Please join us welcoming Ph.D student Luis Caicedo Torres for this week's graduate student seminar.  

Our Graduate Student Seminar gives students the ability to showcase interesting results that they have found in their research. Presenters are typically graduate students in mathemathematics, but can also be undergraduates, students in other disiplines, and faculty as well. 

Presentations should be able to be understood by undergraduate students in mathematics or related disipline. 

Abstract: The scientific literature has produced many examples of the phenomenon known as anomalous diffusion (where particles don’t behave/move “normally”). We wish to model anomalous wave behavior in the Fractional-in-Time Superdiffusive Nonlinear Schrodinger Equation (F-SNLS).  This model will help explain anomalous diffusion behavior present in quantum systems. While interpolating between the classical Schrodinger Equation and the Wave Equation, the F-SNLS will exhibit wave-like behavior but enjoy none of the usual (very nice) behaviors expected such as conserved quantities and a semigroup property. In this talk, we introduce the model and prove an existence result for the inhomogenous problem through the help of our friend, the Laplace Transform. This talk will be accessible to undergrads so all are welcome!