We discuss a relationship between a class of derivations and a class of automorphisms on the noncommutative algebra of formal power series in two variables. Each class relates bijectively by exponential and logarithm maps. In this talk we define a specific class of derivations, which generates a noncommutaive Lie algebra whose defining relations are related to a classical Witt algebra. The main claim in the talk is the explicit description of the automorphisms which are corresponding to the derivations via exponential map.

(Note: Dr. Kentaro Ihara wrote a famous Compositio Math. paper with. Don Zagier on multi-zeta function, and number theorists are particularly welcomed to come.)

Packets of large amplitude internal solitary waves generated by the interaction of density-stratified flows with bottom topography have been observed in many coastal regions. Their wave amplitudes often exceed 100 m and, therefore, these waves cannot be described by classical weakly nonlinear models. A strongly nonlinear asymptotic model to describe such waves was proposed some time ago, but the model has been known to suffer from the Kelvin-Helmholtz instability and to be ill-posed. In this talk, a regularized model free from such instability will be introduced and an iterative numerical scheme to solve the regularized time-dependent model will be discussed.

We discuss structures of few financial derivatives and
explain why such financial products are built up and traded.

The graph finding problem is to find the edges of an unknown graph by
using a certain type of queries. Its extension to hypergraphs is
closely related to the problem of learning linkage in molecular
biology and artificial intelligence. In this talk, we introduce the
hypergraph finding problem and the linkage learning problem and
present our recent results for the query complexity of those problems.

Mathematical logic deals with symbols and strings, which are specialties of computers. So it is natural to use computers in practicing logic in various occasions. For instance, the verification of formal proofs, which are just the strings that follow some specific rules, is quite often tedious and time consuming--it is a job best suited for computers.

In this talk, a formal proof system called "Fitch" is introduced, and demonstrated as implemented at http://www.proofmood.com.

I will construct a moduli space of $q$ pairwise commuting nilpotents of $\mathfrak gl_d$ and give a natural compactification of it for the case $d = 3$.

Recently, a new sampling theory called compressive sampling theory was
proposed in signal processing community. According to compressive
sampling, very accurate reconstruction is possible even from very
limited data measurements which breaking Nyquist sampling limit if the
unknown signal is sparse. Furthermore, even if the signal itself is
not sparse, as long as it can be represented sparsely by appropriate
sparsifying transform, compressive sampling can be still very
effectively applied. In this talk, we introduce the basic theory for
compressive sensing, and demonstrate how this can be applied to
various bio-imaging area.

This is an introductory talk on higher Chow groups. It will be understandable for graduate students in algebra and geometry. A Chow group is used by various mathematicians in various fields. For complex geometers, Chow groups are the place where the fundamental cohomology classes originate. For number theorists, Chow groups are equal to the ideal classes groups. For some people, the group of line bundles, so called the Picard groups, is given by this. For those work in Riemann surfaces, a subgroup of a Chow group is named the Jacobian variety. I will explain how this object is related to these, and how one can see this object as an analogue of singular homology for algebraic varieties. 

In shape matching, we are given two geometric objects and we compute their distance according to some geometric similarity measure. The Fréchet distance is a natural distance function for continuous shapes such as curves and surfaces, and is defined using reparameterizations of the shapes.

Motivated by a practical application in designing safe control scheme
for automated guided vehicles or robots in industrial settings, graph
braid groups were first proposed and studied by R. Ghrist and A.
Abrams in 1999. We will quickly summarize the history of the theory
including the recent breakthrough on a conjecture by the pioneers.

How can we recognize mapping spaces from other spaces? 
We can use natural operations on them as a universal algebra and  we may use this to recognize mapping spaces up to weak equivalence. In the case of mapping spaces, n-fold loop spaces, of pointed maps from the n-sphere, we can show that any space X having such a universal algebra structure is weakly equivalent to the n-fold loop space of B(X), delooping space. I will explain its categorical frame so that it may be applicable to other problems, e.g.,moduli spaces, deformation problems etc.

The fractional weak discrepancy of a poset (partially ordered set) P, written wd(P), is the least k such that some  satisfies f(y)-f(x)≤1 for  and |f(y)-f(x)|≤k for x|y. Minimal forbidden subposets are often called obstructions. Shuchat, Shull, and Trenk determined the obstructions for the property wd(P)<1: the obstructions are 2+2 and 3+1. We determine the obstructions for the property wd(P)≤k when k is an integer. In this talk, the complete collection of the obstructions for wd(P)≤k for each k≥2 - which is an infinite set - will be discussed.

This is joint work with Douglas B. West.

Given a line bundle L on a projective variety, it is natural to consider the graded section ring R(L) given by all sections of multiples of L. We call R(L) a complete section ring. Then we define a general section ring to be a subring of R(L). We will define a certain class of (not necessarily complete) section rings associated to adjoint line bundles, which contains the usual canonical rings. We will discuss its properties and why we need those rings.

Plasma is a state of matter in which electrons
disassociate from their nuclei, resulting in
electrically conducting clouds of positively
and negatively charged ions. Mathematically,
plasma can be modeled on a variety of scales,
resulting in various kinetic, fluid, and hybrid
models.

In this talk we first  consider the simplest plasma fluid
model: the ideal MHD (magnetohydrodynamic) system.
We review some of the mathematical difficulties
associated with the divergence-free condition
on the magnetic field. We will then describe a
class of discontinuous Galerkin (DG) methods for
approximately solving this system.

Next we consider two genuinely two-fluid models of
plasma: Euler-Maxwell (5-moments) and extended
Euler-Maxwell (10-moments). We focus our discussion
on the problem of collisionless magnetic reconnection.
We first describe this problem and then our efforts to
apply two-fluid models to it, again using discontinuous
Galerkin methods.

Scattering refers an asymptotic behavior that a nonlinear solution converges to a linear solution as time goes to infinity. It appears in defocusing equations. I will begin with basics of dispersive equations and properties of linear solutions, and then go on nonlinear scattering problems. I will discuss this with some model equations, the nonlinear Schrodinger equation and the generalized KdV equations.

The fifth-order KdV equation arises in the KdV hierarchy. I will discuss local well-posedness and ill-posedness of the initial value problem in the Sobolev spaces with low regularity. Unlike the KdV equation, strong low-high frequency interaction become a major obstacle for well-posedness result, but a hint for ill-posedness result. I will explain how it works in both directions. 

This is the third part of this introductory lecture series on p-adic Hodge theory.

This is the first part of this introductory lecture series on p-adic Hodge theory.

This is the second part of this introductory lecture series on p-adic Hodge theory.

We give an introduction to the classification of varieties of 
almost minimal degree. This is done by projections of 
varieties of minimal degree that are classically well-known. 
In the second part of  the talk we derive several 
applications related to the depth conjecture, the classification 
of non-normal Dell Pezzo varieties, and the classification 
of non-normal hypersurfaces of degree three. We end with 
problems about secant and tangent varieties of rational normal scrolls. 

09:30 - 09:40 Welcome Remarks by Vice President Minho Kang
09:40 - 10:20 'Form Radiative Transfer Theory to Fast Algorithms for Cell Phones' by Prof. T.Kailath
10:20 - 10:50 Q/A Session
10:50 - 11:30 'Searching for Spectrum Efficiency' by Prof.A.Paulraj
11:30 - 12:00 Q/A Session
12:00 - 01:00 Luncheon (고급 샌드위치 제공)