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.
Affine maps reveal higher rank structures in certain spaces.
The paper encourages Kleinian group thinking for higher rank Lie groups.
Confirming a conjecture, new CAT(0) spaces of higher rank are rigid.
We prove two rigidity results for complete Riemannian three-manifolds of higher rank. Complete three-manifolds have higher spherical rank if an only if they are spherical space forms. Complete finite volume three-manifolds have higher hyperbolic rank if and only if they are hyperbolic space forms.
We prove that any action of a higher rank lattice on a Gromov-hyperbolic space is elementary. More precisely, it is either elliptic or parabolic. This is a large generalization of the fact that any action of a higher rank lattice on a tree has a fixed point. A consequence is that any quasi-action of a higher rank latti…
Study higher rank inner products and their tilings to describe tori degenerations.
Study critical exponents for L^p-cohomology of higher rank Lie groups and manifolds.
Characterizes higher rank model geometries using antipodal sets.
New proof for higher rank subvarieties in genus three.
New concept of coarse medians for higher rank symmetric spaces.
The study proves conditions for CAT(0) spaces with higher rank rigidity.
We show that polar actions of cohomogeneity two on simple compact Lie groups of higher rank, endowed with a biinvariant Riemannian metric, are hyperpolar. Combining this with a recent result of the second-named author, we are able to prove that polar actions induced by reductive algebraic subgroups in the isometry grou…
The paper proves actions of lattices in higher rank groups have cost one.
We give very flexible, concrete constructions of discrete and faithful epresentations of right-angled Artin groups into higher-rank Lie groups. Using the geometry of the associated symmetric spaces and the combinatorics of the groups, we find a general criterion for when discrete and faithful representations exist, and…
Improved homological dimension for certain subgroups in Lie groups.
The paper proves rigidity and ergodicity of horospherical foliations.
New dHYM connections found on complex vector bundles.
For convex real projective manifolds we prove an analogue of the higher rank rigidity theorem of Ballmann and Burns-Spatzier.
The aim of this paper is to study the spectrum of the Laplacian and the dynamics of the heat semigroup on non-compact locally symmetric spaces of higher rank. Our work here generalizes previously obtained results in the setting of locally symmetric spaces of rank one to higher rank spaces. Similarly as in t…
In this paper, we introduce the notion of motif closure and describe higher-order ranking and link prediction methods based on the notion of closing higher-order network motifs. The methods are fast and efficient for real-time ranking and link prediction-based applications such as web search, online advertising, and re…
We show that sufficiently irreducible Anosov actions of higher rank abelian groups on tori and nilmanifolds are smoothly conjugate to affine actions.
Anosov representations give a higher-rank analogue of convex cocompactness in a rank-one Lie group which shares many of its good geometric and dynamical properties; geometric finiteness in rank one may be seen as a controlled weakening of convex cocompactness to allow for isolated failures of hyperbolicity. We introduc…
Develops sublinear Morse theory in symmetric spaces.
The paper proves that certain spaces have injective balls of any radius.
We generalize the higher rank rigidity theorem to a class of Finsler spaces, i.e. Berwald spaces. More precisely, we prove that a complete connected Berwald space of finite volume and bounded nonpositive flag curvature with rank at least whose universal cover is irreducible, is a locally symmetric space or a locall…
Classifies measures for Anosov subgroups in higher ranks.
Researchers show how to perturb free group representations into higher rank groups.
The study finds discrete subgroups with full limit sets in higher rank Lie groups.
Develops complex harmonic maps for Teichmüller theory, proving new theorems.
In this paper the notion of Measure Equivalence (ME) of countable groups is studied. ME was introduced by Gromov as a measure-theoretic analog of quasi-isometries. All lattices in the same locally compact group are Measure Equivalent; this is one of the motivations for this notion. The main result of this paper is ME r…
We classify all holomorphic actions of higher rank lattices on compact Kaehler manifolds of dimension 3. This provides a complete answer to Zimmer's program for holomorphic actions on compact Kaehler manifolds of dimension at most 3.
The prime geodesic theorem for regular geodesics in a higher rank locally symmetric space is proved. An application to class numbers is given. The proof relies on a Lefschetz formula that is based on work of Andreas Juhl.
In this paper we study a proposal of Nekrasov, Rosly and Shatashvili that describes the effective twisted superpotential obtained from a class S theory geometrically as a generating function in terms of certain complexified length-twist coordinates, and extend it to higher rank. First, we introduce a higher rank analog…
The paper explores higher property T in lattices and its connections to geometric phenomena.
The paper describes correlations of spectra for higher rank Anosov representations.
For real hyperbolic spaces, the dynamics of individual isometries and the geometry of the limit set of nonelementary discrete isometry groups have been studied in great detail. Most of the results were generalised to discrete isometry groups of simply connected Riemannian manifolds of pinched negative curvature. For sy…
Extends Hopf-Tsuji-Sullivan dichotomy to higher rank groups and applies to Anosov subgroups.
We say that a Riemannian manifold M has rank at least k if every geodesic in M admits at least k parallel Jacobi fields. The Rank Rigidity Theorem of Ballmann and Burns-Spatzier, later generalized by Eberlein-Heber, states that a complete, irreducible, simply connected Riemannian manifold M of rank at least 2 (the high…
FedLoRU improves FL efficiency by using low-rank updates.
Research examines coamenable subgroups in higher rank groups.
Extends confining subset theory to describe hyperbolic actions of solvable groups with higher rank abelianizations.
Study critical exponents in normal subgroups of higher rank Lie groups.
Proves finite measure implies product structure for certain discrete subgroups.
New rigidity result for CAT(0) spaces of higher rank.
Prove a global shadow lemma for Patterson-Sullivan measures associated with relatively Morse subgroups in higher-rank semisimple Lie groups.
Proposes a method to enhance multi-view learning by maximizing higher order correlations.
Witten's conjecture suggests that the polynomial invariants of Donaldson are expressible in terms of the Seiberg-Witten invariants if the underlying four-manifold is of simple type. A higher rank version of the Donaldson invariants was introduced by Kronheimer. Before even having been defined, the physicists Mariño and…
We uncover a large and significant low-minus-high rank effect for commodities across two centuries. There is nothing anomalous about this anomaly, nor is it clear how it can be arbitraged away. Using nonparametric econometric methods, we demonstrate that such a rank effect is a necessary consequence of a stationary rel…