Young-Heon Kim's
Research
Research Interests:
Differential Geometry, Geometric Analysis, and Partial Differential
Equations:
- Analysis and Geometry of Optimal Transportation / Monge-Ampere
Equations
- Riemannian Geometry
- Spectral Geometry: Analytic Torsion (Determinants of Laplacians),
Isospectrality
- Analysis of Riemann surfaces (Teichmueller Theory)
- Inverse Problems
Publications & Preprints: One-Page Summary of Research
- Counterexamples
to continuity of optimal transportation on positively curved Riemannian
manifolds. Preprint, Sept 2007. Submitted.
- Curvature
and continuity of optimal transport, with Robert J. McCann. An
extended abstract. Oberwolfach
Report 35/2007:26--29.
- Continuity,
curvature, and the general covariance of optimal transportation, with
Robert J. McCann.
Preprint, Sept 2007. Submitted.
- On
the cost-subdifferentials of cost-convex functions, with Robert J. McCann.
Preprint, June 2007.
- Surfaces
with boundary: their uniformizations, determinants of Laplacians, and
isospectrality. To appear in Duke
Mathematical Journal.
- Holomorphic
Extensions of Laplacians and Their Determinants. Advances in Mathematics 211(2007) 517--545. (This is the paper
version of my thesis for my PhD degree for Northwestern University in
2005. My thesis advisor was Ezra Getzler.)
- Determinants
of Laplacians, quasifuchsian spaces, and holomorphic extensions of
Laplacians. In the Tradition of
Ahlfors-Bers, IV, Contemporary Mathematics 432 (2007) 143--150. (A summary of my
thesis.)
- Harmonic maps into open manifolds with nonnegative curvature, with
Jin-Whan Yim. Commun. Korean Math. Soc.
11 (1996) no.3,
789--796.
Papers in preparation
- Riemannian submersions, products, and
curvature of optimal transport, with Robert J. McCann.In preparation.
- On the Hoelder continuity of optimal
partial transport maps, with Robert J. McCann. In
preparation.
Presentation Slides
Invited Talks and Lectures
- TBA.
May 2, 2008. Analysis and PDE seminar. UCLA,
Los Angeles, CA.
- Curvature and continuity of optimal
transport. Mar. 16, 2008. AMS 2008
Spring Eastern Meeting, Mar. 15-16, 2008 --Special Session on
Nonlinear Elliptic Equations and Geometric Inequalities. New York, NY.
- Curvature and continuity of optimal
transport. Feb. 20, 2008. Colloquium. University of Oregon, Eugene,
OR.
- Curvature and continuity of optimal
transport. Feb. 18, 2008. Colloquium. Simon Fraser University, Vancouver,
BC.
- Curvature and continuity of optimal
transport. Jan 25 2008. Colloquium. University of Arizona, Tucson,
AZ.
- Determinants of Laplacians as
functions on spaces of metrics. Jan. 17, 2008. Diff. Geom.-Math.
Phys.-PDE Seminar. University of
British Columbia, Vancouver, BC.
- Curvature and continuity of optimal
transport, Jan 16. 2008, Colloquium. University of British Columbia,
Vancouver, BC.
- Curvature and continuity of optimal
transport. Jan. 15, 2008. Colloquium. Lehman College CUNY,
New York, NY.
- Determinants of Laplacians as functions on
spacecs of metrics. Jan 12. 2008. Southern
California Analysis/PDE Conference at UCSD. San Diego, CA. (Sat-Sun)
January 12-13, 2008.
- Curvature and continuity of optimal
transport, Jan. 11, 2008. Partial Differential Equations Seminar.
UCSD, San Diego, CA.
- Curvature and continuity of optimal
transport. Jan. 8, 2008. University of Edinburgh. Edinburgh,
UK.
- Curvature and continuity of optimal
transport. Jan. 7, 2008. Hausdorff Center for
Mathematics. Bonn, Germany.
- Curvature and continuity of optimal
transport. Dec. 2008. Canadian Mathematical
Society Winter 2007 Meeting, Dec. 8 -10, 2007--Special session:
Calculus of Variations in Physics, Geometry and Economics. London,
Ontario, Canada.
- Curvature and continuity of optimal
transport. Nov. 2007. Prairie Analysis Seminar 2007
(Nov 2-3, 2007). Kansas State
University, Manhattan, Kansas.
- Curvature and the continuity of optimal transportation maps,
July 24, 2007, MSRI(Berkeley)Summer
Microprogram on Nonlinear Partial Differential Equations (July 23, 2007
to August 10, 2007 ).
- Curvature and the continuity of optimal transportation maps,
July 19, 2007, Conference Optimal Transportation, and
Applications to Geophysics and Geometry (Jul 16, 2007 -- Jul 20,
2007) , ICMS, University of Edinburgh.
- Determinants of Laplacians and
isospectrality, July 10, 11, & 12, 2007, KIAS (Seoul)
Summer
school on Dirac and Laplace Operators (Jul 09, 2007 ~ Jul 13,
2007).
- Determinants of Laplacians and their
holomorphic extensions, July 3, 2007, KIAS (Seoul)
Seminar.
- Curvature and the continuity of optimal transportation maps,
June 20, 2007, Banff workshop Geometric
Inequalities (Sun. June 17, 2007 -- Fri. June 22, 2007).
- Curvature and the continuity of optimal transportation maps,
April 13, 2007, Fields Institute, Young
Mathematicians' Conference in PDE and Dynamical Systems IV (April 13-14,
2007).
- Determinants of Laplacians as functions on spaces of metrics,
Nov. 17, 2006, Princeton University, Geometric Analysis
Seminar.
- Determinants of Laplacians and isospectrality of compact surfaces
with boundary, Oct. 30, 2006, University of Waterloo,
Geometry/Topology Seminar.
- Determinants of
Laplacians and their holomorphic extensions,Apr. 18, 2006, Ohio State
University, Analysis/Geometry Seminar.
- Determinants of Laplacians and Quasifuchsian Spaces, Feb. 3, 2006, Northwestern
University, Geometry/Physics Seminar.
- Determinants of Laplacians and their holomorphic extensions ,
Feb. 2, 2006, University
of Chicago, Geometry/Topology Seminar.
- Determinants of Laplacians and their
holomorphic extensions, May 19, 2005,
Workshop on The Weil-Petersson Geometry of Teichmuller
Space, 2005
Ahlfors Bers Colloquium, University of Michigan, Ann Arbor,
Michigan.
- Holomorphic extensions of determinants of Laplacians, April 9,
20052005
Bloomington Geometry Workshop, Indiana University, Bloomington,
Indiana.
Local Seminar Talks
- Curvature and the continuity of optimal transport maps, March
8, March 22, 2007 Fields
Analysis Working Group Seminar
- Determinants of Laplacians as functions on spaces of metrics,
Nov. 20, 2006, University of Toronto, Geometry and Topology
Seminar.
- Regularity results for optimal
transport problems with general costs , Oct. 26, Nov. 2, 2006.
Fields
Analysis Working Group Seminar.
- Determinants of Laplacians and isospectrality of compact surfaces
with boundary. Oct. 13, 2006, University of Toronto, PDE/Applied
Math/Analysis Seminar.
- Determinants of Laplacians and their
holomorphic extensions, Nov. 17, 2005, Fields Insititute, Mini
course.
Conferences and Programs (which I
have participated in, will attend, or am interested in)
- PDE. June, July, Aug, 2009. UBC, Vancouver, BC.
- Geometric Partial Differential Equations. Sep 2008 -- April 2009. IAS,
Princeton, NJ.
- Workshop on Transport, Optimization, Equilibrium in Economics. July 14
-- July 20, 2008. University of British Columbia, Vancouver, BC.
- Calculus of Variations, July 6th - 12th, 2008. Oberwolfach,
Germany.
- Evolution equations. June 23 - July 18, 2008. Clay
Institute 2008 Summer School. ETH, Zurich, Switzerland.
- 2008 CNA Summer
School May 29 – June 7, 2008, Center for Nonlinear Analysis,
Carnegie Mellon University, Pittsburgh, PA
- Optimal
Transport, March 10 - June 13 2008, IPAM(UCLA).
- AMS
2008 Spring Eastern Meeting, Mar. 15-16, 2008 (Sat-Sun) --Special
Session on Nonlinear Elliptic Equations and Geometric Inequalities. New
York, NY.
- Southern California Analysis/PDE Conference at UCSD. San Diego, CA. (Sat-Sun)
January 12-13, 2008.
- Canadian Mathematical
Society Winter 2007 Meeting, Dec. 8 -10, 2007. Hilton Hotel London
(Ontario, Canada) --special session: Calculus of Variations in Physics,
Geometry and Economics.
- Prairie Analysis Seminar
2007 (Fri-Sat. Nov 2-3, 2007). Kansas State University,
Manhattan, Kansas.
- MSRI(Berkeley) Summer
Microprogram on Nonlinear Partial Differential Equations (July 23,
2007 to August 10, 2007 ). Berkeley, CA.
- ICMS (Edinburgh): Optimal Transportation, and
Applications to Geophysics and Geometry (Jul 16, 2007 -- Jul 20,
2007). Edinburgh, UK.
- KIAS
(Seoul) Summer school on Dirac and Laplace Operators (Jul 09, 2007 ~ Jul
13, 2007). Korea.
- BanffGeometric
Inequalities (Sun. June 17, 2007 - Fri. June 22, 2007). Banff,
Alberta, Canada.
- MPIM (Bonn, Germany) (May 4,
2007 - May 31, 2007).
- IPAM(UCLA): Random Curves, Surfaces,
and Transport. (April 16 - 20, 2007).
- Fields Institute, Toronto:Young
Mathematicians' Conference in PDE and Dynamical Systems IV (April 13-14,
2007).
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