The invariant subspace problem is one of the longstanding open problem in the field of functional analysis and operator theory. It is due to J. von Neumann (in 1932) and is stated as: Does every operator have a nontrivial invariant subspace...

We will show that the averaging formula for Nielsen numbers holds for continuous maps on infra-nilmanifolds: Let M be an infra-nilmanifold with a holonomy group Phi and f : M -> M be a continuous map. Then N(f ) = 1/| Phi | Sum_{A in Phi} | ...

Since Bose and Einstein discovered the condensation of Bose gas, which we now call Bose-Einstein condensation, its mathematical properties have been of great importance for mathematical physics. Recently, many rigorous results have been obta...

Magnetic Resonance Electrical Impedance Tomography (MREIT) is a late medical imaging modality visualizing static conductivity images of electrically conducting subjects. When we inject current into the object, it produces internal distributi...

Abstract: While the typical behaviors of stochastic systems are often deceptively oblivious to the tail distributions of the underlying uncertainties, the ways rare events arise are vastly different depending on whether the underlying tail ...

Many mathematical and computational analyses have been performed for deterministic partial differential equations (PDEs) that have perfectly known input data. However, in reality, many physical and engineering problems involve some level of ...

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...

양자컴퓨터와 양자암호로 대표되는 양자기술의 응용이 대두되면서 그 기반이 되는 양자정보학에 대한 관심이 그 어느때보다 높다. 양자정보학은 양자상태의 정보량 및 양자상태를 전송할 때 전달되는 정보량을 분석하고자 하는 목표를 가지고 있는데 많은 경우...

We consider the problem of identifying the material properties from boundary measurements. For the conductivity case, this is known as Calderon problem: “Is it possible to determine the electrical conductivity inside a domain from the bounda...

Volume entropy of a compact manifold is the exponential growth rate of balls in the universal cover. This seemingly coarse invariant contains a lot of geometric information of the manifold. We will discuss some relations to other invariants,...

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...

..

In this talk, I will introduce the audience to the original beauty that leads to exploring the mathematical elements in music. I will cover the following topics on the connection between music and mathematics. - Harmonics & equations - ...