I will talk on Cannes's Embedding Conjecture, which is considered as one of the most important open problems in the field of operator algebras. It asserts that every finite von Neumann algebra is approximable by matrix algebras in suitable s...

In this talk, we shall discuss the semi-infinite variation of Hodge structure associated to real valued solutions of a Toda equation. First, we describe a classification of the real valued solutions of the Toda equation in terms of their par...

In his survey paper in the Bulletin of the AMS from 2002, R. J. Gardner discussed the Brunn-Minkowski inequality, stating that it deserves to be better known and painted a beautiful picture of its relationship with other inequalities in anal...

Lagrangian Floer theory in symplectic manifold associate a category (A infinity category) to a symplectic manifold. More than 20 years ago a relation of a relation between Lagrangian Floer theory and Gauge theory was studied by Floer himself...

Homology is a method for assigning signatures to geometric objects which reects the presence of various kinds of features, such as connected components, loops, spheres, surfaces, etc. within the object. Persistent homology is a methodology...

Persistent homology produces invariants which take the form of barcodes, or nite collections of intervals. There are various structures one can imposed on them to yield a useful organization of the space of all barcodes. In addition, there...

One of the important problems in understanding large and complex data sets is how to provide useful representations of a data set. We will discuss some existing methods, as well as topological mapping methods which use simplicial complexes ...

Creating information and knowledge from large and complex data sets is one the fundamental intellectual challenges currently being faced by the mathematical sciences. One approach to this problem comes from the mathematical subdiscipline cal...

Since Fourier introduced the Fourier series to solve the heat equation, the Fourier or polynomial approximation has served as a useful tool in solving various problems arising in industrial applications. If the function to approximate with t...

I will give a very personal overview of the evolution of mainstream applied mathematics from the early 60's onwards. This era started pre computer with mostly analytic techniques, followed by linear stability analysis for finite difference a...

수학의 기하학, 위상학 그리고 알고리즘의 건축디자인의 적용 사례 및 이론적 배경

In this talk, I will briefly introduce some properties of the incompressible Navier-Stokes equations. Then, I will review some classical results obtained by harmonic analysis tools.

Non-vanishing modulo a prime of special values of various $L$-functions are of great importance in studying structures of relevant arithmetic objects such as class groups of number fields and Selmer groups of elliptic curves. While there hav...

It is a fascinating and challenging problem to count number fields with bounded discriminant. It has so many applications in number theory. We give two examples. First, we compute the average of the smallest primes belonging to a conjugacy ...

초록 첨부: Void.pdf

We will review a number of topological themes in number theory, starting with homology and ending with a discussion arithmetic homotopy.

In this talk, we will consider the hyperbolic Kac-Moody algebra associated to a certain rank 3 Cartan matrix and generalized Kac-Moody algebras that contain the hyperbolic Kac-Moody algebra. The denominator funtions of the generalized Kac-Mo...

It is usually a difficult problem to characterize precisely which elements of a given integral domain can be written as a sum of squares of elements from the integral domain. Let R denote the ring of integers in a quadratic number field. Thi...