Richard Schoen, Bass Professor of Humanities and Sciences
Tue Mar 12, 2013
The theory of minimal surfaces arose historically from work of J. L. Lagrange and physical observations of J. Plateau almost 200 years ago. Rigorous mathematical theory was developed in the 20th century. In more recent times the theory has found important applications to diverse areas of geometry and relativity. In this talk, which is aimed at a...
Wed Jan 30, 2013
Traveling waves in actin have recently been reported in many cell types. Fish keratocyte cells, which usually exhibit rapid and steady motility, exhibit traveling waves of protrusion when plated on highly adhesive surfaces. We hypothesize that waving arises from a competition between actin polymerization and mature adhesions for VASP, a protein...
Thu Jan 24, 2013
The ability of eukaryotic cells to polarize is essential for their division, differentiation into distinct tissues, and migration. During polarization various polarity proteins segregate to form a distinct front and rear. To understand a mechanism for polarization we consider a simplified PDE model describing the interchange of a polarity protein...
Associate Professor Chiu-Yen Kao
Tue Jan 31, 2012
In this talk, an efficient rearrangement algorithm is introduced to the minimization of the positive principal eigenvalue under the constraint that the absolute value of the weight is bounded and the total weight is a fixed negative constant. Biologically, this minimization problem is motivated by the question of determining the optimal spatial...
Associate Professo Chiu-Yen Kao
Mon Jan 30, 2012
Differential and Integral Equations are powerful tools to model and analyze biological problems. In this talk, two different biological applications will be discussed: one is in biomedical images and the other is in cellular biology.
The basic medical science research and clinical diagnosis and treatment have strongly benefited from the...
Thu Jan 26, 2012
In 1966, Marc Kac in his famous paper 'Can one hear the shape of a drum?' raised the following question: Is a bounded Euclidean domain determined up to isometries from the eigenvalues of the Euclidean Laplacian with either Dirichlet or Neumann boundary conditions? Physically, one motivation for this problem is identifying distant physical objects...
Wed Jan 25, 2012
Modern material sciences focus on studies on the microscopic scale. This calls for mathematical understanding of electronic structure and atomistic models, and also their connections to continuum theories. In this talk, we will discuss some recent works where we develop and generalize ideas and tools from mathematical analysis of continuum...