As it will be clear, the proof of [MSS13] although not being long is very involved and has several novel ideas. So, we start with a significantly simpler setup and we prove relatively weaker statements. As the ideas become more clear we will go over the actual ideas in [MSS13]. The materials of this lecture are based on the work of Batson, Spielman and Srivastava [BSS14] and lecture notes of Ni...

In this paper, single stage stochastic programs with ambiguous distributions for the involved random variables are considered. Though the true distribution is unknown, existence of a reference measure P̂ enables the construction of non-parametric ambiguity sets as Kantorovich balls around P̂ . The resulting robustified problems are infinite optimization problems and can therefore not be solved co...

Raymond A. Harvey, MPH; Jeremy Rassen, ScD; Carly Kabelac, BS; Wendy Turenne, MS; Sandy Leonard, Reyna Klesh, William Meyer III, PhD, D(ABMM), MLS(ASCP)CM; Harvey W. Kaufman, MD, MBA; Steve Anderson, PhD; Oren Cohen, MD; Valentina I. Petkov, Kathy Cronin, Alison L. Van Dyke, Douglas R. Lowy, Norman E. Sharpless, Lynne T. Penberthy, MPH

We analyze Hawking evaporation of the Callan-Giddings-Harvey-Strominger black holes from a quantum geometry perspective and show that information is not lost, primarily because the quantum space-time is sufficiently larger than the classical. Using suitable approximations to extract physics from quantum space-times we establish that (i) the future null infinity of the quantum space-time is suff...

We construct geometric representatives for the C 2 /Z n fractional branes in terms of branes wrapping certain exceptional cycles of the resolution. In the process we use large radius and conifold-type monodromies, and also check some of the orbifold quantum symmetries. We find the explicit Seiberg-duality, in the Berenstein-Douglas sense, which connects our fractional branes to the ones given b...