Ki Hyoung Ko

Professor of Mathematics

Korea Advanced Institute of Science and Technology

Contact

Email knot@knot.kaist.ac.kr
Phone +82-42-350-2719 (Office)
+82-11-450-3184 (Mobile)
+82-42-350-5719 (Fax)
Address Department of Mathematics
Korea Advanced Institute of Science and Technology
Daejeon, 305-701, Korea
Office 4408 Natural Sciences Building
Office Hour Mon 10:00 - 12:00 am, or by appointment

Teaching

Fall, 2009

MAS102 Calculus II

I am coordinating this course and here is the first-day handout. Lectures are given in English. Lecture notes can be downloaded from here.

Spring, 2010

MAS331 Topology

Here is the first-day handout. Lectures are given in English. Weekly lecture notes will be available from here.

MAS101 Calculus I

I am coordinating this course and here is the first-day handout. Lectures are given in English. Weekly lecture notes will be available from here.

Research

Interest

Theory of Knots and Braids, 3-Manifolds, Cryptography based on Non-commutativity, Digital Right Management, Tamper-Resistant Software
 

Articles via search engines

MathSciNet Author = Ko, Ki Hyoung (valid where MathSci is available)
Google Scholar Author = KH KO or KIH KO
arXiv Author=Ki Hyoung Ko or K. H. Ko
Cryptology ePrint Archive Author=Ki Hyoung Ko
 

Selected articles

  • "Seifert Matrices and Boundary Link Cobordisms", Trans. Amer. Math. Soc. 299 (1987) 657-681.

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  • "Triple Points of Immersed Surfaces in Three Dimensional Manifolds", Topology Appl. 32 (1989) 149-159. (with Scott Carter)

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  • "A Seifert-Matrix Interpretation of Cappell and Shaneson's Approach to Link Cobordism", Math. Proc. Camb. Phil. Soc. 106 (1989) 531-545.

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  • "A Combinatorial Matrix in 3-manifold theory", Pacific J. Math. 149 (1991) 319-336. (with Lawrence Smolinsky)

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  • "Boundary Links and Mutations", Canadian Math. Bull. 35 (1992) 376-380. (with Gyo Taek Jin)

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  • "The Framed Braid Group and 3-manifolds", Proc. Amer. Math. Soc. 115 (1992) 541-551. (with Lawrence Smolinsky)

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  • "The Framed Braid Group and Representations", Knots 90 (1992) 289-297. (with Lawrence Smolinsky)

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  • "Adepuate Linds and the Jones Polynomial of Unlinks", Knots 90 (1992) 185-193. (with G. T. Jin; B. B. Kim)

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  • "Band-generator presentation of 4-braid group", Topology Appl. 78 (1997) 39-60. (with E. S. Kang, S. J. Lee)

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  • Genera of some closed 4-braids, Topology Appl. 78 (1997) 61-77. (with S. J. Lee)

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  • "A new approach to the word and conjugacy problems in the braid groups", Adv. Math. 139 (1998) 322-353 (with J. Birman, S. J. Lee)

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  • "On equivariant slice knots", Proc. Amer. Math. Soc. 127 (1999) 2175-2182 (with J. C. Cha)

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  • "Signature Invariants of Links from Irregular Covers and Non-abelian Covers", Math. Proc. Camb. Phil. Soc. 127 (1999) 67-83 (with J. C. Cha)

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  • "New public-key cryptosystem using braid groups", Advances in Cryptology-CRYPTO 2000, LNCS Vol. 1880, Springer-Verlag (2000) 166 - 183 (with 5 others)

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  • "Positive presentations of the braid groups and the embedding problem", Mathematische Zeitschrift, 240 (2002) 211 - 232 (with J. W. Han)

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  • "The infimum, supremum and geodesic length of a braid conjugacy class", Advances in Mathematics, 146 (2001) 41-56 (with J. Birman, S. J. Lee)

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  • "An Efficient Implementation of Braid Groups", Advances in Cryptology-Asiacrypt 2001, LNCS Vol. 2248, Springer-Verlag (2001) 144 - 156 (with 3 others)

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  • "Entropies of braids", Journal of Knot Theory and Its Ramifications, 11 (2002) 647-666 (with J. Los and W. T. Song)

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  • "Signatures of links in rational homology spheres", Topology, 41 (2002) 1161-1182 (with J. C. Cha)

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  • "Parametrizations of 1-bridge torus knots", Journal of Knot Theory and Its Ramifications, 12 (2003) 463-491 (with D. H. Choi)

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  • "Signature Invariants of Covering Links", Transactions of the American Mathematical Society, 358 (2006) 3399-3412 (with J. C. Cha)

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  • "Seifert Matrices of Periodic Knots", Journal of Knot Theory and Its Ramifications, 16 (2007) 45-57 (with W. T. Song)

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  • "Towards Generating Secure Keys for Braid Cryptography", Designs, Codes and Cryptography, to appear (with J. W. Lee and T. Thomas)


    • Projects

    Research related

  • Decision Problems in the braid groups:Combinatorial and dynamical approaches
    		•  1/4/1999 - 31/3/2000 KOSEF
  • Braid Groups and Link Problems
    		•  1/12/1998 - 30/11/1999 KRF
  • Development of One-way Functions for Public-key Cryptosystems
    		•  4/1/1999 - 30/11/1999 ETRI
  • Research Team on Manifolds and Topology (BK21)
    		•  1/9/1999 - 31/8/2002 KRF
  • Mapping Classes of Low Dimensional Manifolds and Classical Knot Invariants
    		•  8/1/2002 - 31/7/2005 KRF
  • Study of 3-Manifolds and Knots via Structures of Group and Geometry
    		•  3/1/2006 - 2/28/2009 KOSEF

    TeX related

  • Public Domain Korean TeX
    		•  9/1990 - 8/1994
  • Korean TeX for Windows
    		•  9/1994 - 8/1995 Hangul and Compter Corp.
  • Probank - Educational DBMS
    		•  3/1994 - 12/1994 Cemtlomedia Corp.
  • Development of Unicode TeX
    		•  1/4/1999 - 30/11/1999 Minstry of Culture

    Book

  • Hangul and TeX (ISBN 89-7088-637-0), Chung Moon Gak, 1995
  • Knot Theory (ISBN 89-374-3624-8), Daewoo Academic Book Series, 1998


    • Activities

  • Advisor of Msquare, the student mathematics club in KAIST established in 1988 who publishes a monthly mathematical magazine "Math Letter"
  • Advisor of Cemtlomedia Corp., a software company that makes "TeXplus".

    • ©1999-2004 Ki Hyoung Ko. All rights reserved.       Last Update: February 25, 2004