Study of massless spectrum in heterotic compactifications.
problem Calculating the massless spectrum of heterotic compactifications.
method From F-term conditions in a four-dimensional effective theory, considering anomaly cancellation.
result Results agree with recent computations of the infinitesimal moduli space.
Four-dimensional Einstein Dehn filling is impossible.
problem Complex-hyperbolic Einstein Dehn filling in four dimensions.
method Proof of impossibility.
result Complex-hyperbolic Einstein Dehn filling cannot be performed in dimension four.
This review discusses G2-Manifolds and their role in M-Theory compactifications.
problem Understanding the mathematical structure of G2-Manifolds for M-Theory compactifications. method Mathematical and physical considerations of G2-Manifolds and their compactifications. result Progress in constructing and understanding G2-Manifolds. In this thesis, we study moduli in compactifications of ten-dimensional heterotic supergravity. We consider supersymmetric compactifications to four-dimensional maximally symmetric space, commonly referred to as the Strominger system. The compact part of space-time X is a six-dimensional manifold of what we refer to …
Derives fluxes in M-theory compactifications and connects them to threebrane sigma-models.
problem Deriving fluxes in M-theory compactifications and understanding their geometric and topological properties.
method Systematic derivation of fluxes from higher Courant brackets and generalized geometry, relating them to threebrane sigma-models.
result Fluxes in M-theory compactifications are understood as generalized Wess-Zumino terms in threebrane sigma-models, linking higher structure to Lie algebroid homotopy.
Derives inequalities for eigenvalues and renormalized volume of Poincaré-Einstein manifolds.
problem Eigenvalues and renormalized volume of Poincaré-Einstein manifolds.
method Integral inequality and eigenvalue estimates.
result Sharp lower bound for first eigenvalue and new upper bound for renormalized volume.
We study the Hamiltonian vector field v=(−∂f/∂w,∂f/∂z) on C2, where f=f(z,w) is a polynomial in two complex variables, which is non-degenerate with respect to its Newton's polygon. We introduce coordinates in four-dimensional neighbourhoods of the "points at infinity", in …
We investigate the local geometry on the moduli space of G_2 structures that arises in compactifications of M-theory on holonomy G_2 manifolds. In particular, we determine the homogeneity properties of couplings of the associated N=1, D=4 supergravity under the scaling of moduli space coordinates. We then find some bra…
We generalize our previous results (Theorem 1 and Corollary 2 in arXiv:1412.4114) and Theorem 1 in arXiv:1502.00668) on the existence of an L2-energy gap for Yang-Mills connections over closed four-dimensional manifolds and energies near the ground state (occupied by flat, anti-self-dual, or self-dual connections) t…
The Planck mass can be derived from gravitational potential behavior in compactifications.
problem Deriving the Planck mass from gravitational potential behavior in compactifications.
method Physical considerations and Weyl law application to gravitational potential behavior.
result The Planck mass can be reconstructed from the asymptotics of the masses of spin 2 Kaluza--Klein modes.
We study the physics of globally consistent four-dimensional N=1 supersymmetric M-theory compactifications on G2 manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these manifolds. We study a rich example that exhibits U(1)3 gauge symmetry and a spectrum o…
Summarizes geometric formulation of Einstein-Scalar-Maxwell theories.
problem Geometric formulation of Einstein-Scalar-Maxwell theories.
method Global geometric formulation using flat symplectic vector bundles.
result Describes scalar-electromagnetic symmetry group and Dirac quantization condition.
I review some recent results on four-manifold invariants which have been obtained in the context of topological quantum field theory. I focus on three different aspects: (a) the computation of correlation functions, which give explicit results for the Donaldson invariants of non-simply connected manifolds, and for gene…
We use the twistorial construction of D-instantons in Calabi-Yau compactifications of type II string theory to compute an explicit expression for the metric on the hypermultiplet moduli space affected by these non-perturbative corrections. In this way we obtain an exact quaternion-Kahler metric which is a non-trivial d…
Many four-dimensional supersymmetric compactifications of F-theory contain gauge groups that cannot be spontaneously broken through geometric deformations. These "non-Higgsable clusters" include realizations of SU(3), SU(2), and SU(3)×SU(2), but no SU(n) gauge groups or factors with n>3. We study poss…
We present a comprehensive classification of supersymmetric vacua of M-theory compactification on seven-dimensional manifolds with general four-form fluxes. We analyze the cases where the resulting four-dimensional vacua have N = 1,2,3,4 supersymmetry and the internal space allows for SU(2), SU(3) or G_2 structures. In…
Researchers find solutions to Einstein equations in higher dimensions.
problem Finding spatially homogeneous solutions to vacuum Einstein equations in general dimensions.
method Assumed spatially homogeneous spacetime, solved Einstein equations for globally hyperbolic spacetimes with specific symmetry groups.
result Spatially homogeneous solutions found, corresponding to Bianchi type II in 4D, and constraints on spacetime expansion.
Study shows Satake compactifications as horofunctions with polyhedral metrics.
problem Understanding horofunction compactifications of symmetric spaces.
method Investigated invariant Finsler metrics and polyhedral metrics for compactification.
result Generalized Satake compactifications realized as horofunction compactifications.
We construct a triangulation of a compactification of the Moduli space of a surface with at least one puncture that is closely related to the Deligne-Mumford compactification. Specifically, there is a surjective map from the compactification we construct to the Deligne-Mumford compactification so that the inverse image…
Study on Kapustin-Witten equations on 4D manifolds, proving moduli space properties.
problem Proving properties of moduli space of Kapustin-Witten equations.
method Use of Taubes' compactness theorem and properties of ASD connections.
result Proves moduli space of Kapustin-Witten equations is non-connected for generic ASD connections.
A new compactification of outer space is an absolute retract.
problem Compactification of outer space for FN-actions on R-trees. method Defining a new compactification CVN as a blow-up of the classical compactification CVN, assigning orientations to arcs. result The new compactification CVN is an absolute retract. The paper constructs examples of compactifications for Einstein metrics.
problem Compactifying Einstein metrics with specific properties.
method Constructing projective and c--projective compactifications. result Neutral signature Einstein metrics can be compactified canonically.
Extends harmonic maps compactification to punctured Riemann surfaces.
problem Compactifying Teichmüller spaces for punctured Riemann surfaces.
method Using harmonic maps rays to extend compactification.
result The compactification still coincides with Thurston's compactification.
Paper relates new compactification to classical moduli space.
problem Relating new compactification to classical moduli space.
method Defining a continuous finite-to-one surjection between compactifications.
result Uniform upper bound on cardinalities of fibers.
The horoboundary of Teichmüller space is path connected and has non-dense Busemann points.
problem Characterizing the horoboundary of Teichmüller space.
method Using the relationship between the horofunction and visual compactifications of Teichmüller spaces.
result The horoboundary of Teichmüller space is path connected and has non-dense Busemann points.
Existence of Kähler-Einstein metrics on compactifications of Lie groups.
problem Existence of Kähler-Einstein metrics on Q-Fano compactifications of Lie groups. method Proving existence through compactifications of Lie groups.
result Classification of Q-Fano compactifications of SO4(C) with Kähler-Einstein metrics. Satake has constructed compactifications of symmetric spaces D=G/K which (under a condition called geometric rationality by Casselman) yield compactifications of the corresponding locally symmetric spaces. The different compactifications depend on the choice of a representation of G. One example is the Baily-Borel-Sata…
Characterizes toroidal and semi-toric compactifications as log minimal models and applies to weak K-moduli.
problem Characterizing and applying toroidal and semi-toric compactifications to weak K-moduli.
method Characterizes toroidal and semi-toric compactifications as log minimal models and applies to weak K-moduli.
result Different proof of a theorem of Alexeev-Engel on weak K-moduli compactifications.
The paper explores ball quotient compactifications and their properties.
problem Smooth toroidal compactifications of ball quotients cannot contain properly holomorphically embedded 3-punctured spheres.
method Use totally geodesic punctured spheres to prove ampleness of KX+αD for α∈(41,1). result First examples of bielliptic ball quotient compactifications are produced.
The paper explores symmetry properties of four-dimensional Walker manifolds.
problem Characterizing geometric properties of Walker manifolds.
method Investigation of curvature tensors and characterization theorems.
result Characterization theorems obtained for four-dimensional Walker manifolds.
The paper studies compactifications of SL(2,C) character varieties for punctured surfaces.
problem Compactifying character varieties of punctured surfaces.
method Projective compactifications using ideal triangulations and Komyo's method.
result Boundary divisors are toric varieties and the boundary complex is a sphere.
Compactifies semi-simple Lie groups to manifolds with corners.
problem Compactification of semi-simple Lie groups.
method hd-compactification to a manifold with corners, 1-1 correspondence with conjugacy classes of parabolic subgroups.
result Harish-Chandra's Schwartz space identified with conormal functions of rapid-logarithmic decay.
New coordinates for Teichmüller space compactification.
problem Compactification of Teichmüller space.
method Defined new coordinates.
result Thurston compactification is radial compactification of Euclidean space.
New compactification for character varieties with good topological properties.
problem Compactification of character varieties with good topological properties.
method Announced a new compactification with interpretations of ideal points.
result Relates to Weyl chamber length compactification and applies to maximal and Hitchin representations.
Embeds Higson compactification into adelic solenoids.
problem Embedding Higson compactification into solenoids.
method Induces isomorphism of 1-dimensional cohomology.
result Higson compactification embeds into adelic solenoids.
We define a compactification of symmetric spaces of noncompact type, seen as spaces of isometry classes of marked lattices, analogous to the Thurston compactification of the Teichmüller space, and we show that it is equivariantly isomorphic to a Satake compactification. We then use it to define a new compactification o…
Researchers create a new compactification of character varieties using geometric and algebraic methods.
problem Compactifying character varieties of finitely generated groups in PSL2(R). method Geometric interpretation of elements of the real spectrum compactification as Γ-actions on R-trees, endowed with an orientation. result Continuous surjection from real spectrum compactification to oriented Gromov equivariant compactification.
Paper studies compactifications of Higgs bundles and self-duality equations.
problem Compactification of Hitchin moduli space and Higgs bundles.
method Analyzes maps between algebraic and analytic compactifications.
result Map between compactifications fails to be continuous at boundary over discriminant locus.
We show that the horofunction compactification of Teichmüller space with the Teichmüller metric is homeomorphic to the Gardiner-Masur compactification.
Paper shows geometric properties preserved by compactifications in relation to coarse structures and group actions.
problem Geometric properties preserved by compactifications in relation to coarse structures and group actions.
method Analyzes compactifications of spaces with coarse structures and group actions, proving preservation of geometric properties.
result Geometric properties are preserved by compactifications when coarse structures and group actions are involved.
No natural topological compactification for Fulton-MacPherson.
problem Compactification of configuration spaces on topological manifolds.
method Using recent work on configuration spaces and compactifications.
result Fulton-MacPherson compactification cannot be extended topologically.
Study finds all 4D neutral manifolds.
problem Classifying neutral manifolds in four dimensions.
method Examined homogeneous semi-symmetric neutral manifolds.
result Identified all four-dimensional neutral manifolds.
New types of Ricci solitons found in 4D Lorentzian geometry.
problem Understanding Ricci solitons in Lorentzian geometry.
method Analyzing four-dimensional Lie groups for left-invariant Lorentz metrics.
result Any connected and simply connected 4D Lie group admits a left-invariant Lorentz metric that is a Ricci soliton.
The paper classifies and computes limits of equivariant compactifications of groups.
problem Classifying and computing limits of equivariant compactifications of groups.
method Equivariant normal R-test configurations and semistable limits.
result Semistable limits of K-unstable Fano group compactifications are computed.
The paper extends end concepts to arbitrary groups and spaces.
problem Extending end concepts to arbitrary groups and spaces.
method Description of maximal coarse compactification and geometric proof of end properties.
result Generalization of Stallings' theorem and definition of ends for coarse spaces.
The study finds only finitely many Kähler-Einstein compactifications for semisimple groups.
problem Classifying Q-Fano compactifications of semisimple groups with Kähler-Einstein metrics. method Proving finiteness through classification of compactifications.
result There are only finitely many Q-Fano compactifications of semisimple groups with Kähler-Einstein metrics. In this paper we present a topological way of building a compactification of a symmetric space from a compactification of a Weyl Chamber.
To study a noncompact Riemannian manifold, it is often useful to find a compactification. We discuss several common compactifications and survey some recent results.