Class field theory for 3-dimensional foliated dynamical systems

The lace expansion is one of the few methods to rigorously prove critical behavior for various models in high dimensions. It was initiated by David Brydges and Thomas Spencer in 1985 to show degeneracy of the critical behavior for weakly se...

그래프 색칠 문제는 그래프 이론에서 중요한 주제로, 인접한 두 정점이 같은 색을 가지지 않도록 그래프를 색칠하는 방법을 연구합니다. 이는 단순한 퍼즐처럼 보일 수 있지만, 수학적 깊이와 다양한 응용 가능성을 지니고 있습니다. 이번 강연에서는 그래프 ...

Nonlocal equations, often modeled using the fractional Laplacian, have received significant attention in recent years. In this talk, we will briefly overview how the classical regularity theory for second-order (elliptic) PDEs (in divergenc...

Homogeneous dynamics, the theory of flows on homogeneous spaces, has been proved useful for certain problems in Number theory. In this talk, we will explain what kind of geometry and dynamics we need to solve certain number theoretic questi...

This talk concerns the problem of classifying long-term dynamics for critical evolutionary PDEs. I will first discuss what the critical PDEs are and soliton resolution for these equations. Building upon soliton resolution, I will further in...

Sullivan sketched a proof of his structural stability theorem for differentiabl group actions satisfying certain expansion-hyperbolicity axioms. We relax Sullivan’s axioms and introduce a notion of meandering hyperbolicity for group a...

In this talk, we investigate some regularity results for non-uniformly elliptic problems. We first present uniformly elliptic problems and the definition of non-uniform ellipticity. We then introduce a double phase problem which is characte...

There have been at least two surprising events to geometers in 80-90s that they had to admit physics really helps to solve classical problems in geometry. Donaldson proved the existence of exotic 4-dimensional Euclidean space using gauge th...

A feature of log-correlation naturally appears in diverse objects such as random matrices, random discrete geometries and Riemann zeta function. In this talk, I will give an overview on the theory of log-correlated fields and talk about rec...

This talk concerns maximal functions given by averages over some family of geometric objects. I will discuss the boundedness of those maximal functions on the Lebesgue spaces and its role in problems of harmonic analysis.

고전컴퓨터는 모든 정보를 이진수로 표현하여 계산을 0과 1의 전기신호로 구현하는데 반해서 양자컴퓨터는 정보를 벡터(양자상태)로 표현하여 유니터리 변환을 통해 계산을 수행한다. 양자컴퓨터가 관심을 끄는 이유는 얽힌 양자상태 덕분에 빠른 계산이 가능...

Concordance is a relation which classifies knots in 3-space via surfaces in 4-space, and it is closely related with low dimensional topology. Satellite operators are one of the main tools in the study of knot concordance, and it has been wi...