A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
In 1969, P. Deligne and D. Mumford compactified the moduli space of curves. Their compactification is a projective algebraic variety, and as such, it has an underlying analytic structure. Alternatively, the quotient of the augmented Teichmueller space by the action of the mapping class group gives a compactification of…
Paper studies compactifications of Higgs bundles and self-duality equations.
The group of direct isometries of the real n-dimensional hyperbolic space is G=SOo(n,1). This isometric action admits many differentiable compactifications into an action on the closed ball. We prove that all such compactifications are topologically conjugate but not necessarily differentiably conjugate. We give the cl…
In this paper we study the relationship between three compactifications of the moduli space of Hermitian-Yang-Mills connections on a fixed Hermitian vector bundle over a projective algebraic manifold of arbitrary dimension. Via the Donaldson-Uhlenbeck-Yau theorem, this space is analytically isomorphic to the moduli spa…
Constructs a combinatorial model for bordered Riemann surfaces with a compactification.
It is known that the hyperbolic plane admits a countable infinity of compactifications into a closed disk such that the isometric action of SL(2;R) acts analytically on the compactified space. We prove that among those compactifications, only the two most classical ones (namely the closures of Poincaré's disk and Klein…
Compactifies Calabi-Yau to weak Fano manifolds.
On an odd-dimensional oriented hyperbolic manifold of finite volume with strongly acyclic coefficient systems, we derive a formula relating analytic torsion with the Reidemeister torsion of the Borel-Serre compactification of the manifold. In a companion paper, this formula is used to derive exponential growth of torsi…
This is Part II of a series on noncompact isometry groups of Lorentz manifolds. We have introduced in Part I, a compactification of these isometry groups, and called ``bi-polarized'' those Lorentz manifolds having a ``trivial '' compactification. Here we show a geometric rigidity of non-bi-polarized Lorentz manifolds; …
Vortices and coupled vortices arise from Yang-Mills-Higgs theories and can be viewed as generalizations or analogues to Yang-Mills connections and, in particular, Hermitian-Yang-Mills connections. We proved an analytic compactification of the moduli spaces of vortices and coupled vortices on hermitian vector bundles ov…
The paper connects harmonic forms to tree maps and character varieties.
We provide new insight into the analysis of N-body problems by studying a compactification of that is compatible with the analytic properties of the -body Hamiltonian . We show that our compactification coincides with the compactification introduced by Vasy using blow-ups in order to stu…
In this work we generalize the classical notion of a (compact) twistor line in the period domain of compact complex tori. We introduce two new types of lines, which are non-compact analytic curves in the period domain of complex tori. We study the analytic properties of the compactifications of the curves, the preserva…
The paper finds symplectic compactifications of coadjoint orbits.
Let be a complex manifold and be an embedding of complex submanifold. Assuming that the embedding is -linearizable or -comfortably embedded, we construct via the deformation to the normal cone a diffeomorphism from a small neighborhood of the zero section in the normal bundle …
Yau proved an existence theorem for Ricci-flat Kähler metrics in the 1970's, but we still have no closed form expressions for them. Nevertheless there are several ways to get approximate expressions, both numerical and analytical. We survey some of this work and explain how it can be used to obtain physical predictions…
Let be an action of a Lie group on a manifold with boundary that is transitive on the interior. We study the set of actions that are topologically conjugate to , up to smooth or analytic change of coordinates. We show that in many cases, including the compactifications of negatively curved symmetric spaces, …
For an odd-dimensional oriented hyperbolic manifold with cusps and strongly acyclic coefficient systems we define the Reidemeister torsion of the Borel-Serre compactification of the manifold using bases of cohomology classes defined via Eisenstein series by the method of Harder. In the main result of this paper we rela…
Analytic torsion and Reidemeister torsion help show exponential growth of torsion in cohomology.
We show the analytic continuation of the resolvent of the Laplacian on asymptotically hyperbolic spaces on differential forms, including high energy estimates in strips. This is achieved by placing the spectral family of the Laplacian within the framework developed, and applied to scalar problems, by the author recentl…
Paper connects geometric and analytic aspects of Higgs bundles and pleated surfaces.
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…
We establish a Cheeger-Muller theorem for unimodular representations satisfying a Witt condition on a noncompact manifold with cusps. This class of spaces includes all non-compact hyperbolic spaces of finite volume, but we do not assume that the metric has constant curvature nor that the link of the cusp is a torus. We…
Extends harmonic maps compactification to punctured Riemann surfaces.
Paper relates new compactification to classical moduli space.
We consider horofunction compactifications of symmetric spaces with respect to invariant Finsler metrics. We show that any (generalized) Satake compactification can be realized as a horofunction compactification with respect to a polyhedral Finsler metric.
Existence of Kähler-Einstein metrics on compactifications of Lie groups.
The horoboundary of Teichmüller space is path connected and has non-dense Busemann points.
Characterizes toroidal and semi-toric compactifications as log minimal models and applies to weak K-moduli.
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…
Analyzes the moduli space of Higgs bundles to prove its quasi-projectivity.
The paper studies compactifications of SL(2,C) character varieties for punctured surfaces.
New coordinates for Teichmüller space compactification.
New compactification for character varieties with good topological properties.
Embeds Higson compactification into adelic solenoids.
We discuss the `hd-compactification' of a semi-simple Lie group to a manifold with corners; it is the real analog of the wonderful compactification of deConcini and Procesi. There is a 1-1 correspondence between the boundary faces of the compactification and conjugacy classes of parabolic subgroups with the boundary fa…
We show that the horofunction compactification of Teichmüller space with the Teichmüller metric is homeomorphic to the Gardiner-Masur compactification.
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…
We construct several examples of compactifications of Einstein metrics. We show that the Eguchi--Hanson instanton admits a projective compactification which is non--metric, and that a metric cone over any (pseudo)--Riemannian manifolds admits a metric projective compactification. We construct a para----projective co…
Researchers create a new compactification of character varieties using geometric and algebraic methods.
No natural topological compactification for Fulton-MacPherson.
Paper shows geometric properties preserved by compactifications in relation to coarse structures and group actions.
We describe the closure of the strata of abelian differentials with prescribed type of zeros and poles, in the projectivized Hodge bundle over the Deligne-Mumford moduli space of stable curves with marked points. We provide an explicit characterization of pointed stable differentials in the boundary of the closure, bot…
The paper classifies and computes limits of equivariant compactifications of groups.
The study finds only finitely many Kähler-Einstein compactifications for semisimple groups.
The paper extends end concepts to arbitrary groups and spaces.
I consider the semiclassical approximation of the graded Chern-Simons field theories describing certain systems of topological A type branes in the large radius limit of Calabi-Yau compactifications. I show that the semiclassical partition function can be expressed in terms of a certain (differential) numerical invaria…
In this paper we present a topological way of building a compactification of a symmetric space from a compactification of a Weyl Chamber.