젊은과학자상 수상기념강연: From particle to kinetic and hydrodynamic descriptions to flocking and synchronization
In this talk, I will report a recent progress for the modeling of collective behaviors of complex systems, in particular ocking and synchronization. Flocking and synchro-nization are ubiquitous in our daily life, for example, ocking of birds...
Noncommutative Geometry. Quantum Space-Time and Diffeomorphism Invariant Geometry
A general goal of noncommutative geometry (in the sense of A. Connes) is to translate the main tools of differential geometry into the Hilbert space formalism of quantum mechanics by taking advantage of the familiar duality between spaces an...
Ergodic theory of horocycle flow and nilflow has been proved to be useful for analyzing the randomness of Mobius function, a function which reveals the mystery of prime numbers. In this survey talk, we will introduce Mobius function and seve...
Non-commutative Lp-spaces and analysis on quantum spaces
In this talk we will take a look at analysis on quantum spaces using non-commutative Lp spaces. We will first review what a non-commutative Lpspace is, and then we will see few examples of quantum spaces where Lp analysis problems arise natu...
학부생을 위한 ε 강연회: Mathematics from the theory of entanglement
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...
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 ...
Fefferman's program and Green functions in conformal geometry
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...
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 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...
Random conformal geometry of Coulomb gas formalism
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...
A W-algebra is introduced as a symmetry algebra in 2-dimensional conformal field theory. Mathematical realization of a W-algebra was introduced by the theory of vertex algebras. Especially, W-algebras related to Lie superalgebras have been s...
<학부생을 위한 ɛ 강연> Geometry and algebra of computational complexity
학부생을 위한 이 강연에서는 고전적 튜링 기계의 기본적 정의로부터 시작하여 • 튜링기계를 비롯한 다양한 컴퓨터 모델의 복잡도 개념; • 계산(불)가능성 – 특히 디오판틴 방정식의 알고리즘적 해결법 (힐버트의 10번째 문제); • Non-deterministic 튜링 기계...
