We provide a general introduction to the field of inverse boundary problems for elliptic PDE, with the celebrated Calderon problem serving as a prototypical example. The emphasis of the talk is on the techniques based on Carleman estimates and their role in the construction of complex geometric optics solutions. We also survey some of the more recent developments, including partial data problems, inverse boundary problems on manifolds, as well as inverse boundary problems for non-linear equations.
A typical result in graph/hypergraph theory has the following structure: Every G satisfying certain conditions must have some target property P. For example, a classical theorem by Dirac asserts that every graph on n vertices and with minimum degree at least n/2 must contain a hamiltonian cycle (that is, a cycle that passes through every vertex).
After establishing such a theorem, it is natural to ask how ``robust'' is G with respect to this property P. In this talk we discuss some possible measures of ``robustness'' and illustrate them with many examples.
iFEM is a MATLAB software package containing robust, efficient, and easy-following codes for the main building blocks of adaptive finite element methods on unstructured simplicial grids in both two and three dimensions. Besides the simplicity and readability, sparse matrixlization, an innovative programming style for MATLAB, is introduced to improve the efficiency. In this novel coding style, the sparse matrix and its operations are used extensively in the data structure and algorithms.
In this seminar we will examine the question of "What is reasonable?" in the context of a professor's expectations for teaching assistants in the Department of Mathematics at UCI.
We will break up into small groups; each group will be asked to determine the reasonableness of a particular expectation taken from an exemplary list and then present to the entire class a summary of its findings.
Furthermore, we will open the discussion to any particular expectations that graduate students have encountered that they found unreasonable, and the various ways for handling such situations.
Are most people reasonable? Be prepared to explore this question and candidly share your experiences.
