Ngin-Tee Koh

Department of Mathematics
University of Illinois at Urbana-Champaign
1409 W. Green Street (MC-382)
Urbana, IL 61801-2975

Office: 346 Illini Hall
Phone: (217) 333-6328
Fax: (217) 333-9576
Email: nkoh@illinois.edu

Educational Background

Ngin-Tee Koh received his B.Sc.(Hons) degree with First Class Honors from the National University of Singapore and his M.Sc. degree from the University of Illinois at Urbana-Champaign. He has defended his Ph.D. thesis and expects to receive his Ph.D. degree from the University of Illinois at Urbana-Champaign no later than May 2009. For his Ph.D. dissertation, he did research on approximable quasidisks under the direction of Professor Aimo Hinkkanen.

Teaching

Math 225 Introductory Matrix Theory, Fall 2008
Math 234 Calculus for Business I, Spring 2007
Math 231 Calculus II, Fall 2006
Math 230 Calculus II, Spring 2006 & Fall 2005
Math 220 Calculus I, Spring 2005 & Fall 2004

Research Specialization

Primary interests include geometric function theory, quasiconformal mappings and quasidisks.
Secondary interests include value distribution theory, complex dynamics and geometric measure theory.

Research Publications & Preprints

Approximable Quasidisks. Accepted for publication in Ann. Acad. Sci. Fenn. Math.
Abstract: We study a question posed by Anderson and Hinkkanen: what quasidisks are approximable? We show that a Jordan domain bounded by an analytic curve is an approximable quasidisk.
Some Estimates for Normalized Quasiconformal Self-Mappings of the Unit Disk. Accepted for publication in Complex Var. Elliptic Equ.
Abstract: We provide an integral estimate for the boundary values of a normalized quasiconformal self-mapping of the unit disk. Estimates are also given for the partial derivative of the Douady-Earle extension.
On Conformal Mappings onto Quasidisks. In preparation.
Abstract: We prove a distortion theorem for conformal mappings whose images are quasidisks. As an application, we construct a quasiconformal reflection with bounded partial derivatives near the reflection boundary based on the Douady-Earle extension.

Invited Presentations

AMS Meeting: Special Session on Complex Dynamics and Value Distribution, Urbana, IL, March 2009.
AMS-MAA Joint National Meetings: Special Session on Complex Dynamics and Complex Function Theory, Washington, D.C., January 2009.

Mathematical Animations

Click on the images below to view the 3D shadows of some rotating 4D surfaces. You'll need the free DPGraph Viewer to see the animations. I was introduced to this software in a computer graphics and geometrical visualization course taught by Professor George Francis.