December 16-20, 2009, Ewha Womans University, Seoul, Korea
Plenary Speakers

 Plenary Speakers

Hee Oh
Professor of Mathematics
The Mathematics Department, Brown University
Ph.D, Yale University, 1997
B.Sc., Seoul National University 1992
Professor, Brown University, July 2006-present
Professor, California Institute of Technology, April 2006-August 2007
Associate Professor with tenure, California Institute of Technology, June 2003-March 2006 
Assistant Professor, Princeton University, Sep 1999-June 2003
Golda Meir Postdoctoral Fellow, The Hebrew University, Oct 1998-June 1999
Visiting Assistant Professor, Oklahoma State University, Aug 1997-May 1998
Plenary Lecture - 1 | 10:00-10:50, December 16 (Wed), 2009
Speaker : Hee Oh (Brown University)
Chair : Georgia Benkart (University of Wisconsin)
Counting circles and Ergodic theory of Kleinian groups
There are many interesting examples of Kleinian groups whose limit sets on the unit sphere provide circle packings. For instance, one can obtain Sierpinski curves or Apollonian gaskets in this way. Given such a circle packing on the unit sphere, we discuss how the ergodic theory of Kleinian groups can be used to answer the question "How many circles are of radius  at least  r as r tends to 0?"



Terence Tao
Professor of Mathematics
The Department of Mathematics, UCLA
Ph. D., Princeton University, 1996 
M. Sc., Flinders University, 1992
B. Sc., (Hons), Flinders University, 1991
Honourary Professor, ANU, 2001-2003
Full Professor, UCLA, 2000-present
Visiting Professor, UNSW, 2000
CMI Long-term Prize Fellow, Clay Mathematical Institute, 2001-2003
Assistant Professor, UCLA, 2000
Visiting Fellow UNSW, 1999
Acting Assistant Professor, UCLA, 1999
Member, MSRI, Fall 1997
Hedrick Assistant Professor, UCLA, 1996-1998
Assistant Researcher, Princeton University, 1993-1994
Assistant Researcher, Flinders Medical Centre, 1992-1994
Terence Tao was born in Adelaide, Australia in 1975. Tao's areas of research include harmonic analysis, PDE, combinatorics, and number theory. He has received a number of awards, including the Salem Prize in 2000, the Bochner Prize in 2002, the Fields Medal and SASTRA Ramanujan Prize in 2006, the MacArthur Fellowship and Ostrowski Prize in 2007, and the Waterman Award in 2008. Terence Tao also currently holds the James and Carol Collins chair in mathematics at UCLA, and is a Fellow of the Royal Society, the Australian Academy of Sciences (Corresponding Member), the National Academy of Sciences (Foreign member), and the American Academy of Arts and Sciences.
Plenary Lecture - 2 | 11:00-11:50, December 16 (Wed), 2009 
Speaker : Terence Tao (University of California, Los Angeles)
Chair : Kyewon Koh Park (Ajou University)
The proof of the Poincaré conjecture
In a series of three terse papers in 2003 and 2004, Grisha Perelman made spectacular advances in the theory of the Ricci flow on 3-manifolds, leading in particular to his celebrated proof of the Poincare conjecture (and most of the proof of the more general geometrization conjecture). Remarkably, while the Poincare conjecture is a purely topological statement, the proof is almost entirely analytic in nature, in particular relying on nonlinear PDE tools together with estimates from Riemannian geometry to establish the result. In this talk we discuss some of the ingredients used in the proof, and sketch a high-level outline of the argument.


Bumsig Kim
Professor of Mathematics
School of Mathematics, Korea Institute for Advanced Study
Ph. D., in Mathematics, University of California at Berkeley, 1996
B. S., in Mathematics, Seoul National University 1989
Professor, Korea Institute for Advanced Study, 2003-present
Associate Professor, Pohang University of Science and Technology, 2001-2003
Assistant Professor, Pohang University of Science and Technology, 1999-2001
Visiting Research Assistant Professor, University of California at Davis, 1997-1999
Postdoctoral Fellow, Mittag-Leffler Institute, 1996-1997
Plenary Lecture - 3 | 11:00-11:50, December 17 (Thur), 2009
Speaker : Bumsig Kim (Korea Institute for Advanced Study)  
Chair : Yong Seung Cho (Ewha Womans University)
Stable quasi-maps to GIT quotients
A virtually smooth algebraic stack generalizes the notion of an algebraic manifold and is still good enough to do geometry. In particular, the constructions of moduli spaces as stacks are much easier and even more desired. I will show some examples, including one which I wanted for a long time. The latter is joint work with Ciocan-Fontanine and Maulik. 


YoungJu Choie
Professor of Mathematics
Department of Mathematics, Pohang University of Science and Technology
Ph. D., Temple University, PA, 1986
B. S., Ewha-Woman's University, 1982
Visiting Professor, Stanford University, Palo Alto, CA, USA, 2005
Visiting scholar, University of Cambridge, England, 1995
Professor, POSTECH, Korea, 1990-present
Assistant Professor, University of Colorado, Boulder, U.S.A., 1989-1990
Visiting Assistant Professor, University of Maryland, U.S.A., 1988-1990
Lecturer, Ohio State University, Columbus, U.S.A., 1986-1988
Plenary Lecture - 4 | 13:30-14:20, December 17 (Thur), 2009
Speaker : YoungJu Choie (Pohang University of Science and Technology)
Chair : Myung-Hwan Kim (Seoul National University)
Not quite modular 
Counting branched coverings of Riemann surfaces, fixing base surface and a ramification type, is called the Hurwitz problem. It turns out that the generating functions of counting branched coverings with various ramification types have a quasi-modular property. These are spaces of functions not quite modular, but still have various  arithmetic properties. Mock modular forms, Eichler integrals and Quasimodular forms are such examples. We show that there is a systematic way to study  such  a generating function, namely, a quasi-modular form.  The parallel theories, such as Hecke operator,
L-functions and connection with various forms,  similar to those of modular forms can be developed. It turns out that this space is isomorphic to that of the vector valued forms with symmetric power representations.

James McKernan 
Norbert-Wiener Professor of Mathematics
Massachusetts Institute of Technology
James McKernan was born in London, England in 1964. He received his BA in mathematics from Cambridge University in 1985, whilst attending Trinity College, and his PhD in mathematics from Harvard University under the supervision of Joseph Harris in 1991. He then
held temporary positions at the University of Utah, 1991-1993, University of Texas, at Austin 1993-1994, and Oklahoma State University, Stillwater 1994-1995. He joined the faculty at the University of California, Santa Barbara in 1995 and the faculty at Massachusetts Institute
of Technology in 2007, where he is Norbert-Wiener Professor of Mathematics. In 2007 he received a Clay Research award and in 2009 the Cole Prize in Algebra. His research interests are in algebraic geometry, especially birational geometry and the classification of algebraic
Plenary Lecture - 5 | 11:00-11:50, December 19 (Sat), 2009 
Speaker : James McKernan (Massachusetts Institute of Technology)
Chair : Sijong Kwak (Korea Advanced Institute of Science and Technology)
Finite Generation of the Canonical ring
Given any smooth projective variety the  canonial ring is the ring of all global holomorphic differential forms.  In this talk I will explain the geometric significance of the canonical ring and the fact that this ring is finitely generated.  


Van Vu
Professor of Mathematics
Mathematics Department, Rutgers University

Ph. D., Yale University, 1998
B. S., Eotvos Univerisity (Budapest, Hungary), 1994

Professor II, Department of Mathematics, Rutgers University, July 2009-present
Full Professor, Department of Mathematics, Rutgers University, September 2005-June 2009
Leader of Focus program "Arithmetic Combinatorics", Institute for Advance Study, Fall 2007
Visiting Professor, Institute Henry Poincare (Paris, France), June 2006-July 2006
Full Professor, Department of Mathematics, UCSD, July 2005-December 2005
Associate Professor, Department of Mathematics, UCSD, July 2003-June 2005
Assistant Professor, Department of Mathematics, UCSD, July 2001- June 2003
Postdoc Researcher, Theory group, Microsoft Research, June 1999-June 2001
Member, Institute for Advance Study, Princeton University, September 1998-June 1999
Plenary Lecture - 6 | 13:30-14:20, December 19 (Sat), 2009 
Speaker : Van Vu (Rutgers University)
Chair : Jeong Han Kim (National Institute For Mathematical Science)
From the Littlewood-Offord problem to the Circular Law conjecture
The famous Circular Law in random matrix theory asserts that if M_n is an n by n matrix with iid entries of mean zero and variance one, then the empirical spectral distribution (after a proper normalization) tends to the uniform distribution on the unit disk. This is usually seen as the non-hermitian "brother" of the classical Wigner semi-circle law. After a long sequence of partial results that verified the law under various extra assumptions, the Circular Law is now known to be true in its mot general form, due to a result of Tao and Vu (2008). In this talk, we discuss a few main ideas of the proof, in particular recent advances in understanding the Littlewood-Offord problem in combinatorics.
Ki-ahm Lee
Tenured Associate Professor of Mathematics
Department of Mathematics, Seoul National University
Ph. D. in mathematics, Courant Institute, New York University, September '93- September '98
                                University of Texas at Austin, Fall ’97 -Summer ’98
B. A. in Mathematics, Seoul National University, March '88-February '92

Tenured Associate Professor, Seoul National University, February '06-present
Adjunct Assistant, University of Texas at Austin, January '05-August '05
Assistant Professor, Seoul National University, December '01-February '06
Instructor, University of Texas at Austin, Fall '00-Fall '01
Visiting Assistant Professor, University of California at Irvine, Fall '98-Spring '00

Plenary Lecture - 7 | 10:40-11:30, December 20 (Sun), 2009
Speaker : Ki-ahm Lee (Seoul National University)
Chair : Minkyu Kwak (Chonnam National University)
Nonlinear Elliptic and Parabolic Equations: Analysis and Applications
In this talk, let us introduce the important issues in the second-order nonlinear elliptic and parabolic equations of divergence type and non-divergence type.
First, we will consider degenerate equations where  the degeneracy of the diffusion coefficient will give us non-trivial balance between the second derivatives and requires non-trivial understanding on the concept of derivatives and its estimate. Another interesting class of nonlinear equation is non-local partial differential equations like fractional Laplace operator. The operator is given as an integral of second differential quotients with a singular weight function, where two points away from each other has stronger interaction than standard diffusion. So the kernel has thicker tail than that of standard local equations. Finally, we will consider the difficulties and applications when the data is highly oscillating or domain has hole like a perforated domains. We are going to discuss how to filter the oscillation of solutions caused by the oscillation of data or domain, and to prove the effective equation describes different averaging on each problem.

Minhyong Kim
Professor of Pure Mathematics
Department of Mathematics, University College London
Ph. D. in Mathematics, Yale University, 1985-1990
B. S. in Mathematics, Seoul National University, 1982-1985
Professor of Pure Mathematics, University College London, 2007-present
Professor, Purdue University, 2005-2007
Professor, University of Arizona, 2004-2007
Professor, Korea Institute for Advanced Study, 2001-2002
Associate Professor, University of Arizona, 1998-2003
Assistant Professor, University of Arizona, 1995-1998
J.F. Ritt Assistant Professor, Columbia University, 1993-1996
C. L. E. Moore Instructor, Massachusetts Institute of Technology, 1990-1993

Plenary Lecture - 8 | 11:40-12:30, December 20 (Sun), 2009
Speaker : Minhyong Kim (University College London)  
Chair : Jae-Hyun Yang (Inha University)
Diophantine geometry and Galois Theory
In his manuscripts from the 1980's Grothendieck proposed ideas that have been interpreted variously as embedding the theory of schemes into either
 -group theory and higher-dimensional generalizations;
 -or homotopy theory.
It was suggested, moreover, that such a framework would have profound implications for the study of Diophantine problems. In this talk, we will discuss mostly the little bit of progress made on this last point using some mildly non-abelian motives associated to hyperbolic curves. 

 Public Lecturer




Frank Morgan 
Webster Atwell ‘21 Professor of Mathematics
Department of Mathematics and Statistics, Williams College

PhD, Princeton University, 1977
MA, Princeton University, 1976
SB, MIT, 1974

Webster Atwell ‘21 Professor of Mathematics, Williams College, 2003-present
Dennis Meenan ‘54 Third Century Professor of Mathematics, Williams College, 1997-2003
ScD (honorary), Cedar Crest College, 1995
Chair, Williams College, 1988-94
Cecil and Ida Green Career Development Chair, MIT, 1985-86
Chairman, Undergraduate Mathematics Office, MIT, 1979-82
C.L.E. Moore Instructor, MIT, 1977-79

Public Lecture | 18:00-18:50, December 16 (Wed), 2009
Speaker : Frank Morgan (Williams College)
Chair : Jaigyoung Choe (Korea Institute for Advanced Study)
From Soap Bubbles to the Poincaré Conjecture
A round soap bubble provides the least-perimeter way to enclose a given volume of air, as was conjectured by the Ancient Greeks and proved mathematically by Schwarz in 1884. Similarly the double bubble that forms when two soap bubbles come together provides the least-perimeter way to enclose and separate two given volumes of air, although that was not proved until 2002 by Hutchings, Morgan, Ritoré, and Ros. Such "isoperimetric" theorems have played any important role throughout mathematics, including Perelman's 2003 proof of the Poincaré Conjecture. The talk will include soap bubble demonstrations, recent results by undergraduates, and open questions.