Research

Index   Teaching  Links

Conferences and Workshop  Talks Preprints Selected Publications Books Travel Plans

Reviews

Graduate student homepage : Their research papers, presentations, and so on and our workshops.

Currently I am looking for graduate and undergraduate students to work towards Master's degrees and/or Ph.D. degrees.
Foreign students can also apply for Ph.D. degrees with me if they have finished the BA or MA programs in mathematics and related fields.
However, there are very limited support that I can provide. In Republic of Korea, the university admission rules are very strict and hence must be very accurate.
They should follow the procedures of
the Office of Admissions of KAIST.


Conferences and workshops: organizations (more in Graduate student homepage)

JNU-KAIST Geometric Topology Fair, (June 12-16, 2017) Jeju National Univ, South Korea

Geometric Structures and Character Varieties, (December 28-30, 2015) Jeju National University, South Korea

Workshop on Geometric Structures, Hitchin Components and Representation Varieties, (October 20 - 24, 2015) KIAS, Seoul, Korea

 ICM 2014 Satellite Conference: Geometry on Groups and Spaces, (August 7 – 12, 2014) KAIST(Daejeon) Videos of invited talks is available here.

The 11th KAIST Geometric Topology Fair, August 12 - 6, Jeonju, Korea  

The 10th KAIST Geometric Topology Fair, Daejeon, August 13-17, 2012


Selected Talks

Deformations of convex real projective structures on orbifolds, AMS-TIMC joint meeting, Banaras Hindu University (December 16, 2016)

Tropical computational experiments with compactifications of the deformation spaces of convex real projective structures on 2-orbifolds and surfaces, Avignon talk, Feb 23, 2016 (Here I show that the compactification dimension always collapses. The talk I gave in GMU August 2015 was not correct in this part.)

The deformation spaces of convex real projective structures on manifolds or orbifolds with ends: openness and closedness, Topology seminar, UCSB (June 9, 2015) Geometry/Topology Seminar UC Davis (May 14 2015)

The ends of convex real projective manifolds and orbifolds, Geometry/Topology Seminar UC Davis (April 28, 2015)

An introduction to convex real projective manifolds (orbifolds), Univ. Texas Pan American (January 30, 2014)

Deforming convex RP3-structures on 3-orbifolds, Boston University, October 23, 2012, Ohio State University October 25, 2012

The topological and geometrical finiteness of complete flat Lorentzian 3-manifolds with free fundamental groups, October 16, 2012, CRM, Montreal

Deforming convex real projective 3-orbifolds, March 17, 2011, Oxford University, MOS Newton Institute Workshop

 

Spherical triangles and the two components of the SO(3)-character space of the fundamental group of a closed surface of genus 2, A talk at a workshop in IMA, NUS Singapore July, 2010

A NIMS-KIAS workshop Hyperbolic geometry: algorithmic, number theoretic and numerical aspects, (A graduate student workshop ) March 15-19, 2010 at KIAS, Seoul. Notes of my talk.

Real projective structures on 3-orbifolds and projective invariants, Melbourne Talk, May 18, 2009

A survey of projective structures on 2-,3-manifolds, (Colloquium, October 1, 2008, Tokyo Institute of Technology)


Preprints

Tameness of Margulis space-times with parabolics, (with Todd Drumm, William Goldman) in preparations.

Convex projective generalized Dehn fillings,
(with Suhyoung Choi, Gye-seon Lee, And Ludovic Marquis) arXiv:1611.02505

Deformations of convex real projective structures on manifolds and orbifolds,
(with Gye-Seon Lee, Ludovic Marquis) arXiv:1605.02548, to appear in the Handbook of Group Actions, (L. Ji, A. Papadopoulos, S.-T. Yau, eds.) Higher Education Press and International Press, Boston

The following articles will be combined into a monograph to be written. The working title is:
"RPn-orbifolds with ends and their deformation spaces":

Convex real projective orbifolds with radial or totally geodesic ends: a survey of some partial results, Contemp. Math. 696 (2017), 51- 86. arXiv:1601.06952

A classification of radial and totally geodesic ends of properly convex real projective orbifolds III: the convex but nonproperly convex and non-complete-affine radial ends, arXiv:1507.00809

The classification of ends of properly convex real projective orbifolds II: Properly convex radial ends and totally geodesic ends, arXiv:1501.00352

A classification of radial or totally geodesic ends of real projective orbifolds I: a survey of results, arXiv:1501.00348, to appear in the Advanced Studies in Pure Mathematics, MSJ, Tokyo, Japan.

The convex real projective orbifolds with radial or totally geodesic  ends: The closedness and openness of deformations, arXiv 1011.1060A mathematica file for developing map graphics. 

Convex and concave decompositions of affine 3-manifolds, arXiv:1411.1273.

 

The PL-methods for hyperbolic 3-manifolds to prove tameness, February, 2006


Selected Publications

Topological tameness of Margulis spacetimes, (with William Goldman) American Journal of Mathematics 139 no2. (2017), 297-345, arXiv:1204.5308, mathematica file action2.nb.

Projective deformations of weakly orderable hyperbolic Coxeter orbifolds, (with Gye-Seon Lee) Geometry & Topology 19 no.4 (2015) 1777-1828, arXiv:1207.3527

The definability criterion for cocompact convex projective polyhedral reflection groups, (with Kanghyun Choi) Geom. Dedicata 175, no. 1, (2015) 323-346, arXiv:1206.2387

Projective deformations of hyperbolic Coxeter 3-orbifolds, (with Craig D. Hodgson and Gye-Seon Lee) Geom. Dedicata vol. 159 no. 1 (2012) 125-167 aXiv:1003.4352 

Spherical triangles and the two components of the SO(3)-character space of the fundamental group of a closed surface of genus 2,

Int. J. Mathematics, Vol 22. no. 9 (2011) 1261-1364

The maximal tubes under the deformations of a class of 3-dimensional hyperbolic cone-manifolds, (with J. Lee) Siberian Mathematical Journal vol. 47 (2006) 955-974

The deformation spaces of projective structures on 3-dimensional Coxeter orbifolds, Geom. Dedicata, 119 (2006), 69-90

The deformation spaces of convex RP2-structures on 2-orbifolds, (with William Goldman) American Journal of Mathematics 127 (2005), 1019-1122

Geometric structures on low-dimensional manifolds, J. Korean Math. Soc. 40 (2003), no.2. 319--340,  errata.

The decomposition and classification of radiant affine 3-manifolds, Memoirs of Amer. Math. Soc. (2001) Vol. 730 pp. 1-122 (2001) errata

The universal cover of an affine 3-manifold with holonomy of shrinkable dimension 2 ,  International Journal of Mathematics, vol. 11 pp. 305-365 (2000)

The convex and concave decompostion of manifolds with geometric structures modelled on real projective spaces, Memoires Soc. Math. France, issue No. 78, pp. 1-102 (1999)

The classification of real projective structures on surfaces, (with William Goldman) Bull. Amer. Math. Soc. (1997) vol. 34, p. 161-171.

The Margulis lemma and the thick and thin decomposition for convex real projective surfaces,  Advances in Mathematics (1996) vol. 122, p. 150-191.

Convex decompositions of real projective surfaces I, II, III, Journal of Differential Geometry (1994) vol. 40, p. 165-208, p. 239-283, J. Korean Math. Soc. (1996) vol. 33, no.4, p. 1139-1171.

Convex real projective structures on closed surfaces are closed, (with William Goldman)  Proc. Amer. Math. Soc. (1993) vol. 118 p. 657-661.

My mathscinet page


Books

Geometric structures on 2-orbifolds: exploration of discrete symmetry (Math. Soc. of Japan Memoirs, Vol. 27, 2012)

The proceedings of the conference on geometric structures on manifolds, GARC Lecture Note Number 46. in gzipped psfiles.

This is a proceedings of the conference held in 1997 (organized by S. Choi, H. Kim, H. Lee). Writers are Boris Apanasov (U. Oklahoma), Thierry Barbot (ENS-Lyon), Suhyoung Choi (SNU), Christopher Herald (Swarthmore College), Yoshinobu Kamishima (Tokyo Metropolitan University), Sadayoshi Kojima (Tokyo Institute of Technology), Kenichi Ohshika (University of Tokyo), Teruhika Soma (Tokyo Denki University), Myunghee Sung (American University)


Travel

The third gear retreat, Stanford University, July 30 - August 12, 2017

JNU-KAIST Geometric Topology Fair, (June 12-16, 2017) Jeju National Univ, South Korea

Differential geometry, and Teichmuller theory, AMS and TIMC, Banaras Hindu University, Varanasi, December 14-17, 2016

Geometry, Topology and Dynamics of Moduli Spaces, NUS, IMA, Singapore, August 1-19, 2016

Geometries, Surfaces and Representations of Fundamental Groups, University of Maryland, College Park, MD, USA, June 22 - June 24, 2016

University of Avignon, Avignon, France, February, 22-26, 2016

Differential geometry research group, University of Heidelberg, Heidelberg, Germany, February 8-19, 2016

Geometry of Moduli Spaces of Low Dimensional Manifolds, RIMS, Kyoto, Japan, December 14-18, 205

Department of Mathematics, Univ. California, Davis, visiting researcher, January 12, 2015 to August 31, 2015

Dynamics on Moduli Spaces of Geometric Structures, a program of MSRI, Berkeley, research member, January 12, 2015 to May 22, 2015

The Ahlfors-Bers Colloquium VI, Yale University, Oct. 23-26, 2014

Hyperbolic Geometry and Geometric Group Theory,  University of Tokyo, July 30-August 5, 2014

What's next? the mathematical legacy of Bill Thurston, Cornell University, June 23-27, 2014

AMS national meeting, Baltimore, MD, January 15-18, 2014 (Univ. Maryland, U. Texas, Austin, U. Texas, Pan American, until the end of January)

Exotic Geometric Structures,  ICERM, Brown University, Providence, RI, September 16-20, 2013

CRM workshop: Higher Teichmüller-Thurston theory, Montreal, October 15-19, 2012

Workshop: Mathematics and Physics of Moduli Spaces, Heidelberg, September 24-28, 2012


 

Reviews

AMS mathscinet

I also refereed for American Journal of Mathematics, Proc. Amer. Math. Soc., Journal of Differential Geometry, Geometriae Dedicata, Geometry & Topology, Groups, Geometries, and Dynamics, and so on.