If K is a compact Lie group and g ≥ 2 an integer, the space K is endowed with the structure of a Hamiltonian space with a Lie group valued moment map Φ. Let β be in the centre of K. The reduction Φ(β)/K is homeomorphic to a moduli space of flat connections. When K is simply connected, a direct consequence of a recent paper of Bott, Tolman and Weitsman is to give a set of generators for the K-eq...

Abstract Consider the cubic nonlinear Schrödinger equation set on a d -dimensional torus, with data whose Fourier coefficients have phases which are uniformly distributed and independent. We show that, average, evolution of moduli is governed by so-called wave kinetic , predicted in turbulence theory, nontrivial timescale.

We determine the possible even sets of nodes on sextic surfaces in P, showing in particular that their cardinalities are exactly the numbers in the set {24, 32, 40, 56}. We also show that all the possible cases admit an explicit description. The methods that we use are an interplay of coding theory and projective geometry on one hand, of homological and computer algebra on the other. We give a ...

We study the moduli spaces and compute the fundamental groups of plane sextics of torus type with the set of inner singularities 2A8 or A17. We also compute the fundamental groups of a number of other sextics, both of and not of torus type. The groups found are simplest possible, i.e., Z2 ∗Z3 and Z6, respectively.

In the moduli space of quadratic differentials over complex structures on a surface, we construct a set of full Hausdorff dimension of points with bounded Teichmüller geodesic trajectories. The main tool is quantitative nondivergence of Teichmüller horocycles, due to Minsky and Weiss. This has an application to billiards in rational polygons.

The moduli spaceMg of compact Riemann surfaces of genus g has orbifold structure, and the set of singular points of such orbifold is the branch locus Bg. For g 6≡ 3 mod 4, g ≥ 26, g 6= 37, there exists isolated strata corresponding to families of pentagonal Riemann surfaces.

We investigate the conditions for a QCD axion to coexist with stabilised moduli in string compactifications. We show how the simplest approaches to moduli stabilisation give unacceptably large masses to the axions. We observe that solving the F-term equations is insufficient for realistic moduli stabilisation and give a no-go theorem on supersymmetric moduli stabilisation with unfixed axions ap...

Forced Chemical Vapor Infiltration (FCVI) method was used in fabricating the Nicalon TM!Silicon Carbide composites. Both through-thickness and In-plane (fiber fabric plane) moduli were determined using ultrasonic techniques. The through-thickness moduli were found to be much less than the inplane moduli. Both in-plane and through-thickness moduli were significantly decreased with an increased p...

We introduce the notion of an adequate moduli space. The theory of adequate moduli spaces provides a framework for studying algebraic spaces which geometrically approximate algebraic stacks with reductive stabilizers in characteristic p. The definition of an adequate moduli space generalizes the existing notion of a good moduli space to characteristic p (and mixed characteristic). The most impo...

The magnitude of the vacuum expectation value Gukov-Vafa-Witten superpotential | W 0 $|W_0|$ plays a central role in phenomenology type IIB flux compactifications. Recent analytical constructions have shown that perturbatively flat vacua can be used to obtain very low values . We present systematic algorithms carry out exhaustive numerical searches for such vacua. also analyse them statistical ...