From 1980’s, the study of Kleinian groups has been carried out in the framework of the paradigm of “Thurston’s problems”. Now they are all solved, and we can tackle deeper problems; for instance to determine the topological types of the defo...

A classical theorem of Jacobs, de Leeuw and Glicksberg shows that a representation of a group on a reflexive Banach space may be decomposed into a returning subspace and a weakly mixing subspace. This may be realized as arising from the idem...

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...

SNU-LeeAbstract.pdf

The original Riemann-Hilbert problem is to construct a liner ordinary differential equation with regular singularities whose solutions have a given monodromy. Nowadays, it is formulated as a categorical equivalence of the category of regular...

Normal form method is a classical ODE technique begun by H. Poincare. Via a suitable transformation one reduce a differential equation to a simpler form, where most of nonresonant terms are cancelled. In this talk, I begin to explain the not...

Several cluster interfaces in 2D critical lattice models have been proven to have conformally invariant scaling limits, which are described by SLE(Schramm-Loewner evolution) process, a family of random fractal curves. As the remarkable achie...

In 1980s, Donaldson discovered his famous invariant of 4-manifolds which was subsequently proved to be an integral on the moduli space of semistable sheaves when the 4-manifold is an algebraic surface. In 1994, the Seiberg-Witten invariant w...

Many aspects of the differential geometry of embedded Riemannian manifolds, including curvature, can be formulated in terms of multi-linear algebraic structures on the space of smooth functions. For matrix analogues of embedded surfaces, one...

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...

After a review of various types of tilings and aperiodic materials, the notion of tiling space (or Hull) will be defined. The action of the translation group makes it a dynamical system. Various local properties, such as the notion of "Finit...

The mapping class group of a surface S is the component group of orientation-preserving homeomorphisms on S. We survey geometric and algebraic aspects of this group, and introduce a technique of using right-angled Artin groups to find geomet...

In the early 90's, physicists Bershadsky-Cecotti-Ooguri-Vafa conjectured that the analytic torsion was the counterpart in complex geometry of the counting problem of elliptic curves in Calabi-Yau threefolds. It seems that this conjecture is ...

Motivated by the analysis of the singularity of the Bergman kernel of a strictly pseudoconvex domain, Charlie Fefferman launched in the late 70s the program of determining all local biholomorphic invariants of strictly pseudoconvex domain. T...

Volume conjecture를 설명하고 현재까지의 연구결과 그리고 앞으로의 연구계획을 소개한다.

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...

Studies on PDEs are mostly focused on ?nding properties of PDEs within a speci?c discipline and on developing a technique specialized to them. However, ?nding a common structure over di?erent disciplines and unifying theories from di?erent s...

The main topic of the talk is a determinantal formula for high dimensional tree numbers of acyclic complexes via combinatorial Laplace operators . This result is a generalization of Temperley's tree number formula for graphs, motivated by a ...

The notion of entanglement is now considered as a basic resource for the current quantum information and quantum computation theory. We discuss what kinds of mathematics are related to the theory. They include operator algebras, matrix theor...

Several L-functions with the names Dirichlet, Dedekind, Elliptic, and so on usually have p-adic counterparts, so called p-adic L-functions, which share many similar properties such as an evaluation formula at s=1, class number formula, and e...