive curvature of metric cell complexes. The second lecture will have more group theoretic questions in mind. As a key example of non-positively curved groups, we study right-angled Artin groups (RAAGs). Using techniques developed in the first lecture, we will investigate hyperbolic 2- and 3-manifold subgroups in RAAGs.   제 3회 Topology Workshop Lefschetz fibration and symplectic 4-manifolds Yun, Kiheon (Sungshin Women's University) 2010-08-03   Lefschetz fibration과 symplectic 4-manifold의 관계를 살펴본 후, Lefschetz fibration을 이용하여 4차원 위상수학에서 얻은 결과들을 소개한다.   제 3회 Topology Workshop Orbibundle and Multisection Cho, Cheolhyun (Seoul National University) 2010-08-03   Euler class of a vector bundle can be given by the zero set of a generic (transversal) section. Multisections were introduced to resolve transversality issues for orbifold vector bundles, as the equivariancy and transversality cannot be satisfied at the same time in many cases. We give a basic introduction to these notions.   제 3회 Topology Workshop Homological vector fields and algebraic structures Cho, Cheolhyun (Seoul National University) 2010-08-03   Algebraic structures such as associative algebras, Lie algebras and their modules is known to correspond to certain vector fields Q with the property [Q,Q]=0. In fact, such framework provide naturally generalized notions such as homotopy algebras, Lie algebroids and so on. We give an elementary introduction of such correspondence. If time remains, the relation between the de Rham theory and homology theories of these algebraic structures such as Hochschild or Chevalley-Eilenberg homology theory will be explained.   2010 Summer Workshop for Young Mathematicians in Korea Introduction to affine processes and its applications to mathematical finance Kang, Chulmin (KAIST) 2010-08-02    The aim of this talk is to introduce the affine processes which is important in the modelling of short rates, default intensities, and stochastic volatilities. Importance of the affine processes comes from the analytic tractability, nonnegativity, and the mean-reverting property. In this talk, I will focus mainly on the analytic tractability of affine processes. In general, the characteristic functions of affine processes can be obtained by solving the generalized Ricatti differential equation, and in some special cases the equation admits closed form solution. Using the characteristic function, one can easily compute the price of various options including bond derivatives, quantos, foreign bond options, and chooser options . If time permits, we will discuss recent development of affine processes on positive semi-definite matrices.   2010 Summer Workshop for Young Mathematicians in Korea Fourier restriction conjecture and its interplay with geometric measure theory : the Kakeya conjecture Bae, Joonsik (POSTECH) 2010-08-02   When can we estimates the "size" of fourier transform of a function in terms of "the" function? It is a basic question in analysis. As you know, there is an well-known inequality : Housdorff-Young inequality. But, what will happen if we restrict the space to a hypersurface instead of $R^n$? This is the Fourier restriction conjecture. In fact, Fourier transform has amazing relationships with the Kakeya set - a compact set in $R^n$ which contains unit lines in every direction. It seems that there is no relationship between them at all !! I will talk about the Fourier restriction conjecture mostly, which is one of the most famous problem in harmonic anlaysis, and introduce you some consequence about the relationship between the Fourier restriction conjecture and the Kakeya conjecture(All Kakeya set in n-dimensional Euclidean space have Hausdorff dimension n).   2010 Summer Workshop for Young Mathematicians in Korea Contemporary cryptography introduction Kim, Myungsun (Seoul National University) 2010-08-02   We briefly introduce the notion of public key cryptography as well as various intractability assumptions. The introduction includes RSA and ElGamal encryption and signature schemes as a toy example. Then we turn into our current research topic: computation on encrypted data. For convenience, without any mathematical notation we explain the concept, the notion and some business scenarios for the problem.   KAIST Discrete Math Seminar The uplift principle and the Riordan group Lou Shapiro (Howard University) 2010-07-23   The Riordan group is an easy yet powerful tool for looking at a large number of results in combinatorial enumeration. At the first level it provides quick proofs for many binomial identities as well as a systematic way to invert them. We will see how they arise naturally when looking at the uplift principle as applied to classes of ordered trees. We will also discuss some recent results including the Double Riordan group, summer – winter trees, spoiled child trees, and will mention a few open problems as well. The main tools involved are generating functions, matrix multiplication, and elementary group theory.

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