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

Spring, 2011

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.
 

Fall, 2011

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.
 

Research

Interest

Theory of Knots and Braids, Geometric Group Theory, Braid Cryptography
 

PhD Students

Mathematics Genealogy id=36808
 

Articles via search engines

MathSciNet Author = Ko, Ki Hyoung (valid where MathSci is available)
Google Scholar Author = KH 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, 45 (2007) 317-333 (with J. W. Lee and T. Thomas)

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  • "A family of representations of braid groups on surfaces", Pacific J. Math., 247 (2010) 257-282 (with Byung Hee An)

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  • "Graph braid groups and right-angled Artin groups", Trans. Amer. Math. Soc., 364 (2012) 309-360 (with Jee Hyoun Kim and Hyo Won Park)

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  • "Characteristics of graph braid groups ", Discrete & Computational Geometry, 48 (2012) 915-963 (with Hyo Won Park)

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  • "A family of pseudo-Anosov braids with large conjugacy invariant sets ", Journal of Knot Theory and Its Ramifications (with Byung Hee An)


  • 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