U-dual fluxes and Generalized Geometry

NS-NS fluxes in Hitchin’s generalized geometry

The standard notion of NS-NS 3-form flux is lifted to Hitchin’s generalized geometry. This generalized flux is given in terms of an integral of a modified Nijenhuis operator over a generalized 3-cycle. Explicitly evaluating the generalized flux in a number of familiar examples, we show that it can compute three-form flux, geometric flux and non-geometric Q-flux. Finally, a generalized connectio...

Sigma Models, NS-fluxes and Generalized Kähler Geometry

Heterotic Geometry and Fluxes

We begin by discussing the question, “What is string geometry?” We then proceed to discuss six-dimensional compactification geometry in heterotic string theory with fluxes. A class of smooth nonKähler compact solutions is presented and relations between Kähler and non-Kähler solutions are pointed out.

Generalized Geometry , Parallelizability and Non Geometry

U-statistics in stochastic geometry

A U-statistic of order k with kernel f :X →Rd over a Poisson process is defined in [25] as ∑ x1,...,xk∈η 6= f (x1, . . . ,xk) under appropriate integrability assumptions on f . U-statistics play an important role in stochastic geometry since many interesting functionals can be written as Ustatistics, like intrinsic volumes of intersection processes, characteristics of random geometric graphs, v...