Tuesday, April 17, 2018
04/17/2018 - 4:00pm to 5:00pm
The continuation of NLS solutions beyond the singularity has been an open problem for many years. In the first part of this talk, I will discuss several potential continuations. A common feature of all these continuations is that the solution phase is lost after the singularity. Then I will show that ``loss of phase'' can occur even if the NLS solution does not collapse (e.g., in the subcritical case). Therefore, if two NLS solutions travel a sufficiently long distance (time) before interacting, it is not possible to predict whether they would intersect in- or out-of-phase. Hence, if the underlying propagation model is non-integrable, a deterministic prediction of the interaction outcome becomes impossible. ``Fortunately’’, because the relative phase between the two solutions becomes uniformly distributed in [0, 2π], the statistics of the interaction outcome is universal, and can be efficiently computed using a novel uncertainty-quantification approach, even when the distribution of the noise source is unknown.
04/17/2018 - 4:30pm to 5:30pm
Whenever a finite group G acts on a 2dquantum field theory, it determines a ``gauge anomaly'' living in the fourth integral group cohomology of G. I will describe what I know about H4 for certain sporadic groups, focusing on the most charismatic ones: the Monster and Conway's largest group. In particular, I will suggest thatoften H4(G) is cyclic and generated by the gauge anomaly of a distinguished ``moonshine'' representation of G.