Abstract
Oncogene signaling is known to deregulate cell proliferation re-
sulting in uncontrolled growth and cellular transformation. Gene
amplification and/or somatic mutations of the HER2/Neu (ErbB2)
protooncogene occur in approximately 20% of breast cancers. A
therapeutic strategy that has been used to block HER2 function is
the small molecule tyrosine kinase inhibitor lapatinib. Using human
mammary epithelial cells that overexpress HER2, we determined the
antiproliferative effect of lapatinib through measuring the total cell
number and analyzing the cell cycle distribution. A mathematical
model was used to interpret the experimental data. The model sug-
gests that lapatinib acts as expected by slowing the transition through
G1 phase. However, the experimental data indicated a previously un-
reported late cytotoxic effect, which was incorporated into the model.
Both effects depend on the dosage of the drug in a linearsaturating
fashion. The model separates quantitatively the cytostatic and cy-
totoxic effects of lapatinib and may have implications for preclinical
studies with other antioncogene therapies.
This is joint work with Dr. Shizhen Emily Wang (Department
of Cancer Biology, Vanderbilt University), Dr. Carlos Arteaga (De-
partment of Cancer Biology and Department of Medicine, Vanderbilt
University), and Dr. Glenn F. Webb, (Department of Mathematics,
Vanderbilt University).

In this talk I will describe the progress that has been made so far
concerning the existence of global strong solutions to the
L^{2}-critical defocusing semilinear Schr\"odinger equation. A long
standing conjecture in the area is the existence
of a unique global strong L^{2}
solution to the equation that in addition scatters to a free solution as
time goes to infinity. I will demonstrate the proofs of partial results
towards an attempt for a final resolution of this conjecture.
I will concentrate on the low dimensions but give the flavor of the results in higher dimensions for general or spherically symmetric initial data in certain Sobolev spaces.
Many authors have contributed to the theory of this equation. I will convey my personal involment to the problem and the results that I have obtained recently. Part of my work is in collaboration with D. De Silva, N. Pavlovic, G.
Staffilani, J. Colliander and M. Grillakis.