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...
If a problem has an approximate solution, we try to get some information of the linearized kernel of the problem at the approximate solution to find a real solution. In this talk, I would like to introduce a different approach which is purel...
Chern-Simons invariant and eta invariant for Schottky hyperbolic manifolds
In this talk, I will explain a relationship of the Chern-Simons invariant and the eta invariant for Schottky hyperbolic manifolds. The relating formula involves a defect term given by the Bergman tau function over the conformal boundary Riem...
Brownian motion with darning and conformal mappings
Brownian motion with darning (BMD) is a diffusion process obtained from Brownian motion by shorting each hole in the space into one point. In this talk, I will present a quick introduction to BMD and its basic properties including the zero p...
Category수학강연회소속University of Washington강연자Zhen-Qing Chen
Categorical representation theory, Categorification and Khovanov-Lauda-Rouquier algebras
Representation theory is to study the actions of groups or algebras on vector spaces. Recently, its categorical version, categorical representation theory, attracts researchers in representation theory. In this theory we replace "vector spac...
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...
There are basically two approaches for solving linear systems: one is to exactly solve the linear sytem such as Gaussian-elimination. The other approximates the solution in the Krylov spaces; Conjugate-gradient and General minimum residual m...
Spectral Analysis for the Anomalous Localized Resonance by Plasmonic Structures
We present a mathematical justification of cloaking due to anomalous localized resonance (CALR). We consider the dielectric problem with a source term in a structure with a layer of plasmonic material. Using layer potentials and symmetrizati...
In this talk, we briefly introduce how a combinatorial object, Integer partition, is related with number theoretic subjects : q-series and modular forms. In particular, we will focus on (1) combinatorial proof for q-series identities (2) ari...
Root multiplicities of hyperbolic Kac-Moody algebras and Fourier coefficients of modular forms
In this talk, we will consider the hyperbolic Kac-Moody algebra associated to a certain rank 3 Cartan matrix and generalized Kac-Moody algebras that contain the hyperbolic Kac-Moody algebra. The denominator funtions of the generalized Kac-Mo...
A new view of Fokker-Planck equations in finite and Infinite dimensional spaces
Fokker-Planck and Kolmogorov (backward) equations can be interpreted as linearisations of the underlying stochastic differential equations (SDE). It turns out that, in particular, on infinite dimensional spaces (i.e. for example if the SDE i...
The spaces admitting a rational parameterization are called rational. In particular plane conics, including circles, are rational. We will explain a few interesting applications of the rational parameterization of a circle. Also several exam...
