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.
Study examines the geometry of a group of Fourier-integral operators related to Diff(S^1).
New equations for rigid body motion on infinite-dimensional spaces of operators.
We study the geometry of determinant line bundles associated to Dirac operators on compact odd dimensional manifolds. Physically, these arise as (local) vacuum line bundles in quantum gauge theory. We give a simplified derivation of the commutator anomaly formula using a construction based on noncyclic trace extensions…
Derives numerical formulas for elliptic differential operators on specific groupoids.
For quotients of the -dimensional hyperbolic space by a convex co-compact group , we obtain a formula relating the renormalized trace of the wave operator with the resonances of the Laplacian and some conformal invariants of the boundary, generalizing a formula of Guillopé and Zworski in dimension 2. By writing…
If is a properly embedded minimal surface in a convex cocompact hyperbolic 3-manifold with boundary at infinity an embedded curve , then Graham and Witten showed how to define a renormalized area $\calA$ of via Hadamard regularization. We study renormalized area as a functional on the space of all such m…
We study the effect of a relevant double-trace deformation on the partition function (and conformal anomaly) of a CFT at large N and its dual picture in AdS. Three complementary previous results are brought into full agreement with each other: bulk and boundary computations, as well as their formal identity. We show th…
We prove a dynamical wave trace formula for asymptotically hyperbolic (n+1) dimensional manifolds with negative (but not necessarily constant) sectional curvatures which equates the renormalized wave trace to the lengths of closed geodesics. A corollary of this dynamical trace formula is a dynamical resonance-wave trac…
Kashaev and Reshetikhin proposed a generalization of the Reshetikhin-Turaev link invariant construction to tangles with a flat connection in a principal G-bundle over the complement of the tangle. The purpose of this paper is to adapt and renormalize their construction to define invariants of G-links using the semi-cyc…
The conformal powers of the Laplacian of a Riemannian metric which are known as the GJMS-operators admit a combinatorial description in terms of the Taylor coefficients of a natural second-order one-parameter family of self-adjoint elliptic differential operators. is a non-Laplace-type perturbation …
Let be a polygon in $\RR^2$, or more generally a compact surface with piecewise smooth boundary and corners. Suppose that $Ω_\e$ is a family of surfaces with $\calC^\infty$ boundary which converges to smoothly away from the corners, and in a precise way at the vertices to be described in the paper. Fedosov …
We use modified traces to renormalize Lyubashenko's closed 3-manifold invariants coming from twist non-degenerate finite unimodular ribbon categories. Our construction produces new topological invariants which we upgrade to 2+1-TQFTs under the additional assumption of factorizability. The resulting functors provide mon…
We construct non-semisimple -TQFTs yielding mapping class group representations in Lyubashenko's spaces. In order to do this, we first generalize Beliakova, Blanchet and Geer's logarithmic Hennings invariants based on quantum to the setting of finite-dimensional non-degenerate unimodular ribbon H…
Research covers geometry, analysis, and integration on infinite-dimensional spaces.
Defines a new geometric quantity for hyperbolic manifolds, showing it's well-defined and invariant.
After analyzing renormalization schemes on a Poincaré-Einstein manifold, we study the renormalized integrals of scalar Riemannian invariants. The behavior of the renormalized volume is well-known, and we show any scalar Riemannian invariant renormalizes similarly. We consider characteristic forms and their behavior und…
A trace formula for foliated flows on closed manifolds.
Minimal surfaces in hyperbolic space have a renormalized area criterion.
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…
Study uses renormalized area to determine metric expansion from minimal surfaces.
Defines renormalized volume for bounded regions in asymptotically hyperbolic Einstein spaces.
Study calculates the renormalized area of catenoids in hyperbolic spaces.
Defines and proves properties of weighted renormalized volume coefficients.
We study the critical points of the renormalized volume for acylindrical geometrically finite hyperbolic 3-manifolds that include rank-1 cusps, and show that the renormalized volume is locally convex around these critical points. We give a modified definition of the renormalized volume that is additive under gluing, an…
For a strictly pseudoconvex domain in a complex manifold we define a renormalized volume with respect to the approximately Einstein complete Kähler metric of Fefferman. We compute the conformal anomaly in complex dimension two and apply the result to derive a renormalized Chern--Gauss--Bonnet formula. Relations between…
We study the renormalized volume of a conformally compact Einstein manifold. In even dimensions, we derive the analogue of the Chern-Gauss-Bonnet formula incorporating the renormalized volume. When the dimension is odd, we relate the renormalized volume to the conformal primitive of the -curvature. We show how all t…
We define and study the renormalized volume for geometrically finite hyperbolic -manifolds, including with rank- cusps. We prove a variation formula, and show that for certain families of convex co-compact hyperbolic metrics $g_\eps$ degenerating to a geometrically finite hyperbolic metric with rank- cus…
We interpret the physical -field renormalization group flow in the language of Courant algebroids, clarifying the sense in which this flow is the natural "Ricci flow" for generalized geometry. Next we show that the -field renormalization group flow preserves T-duality in a natural sense. As corollaries we obtain …
For a class of even dimensional conformally compact manifolds (X,g), we define a generalized Krein spectral function by applying a renormalized trace functional to the spectral measure of the Laplacian. We then show that this is the phase of the Kontsevich-Vishik determinant det S(s) of the scattering operator S(s) of …
New adapted renormalized volume for hyperbolic 3-manifolds with compressible boundary.
Paper derives a formula for renormalized area of minimal hypersurfaces in 5D Poincaré-Einstein spaces.
Proves energy expression on Poincaré-Einstein spaces.
New properties are derived of renormalized volume functionals, which arise as coefficients in the asymptotic expansion of the volume of an asymptotically hyperbolic Einstein (AHE) manifold. A formula is given for the renormalized volume of an even-dimensional AHE manifold in terms of an arbitrary totally geodesic compa…
Renormalization in neural networks linked to quantum field theory.
We study the evolution of the renormalized volume functional for asymptotically Poincare-Einstein metrics (M,g) which are evolving by normalized Ricci flow. In particular, we prove that the time derivative of the renormalized volume along the flow is the negative integral of scal(g(t)) + n(n-1) over the manifold. This …
Into a geometric setting, we import the physical interpretation of index theorems via semi-classical analysis in topological quantum field theory. We develop a direct relationship between Fedosov's deformation quantization of a symplectic manifold X and the BV quantization of a one-dimensional sigma model with target X…
New compactification of Teichmüller space via renormalized volume.
Renormalized pruning improves neural network accuracy.
Formula for renormalized area of hypersurfaces in hyperbolic spaces.
We compute renormalized curvature integrals on Poincaré-Einstein manifolds.
We study the infimum of the renormalized volume for convex-cocompact hyperbolic manifolds, as well as describing how a sequence converging to such values behaves. In particular, we show that the renormalized volume is continuous under the appropriate notion of limit. This result generalizes previous work in the subject…
New method calculates volume-renormalized mass from Hamiltonian perspective.
The paper studies circle packings using renormalization and subdivision rules.
Minimal surfaces in hyperbolic space have a sharp area bound.
We derive a new renormalized volume formula for conformally compact asymptotically hyperbolic manifolds in dimension four. The formula generalizes the ones given by Anderson, Albin, and Chang-Qing-Yang for the case of Poincare-Einstein manifolds. We also derive variational formulas for the renormalized seen as a functi…
The renormalized volume is reinterpreted using isoperimetric profiles.
A new Bayesian modeling method is proposed by combining the maximization of the marginal likelihood with a momentum-space renormalization group transformation for Gaussian graphical models. Moreover, we present a scheme for computint the statistical averages of hyperparameters and mean square errors in our proposed met…
The paper generalizes CR invariants using renormalized characteristic forms.