Seth Figueroa is awarded a 2012 National Science Foundation (NSF) Graduate Research Fellowship (GRF). The NSF-GRF fellowship consisting of an annual stipend of $30,000 for three years is considered to be one of the most prestigious graduate research fellowships in US. The title of Seth Figueroa's NSF-GRF application is “Modeling and Simulating Tissue Growth with Stem Cells”. This is the first ever NSF-GRF awarded to a graduate student in the Department of Mathematics at UCI.
A classical result by Pál Turán, estimates the global behavior
of an exponential polynomial on an interval by its supremum on any
arbitrary subinterval. In this talk we discuss Nazarov's extension of this
``global to local reduction'' to arbitrary Borel sets of positive Lebesgue
measure.
Using the idea of "acceleration", which is first introduced by Avila, I will construct a
cerntain class of analytic quasiperiodic Szego cocycles with uniformly positive LE.