Recall that Ωn = SL(n,R)/SL(n,Z) is the space of covolume 1 lattices in R. This space is non-compact, since we can have arbitrarily short vectors in a lattice. We will refer to moduli spaces of translation surfaces as defined in the lectures by Howard Masur in this volume [Ma1, Definition 6] as strata. Note that the case of n = 2 in the space of lattices and the case of the stratum H1(∅) boil d...

We study possible deformations of BPS supertubes keeping their conserved charges fixed. We show that there is no flat direction to closed supertubes of circular cross section with uniform electric and magnetic fields, and also to open planar supertubes. We also find that there are continuously infinite flat deformations to supertubes of general shape under certain conditions.

In this paper we study topology of moduli spaces of tropical curves of genus g with n marked points. We view the moduli spaces as being imbedded in a larger space, which we call the moduli space of metric graphs with n marked points. We describe the shrinking bridges strong deformation retraction, which leads to a substantial simplification of all these moduli spaces. In the rest of the paper, ...

0. Introduction 1 1. Main definitions 3 2. Polarized stable reductive varieties 4 2.1. Classification 4 2.2. Cohomology groups 8 3. Pairs 9 4. Moduli of stable reductive pairs 10 4.1. General remarks on families 10 4.2. One-parameter degenerations 11 4.3. Construction of the moduli space of pairs 13 4.4. Projectivity of the moduli space 17 4.5. Structure of the moduli space 18 5. Connection wit...

We discuss the quantum scattering process in the moduli space consisting of two maximally charged dilaton black holes. The black hole moduli space geometry has different structures for arbitrary dimensions and various values of dilaton coupling. We study the quantum effects of the different moduli space geometries with scattering process. Then, it is found that there is a resonance state on cer...

Let G be a compact connected semisimple Lie group. We extend the techniques of Weinstein [W] to give a construction in group cohomology of symplectic forms ω on ‘twisted’ moduli spaces of representations of the fundamental group π of a 2-manifold Σ (the smooth analogues of Hom(π1(Σ), G)/G) and on relative character varieties of fundamental groups of 2-manifolds. We extend this construction to e...

We prove a general criterion for an algebraic stack to admit a good moduli space. This result may be considered as a generalization of the Keel-Mori theorem, which guarantees the existence of a coarse moduli space for a separated DeligneMumford stack. We apply this result to prove that the moduli stacksMg,n(α) parameterizing α-stable curves introduced in [AFSv14] admit good moduli spaces.

Target space duality symmetries, which acts on Kähler and continuous Wilson line moduli, of a Z N (N = 2) 2-dimensional subspace of the moduli space of orbifold compactification are modified to include twisted moduli. These spaces described by the cosets SU (n,1) SU (n)×U (1) are special Kähler, a fact which is exploited in deriving the extension of tree level duality transformation to include ...

For a 1-connected spectrum E, we study the moduli space of suspension spectra which come equipped with a weak equivalence to E. We construct a spectral sequence converging to the homotopy of the moduli space in positive degrees. In the metastable range, we get a complete homotopical classification of the path components of the moduli space. Our main tool is Goodwillie’s calculus of homotopy fun...

The classical formula of Siegel and Weil identifies the values of Siegel–Eisenstein series at certain critical points as integrals of theta functions. When the critical point is the center of symmetry for the functional equation, the Fourier coefficients of the values of the ‘even’ Siegel–Eisenstein series thus contain arithmetic information about the representations of quadratic forms. It is n...