Free boundary problems arising from mathematical finance
Many problems in financial mathematics are closely related to the stochastic optimization problem because the optimal decision must be made under the uncertainty. In particular, optimal stopping, singular control, and optimal switching prob...
Vlasov-Maxwell equations and the Dynamics of Plasmas
In this colloquium talk, we study the Vlasov-Maxwell equations, a collisionless model in the field of kinetic theory. The model is a fundamental model for the dynamics of plasmas and was introduced in 1938 by Vlasov. Due to the hyperbolic n...
Fixed points of symplectic/Hamiltonian circle actions
A circle action on a manifold can be thought of as a periodic flow on a manifold (periodic dynamical system), or roughly a rotation of a manifold. During this talk, we consider symplectic/Hamiltonian circle actions on compact symplectic mani...
<학부생을 위한 ɛ 강연> Mathematics and music: Pythagoras, Bach, Fibonacci and AI
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 - ...
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...
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...
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...
Analysis and computations of stochastic optimal control problems for stochastic PDEs
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 ...
Heavy-tailed large deviations and deep learning's generalization mystery
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 ...
Role of Computational Mathematics and Image Processing in Magnetic Resonance Electrical Impedance Tomography (MREIT)
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...
The Mathematics of the Bose Gas and its Condensation
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...
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} | ...
<정년퇴임 기념강연> Hardy, Beurling, and invariant subspaces
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...
Global result for multiple positive radial solutions of p-Laplacian system on exterior domain
Global result for multiple positive radial solutions of p-Laplacian system on exterior domain In this talk, we consider p-Laplacian systems with singular indefinite weights. Exploiting Amann type three solutions theorem for the singular syst...
On function field and smooth specialization of a hypersurface in the projective space
In this talk, we will discuss two interesting problems on hypersurfaces in the projective space. The first one is the absolute Galois theory on the function field of a very general hypersurface in the projective space. The other one is the c...
Creation of concepts for prediction models and quantitative trading
Modern mathematics with axiomatic systems has been developed to create a complete reasoning system. This was one of the most exciting mathematical experiments. However, even after the failure of the experiment, mathematical research is still...
