Extended Harper's model arises in a quantum description of a 2d- crystal layer subjected to an external magnetic field. As a first step towards the spectral analysis we shall introduce the Lyapunov exponent and present a
method of computation valid for any analytic cocycle with possible singularities. This enables us to give a description of the metal-insulator properties for extended Harper's model, which so far did not even exist on a heuristic level in physics literature. We finish the
talk with some results on the spectral analysis of the model.

If a random Hermitian Gaussian matrix (GUE matrix) is perturbed additively by a matrix of small rank, the largest eigenvalue undergoes a transition depending on the spectrum of the added matrix. We consider a generalization of this case with general potential. When the potential is convex, the transition phenomenon is universal. However, for non-convex potentials, new types of transition may occur. This is a joint work with Dong Wang.

The limit shape of Young diagrams under the Plancherel
measure was found by Vershik \& Kerov (1977) and Logan \& Shepp
(1977). We obtain a central limit theorem for fluctuations of Young
diagrams in the bulk of the partition '`spectrum''. More
specifically, under a suitable (logarithmic) normalization, the
corresponding random process converges (in the FDD sense) to a
Gaussian process with independent values. We also discuss a link
with an earlier result by Kerov (1993) on the convergence to a
generalized Gaussian process. The proof is based on poissonization
of the Plancherel measure and an application of a general central
limit theorem for determinantal point processes. (Joint work with
Zhonggen Su.)

In the late 1980's I began my efforts to increase the success rate of minorities in first semester calculus. The interventions that I devised were very time consuming and as the number of minority students increased, I could not manage that kind of effort. I developed my Calculus Minority Advising Program in an effort to meet with scores of minority students each semester. This program consists of a twenty-minute meeting with each student at the beginning of each semester. These meetings with students eventually transformed my own attitude about the importance of mathematics in their undergraduate curriculum.

I took over the position of Associate Head for Undergraduate Affairs in the department in 2003. I set a very modest goal for myself: to double the number of mathematics majors. With almost 600 mathematics majors I have reached that goal. I think the next doubling is going to be much harder to achieve. My work with minority students provided me with the tools to accept this new challenge of working with all students.

This talk will describe my own efforts to encourage ALL of our students that a mathematics major, or adding mathematics as a second major, is a great career choice. I will also describe the support that I have from the university and the department that enables me to carry out these tasks.