Welcome to Wasin So's Ph.D. Thesis Page

In 1991, I finished the Ph. D.  thesis entitled "Exponential formulas and spectral indices" under the supervision of Professor Robert C. Thompson. 

Following is the abstract of the thesis.

The object of study is the matrix exponential. We are especially interested in a product of matrix exponentials. Chapter 1 is a collection of basic and known facts about the matrix exponentials. The only new result is a necessary condition on the singular values of a matrix and those of its exponential. In Chapter 2, we study the Campbell-Baker-Hausdorff formula, which expresses the product of two exponentials as the exponential of a "sum". Special attention is given to the estimation of domains of absolute convergence for different presentations of this formula and we use the techniques of majorizing series. For a product of matrix exponentials, we prove some special cases of three conjectured formulas in Chapter 3. As consequences, we have complete proofs of these formulas for 2x2 matrices. These proofs are mainly matrix-theoretic. Chapter 4 is devoted to investigating the possibility of some naive matrix exponential formulas. Finally, as an application of matrix exponential formulas, three different types of spectral indices are proved to be equivalent in Chapter 5.

Following are published papers resulted from the thesis.

Lectures related to the thesis.

This series of lectures is based on my Ph.D. thesis "Exponential Formulas and Spectral Indices", which was finished  in UC Santa Barbara under the supervision of Professor R.C. Thompson. There are 10 lectures, each of which is featured a published article coming out of the thesis. In each lecture, background and history will be provided to understand the research. Then results from the published article will be given. Later work in the same direction will be discussed. Unsolved problems will be posed as conjectures or open questions.