Jae Choon CHA

Teaching

2010 Spring

2009 Fall	POSTECH	MATH 120 Applied Linear Algebra
2009 Fall	POSTECH	MATH 524 Introduction to Algebraic Topology
2009 Spring	POSTECH	MATH 324 Introduction to Geometry
2008 Fall	POSTECH	MATH 608 Homological Algebra
2008 Fall	POSTECH	MATH 624 Algebraic Topology
2008 Spring	POSTECH	MATH 421 General Topology
2007 Fall	POSTECH	MATH 502 Algebra II (Graduate Course)
2007 Spring	ICU	ICE0100 Calculus I
2006 Fall	ICU	ICE0114 Calculus II
2006 Fall	ICU	ICE1210 Algorithm Design and Analysis
2006 Spring	ICU	ICE0100 Calculus I
2005 Fall	ICU	ICE1201 Discrete Mathematics II
2005 Fall	ICU	ICE1210 Algorithm Design and Analysis
2005 Spring	ICU	ICE0100 Calculus
2004 Fall	ICU	ICE1210 Algorithm Design and Analysis
2004 Spring	ICU	ITB0100 Calculus
2004 Winter	ICU	ICE0121 Programming Fundamentals I
2003 Fall	ICU	ICE0121 Programming Fundamentals I
2003 Fall	ICU	ICE0123 Programming Fundamentals II
2003 Summer	Indiana University	M118 Finite Mathematics (course coordinator)
2003 Spring	Indiana University	M118 Finite Mathematics
2001 Fall	KAIST	MA111 Introduction to Linear Algebra
2001 Spring	KAIST	MA531 Algebraic Topology I
2000 Fall	KAIST	MA102 Calculus II

[Show previous semesters]

Research Interest: Geometric Topology

Knot theory: placement problems of manifold pairs
Topology of low dimensional manifolds
Related algebra and homotopy theory

KnotInfo: a table of invariants of classical knots, maintained by Charles Livingston and me.

<New!> Special Session on Knot Theory and Related Topics, Joint meeting of the Korean Mathematical Society and the American Mathematical Society, December 16-20, 2009. (For the official web site of the joint meeting, click here.)

Research Papers

Jae Choon Cha and Stefan Friedl, Twisted torsion invariants and link concordance, arXiv:1001.0926 (26 pages).

Jae Choon Cha and Kent E. Orr, L²-signatures, homology localization, and amenable groups, arXiv:0910.3700 (33 pages).

Jae Choon Cha, Stefan Friedl, and Taehee Kim, The cobordism group of homology cylinders, arXiv:0909.5580 (27 pages).

Jae Choon Cha, Link concordance, homology cobordism, and Hirzebruch-type defects from iterated p-covers, to appear in the Journal of the European Mathematical Society.
An earlier version is available from arXiv:0705.0088 (48 pages).

Jae Choon Cha, Structure of the string link concordance group and Hirzebruch-type invariants, Indiana University Mathematics Journal 58 (2009), 891-928.
Available from IUMJ home page. An earlier version is available from arXiv:0709.2968.

Jae Choon Cha and Taehee Kim, Covering link calculus and iterated Bing doubles, Geometry and Topology 12 (2008), 2173-2201.
Available from G&T home page. An earlier version is available from arXiv:0712.3762.
Jae Choon Cha, Topological minimal genus and L²-signatures, Algebraic and Geometric Topology 8 (2008), 885-909.
Available from AGT home page. An earlier version is available from arXiv:math.GT/0609411.
Jae Choon Cha, Charles Livingston, and Daniel Ruberman, Algebraic and Heegaard-Floer invariants of knots with slice Bing doubles, Mathematical Proceedings of the Cambridge Philosophical Society 144 (2008), 403-410.
Available from Cambridge Journals Online. An earlier version is available from arXiv:math.GT/0612419.
Jae Choon Cha, Injectivity theorems and algebraic closures with coefficients, Proceedings of the London Mathematical Society 96 (2008), no. 1, 227-250.
Available from Oxford Journals home page. An earlier version is available from arXiv:math.GT/0609409.
Jae Choon Cha, The structure of the rational concordance group of knots, Memoirs of the American Mathematical Society 189 (2007), no. 885, x+95pp.
A Preview is available from Google Books. An earlier version is available from arXiv:math.GT/0609408.
Jae Choon Cha and Ki Hyoung Ko, Signature invariants of covering links, Transactions of the American Mathematical Society 358 (2006), 3399-3412.
Available from AMS Journal home page. An earlier version is available from arXiv:math.GT/0108206.
Jae Choon Cha, The effect of mutation on link concordance, 3-manifolds, and the Milnor invariants, Journal of Knot Theory and Its Ramifications 15 (2006), no. 2, 239-257.
Available from JKTR home page. An earlier version is available from arXiv:math.GT/0109134.
Jae Choon Cha and Charles Livingston, Knot signature functions are independent, Proceedings of the American Mathematical Society 132 (2004), 2809-2816.
Available from AMS Journal home page. An earlier version is available from arXiv:math.GT/0208225.
Jae Choon Cha, Fibred knots and twisted Alexander invariants, Transactions of the American Mathematical Society 355 (2003), 4187-4200.
Available from AMS Journal home page. An earlier version is available from arXiv:math.GT/0109136.
Jae Choon Cha and Ki Hyoung Ko, Signatures of links in rational homology spheres, Topology 41 (2002), 1161-1182.
Available from ScienceDirect (license required for full text). An earlier version is available from arXiv:math.GT/0108197.
Jae Choon Cha and Ki Hyoung Ko, On equivariant slice knots, Proceedings of the American Mathematical Society (1999) 127, no. 7, 2175-2182.
Available from AMS Journal home page.
Jae Choon Cha and Ki Hyoung Ko, Signature invariants of links from irregular covers and non-abelian covers, Mathematical Proceedings of the Cambridge Philosophical Society (1999) 127, 67-81.
Available from Cambridge Journals Online (license required for full text).
Jae Choon Cha and Jung Hee Cheon, An identity-based signature from gap Diffie-Hellman groups, PKC 2003, Lecture Notes in Computer Science 2567 (2002), pp. 18-30.
Jae Choon Cha, Ki Hyoung Ko, Sang Jin Lee, Jae Woo Han, and Jung Hee Cheon, An efficient implementation of braid groups, Asiacrypt 2001, Lecture Notes in Computer Science 2248 (2001), pp. 157-174.

Preprints

Jae Choon Cha and Charles Livingston, Unknown values in the table of knots, arXiv:math.GT/0503125. 7 pages.
Jae Choon Cha, A characterization of the Murasugi polynomial of an equivariant slice knot, arXiv:math.GT/0404403, 4 pages.

Papers in Preparation

Jae Choon Cha and Taehee Kim, Rasmussen invariants and link concordance.

[Show more]

Talks

Homology and L²-signatures from amenable groups, The 6th East Asian School of Knots and Related Topics, January 27, 2010, Chern Institute of Mathematics, Tianjin, China.
L²-signature defects and amenable groups, Special Session on Knot Theory and Related Topics, Joint Meeting of the Korean Mathematical Society and the American Mathematical Society, December 18, 2009, Seoul, Korea.
L²-signatures, homology, and amenable groups, International Conference on Symplectic, Contact and Low Dimensional Topology, November 12, 2009, Seoul, Korea.
Links in dimension 3 and their deformation in dimension 4, Chonbuk National University, September 24, 2009, Jeonju, Korea.
Torsion in link concordance and Hirzebruch-type invariants from iterated p-covers, Canadian Mathematical Society Summer Meeting, June 7, 2009, St. John's, Newfoundland, Canada.

Links and intersection form defects, Mathematical Colloquium, Seoul National University, May 14, 2009, Seoul, Korea.
The structure of the rational concordance group of knots, Excellent Research Paper Award Lecture, 2009 Spring Meeting of the Korean Mathematical Society, April 25, 2009, Suwon, Korea.
Links in 3-space and their deformation in 4-space, Mathematical Colloquium, Yonsei University, April 9, 2009, Seoul, Korea.
Local derived series, L2-signatures, and applications to manifolds, The 5th East Asian School of Knots and Related Topics, January 13, 2009, Gyeongju, Korea.
Using Artin reciprocity in knot theory, Kyushu-POSTECH joint workshop on number theory and related topics, January 6, 2009, Pohang, Korea.
Deformation of links in dimension 4, Mathematical Colloquium, Chungang University, November 21, 2008, Seoul, Korea.
4-dimensional deformation of links in the 3-space, Mathematical Colloquium, Sogang University, October 9, 2008, Seoul, Korea.
Slicing and non-slicing iterated Bing doubles, Topology-Geometry Seminar, Indiana University, August 26, 2008, Bloomington, Indiana, USA.
Link concordance, homology cobordism, and iterated p-covers, Fifty years since Fox and Milnor: a conference on knot concordance in honor of the memory of Jerry Levine, Brandeis University, June 3, 2008, Waltham, Massachusetts, USA.
Link concordance and Hirzebruch-type invariants from iterated covers, Pusan Nation University, April 18, 2008, Pusan, Korea.
Slicing iterated Bing doubles, a plenary talk at The 4th East Asian School of Knots and Related Topics, January 21, 2008, Tokyo, Japan.
Non-slice iterated Bing doubles, Topology Seminar, UC Berkeley, November 14, 2007, Berkeley, California, USA.
Homology, injectivity theorems, and algebraic closures with coefficients, East Asian Conference of Algebraic Topology, November 3, 2007, Seoul, Korea.
New Hirzebruch-type invariants from iterated p-covers, The 7th KAIST Geometric Topology Fair, July 9, 2007, Gyeongju, Korea.
An elementary tutorial on provable security, KIAS-KMS Summer workshop on Cryptography, June 29, 2007, Seoul, Korea.
Invariants of homology cobordism and link concordance from towers of itrated abelian p-covers, Geometric Topology Conference, Peking University, June 19, 2007, Beijing, China.
The structure of the rational knot concordance group, Department of Mathematics, POSTECH, May 23, 2007, Pohang, Korea.
Introduction to Geometric Topology and Knot Theory, Departmental Colloquium, Department of Mathematics, Konkuk University, April 13, 2007, Seoul, Korea.
Hirzebruch-Atiyah-Singer type invariants of manifolds and applications to knot theory, Department of Mathematics, Ewha Womans University, March 30, 2007, Seoul, Korea.
Witt class defect invariants, homology cobordism, and link concordance, a talk at The Third East Asian School of Knots and Related Topics in Geometric Topology, February 6, 2007, Osaka, Japan.
Classifications of manifold embeddings, Mathematical Colloquium, Korea Institute for Advanced Study, November 22, Seoul, Korea.
Invariants from Atiyah-type theorems and applications to links, an invited talk at 2006 Geometry & Topology Day at Konkuk University, November 18, 2006, Seoul, Korea.
Homology equivalences, injectivity theorems, and algebraic closures of groups, an invited talk at NIMS Workshop on Geometry and Topology, November 16, 2006, Daejeon, Korea.
The structure of the concordance group of knots in rational homology spheres, an invited talk at 2005 fall meeting of the Korean Mathematical Society, 21 October, 2005, Seoul, Korea.
Algebraic closures with coefficients and torsion-free derived series, a plenary talk at The Second East Asian School of Knots and Related Topics in Geometric Topology, August 4, 2005, Dalian, China.
Algebraic closures with coefficients and applications to homology cobordism, January 31, 2005, Department of Mathematics, Rice University, Houston, Texas, U.S.A.
Homology equivalences and algebraic closures, January 24, 2005, Department of Mathematics, Indiana University, Bloomington, Indiana, U.S.A.
Classification of knots from the viewpoint of manifold theory, November 25, 2004, Department of Mathematics, Konkuk University, Seoul, Korea.
Classification of knots from the viewpoint of manifold theory, November 4, 2004, Department of Mathematics, Ewha Womans University, Seoul, Korea.
Torsion-free derived series, algebraic closures, and link concordance, The First KAIST Geometric Topology Fair, August 25, 2004, Chungju, Korea.
Randomized computation and provable security I, II, Korea Institute for Advanced Study, August 6-7, 2004, Seoul, Korea.
Rational homology concordance of knots, BIRS Workshop on Knots and Their Manifold Stories, May 11, 2004, Banff, Alberta, Canada.
Provable security of ID-based cryptosystems, National Security Research Institute, March 11, 2004, Daejeon, Korea.
Concordance of knots in rational homology spheres, The First East Asian School of Knots, Links, and Related Topics, February 17, 2004, Seoul, Korea.
Localization, surgery and placement problems of manifolds, Departmental Colloquium, Department of Mathematics, Korea Advanced Institute of Science and Technology, December 4, 2003, Daejeon, Korea.
Concordance and rational knots, Korea Advanced Institute of Science and Technology, March 27-28, 2003, Daejeon, Korea.
The structure of the rational knot concordance group, AMS special session, March 14, 2003, Baton Rouge, Louisiana, U.S.A.
The effect of mutation on link concordance, 3-manifolds, and the Milnor invariants, AMS special session, January 17, 2003, Baltimore, Maryland, U.S.A.
Concordance and rational knots, Knots in Washington XV, January 10, 2003, Washington, DC, U.S.A.
Computation of rational knot concordance, October 8, 2002, Brandeis University, Waltham, Massachusetts, U.S.A.
A survey on link concordance, January 15, 2002, Nara Women's University, Nara, Japan.
Implementations of braid cryptosystems, An invited tutorial in International Workshop on Practice and Theory in Public Key Cryptography, February 13, 2001, Cheju, Korea
Link concordance theory in rational homology spheres and its application to concordance of homology boundary links, KNOTS 2000, August 2, 2000, YoungPyong, Kangwon, Korea.