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.
ADDA framework speeds up data augmentation in massive data settings.
We exhibit examples of projective varieties with degenerate Gauss mappings and determine numerical invariants of such varieties. Our examples provide counter-examples to an asserted structure theorem of Griffiths and Harris (Ann. Sci. ENS 1979).
We study statistical inference and distributionally robust solution methods for stochastic optimization problems, focusing on confidence intervals for optimal values and solutions that achieve exact coverage asymptotically. We develop a generalized empirical likelihood framework---based on distributional uncertainty se…
We show that the bi-Hamiltonian structures of the Camassa-Holm and Harry Dym hierarchies can be obtained by applying a reduction process to a simple Poisson pair defined on the loop algebra of . The reduction process is a bi-Hamiltonian reduction, that can be canonically performed on every …
New integrable systems derived from Nijenhuis geometry.
New hierarchies and equations derived from Poisson structures.
Upper bounds on projective rigidity of each homogeneously embedded homogeneous variety are determined; and a new, invariant characterization of the Fubini forms is given.
The study finds solutions to a financial equation related to volatility.
The Horikawa index and the local signature are introduced for relatively minimal fibered surfaces whose general fiber is a non-hyperelliptic curve of genus with unique trigonal structure.
I show that any complex manifold that resembles a rank two compact Hermitian symmetric space (other than a quadric hypersurface) to order two at a general point must be an open subset of such a space.
Three decades ago Cornalba-Harris proved a fundamental positivity result for divisor classes associated to families of stable curves. In this paper we establish an analogous positivity result for divisor classes associated to families of stable differentials.
The dual variety X* for a smooth n-dimensional variety X of the projective space P^N is the set of tangent hyperplanes to X. In the general case, the variety X* is a hypersurface in the dual space (P^N)*. If dim X* < N - 1, then the variety X is called dually degenerate. The authors refine these definitions for a varie…
We give a lower bound for the length of a non-trivial geodesic loop on a simply-connected and compact manifold of even dimension with a non-reversible Finsler metric of positive flag curvature. Harris and Paternain use this estimate in their recent paper [HP] to give a geometric characterization of dynamically convex F…
We define relative Gromov-Witten invariants of a symplectic manifold relative to a codimension two symplectic submanifold. These invariants are the key ingredients in the symplectic sum formula of [IP4]. The main step is the construction of a compact space of `V-stable' maps. Simple special cases include the Hurwitz nu…
The paper solves integrable systems of PDEs, including famous equations.
Study counts ergodic measures in surface lamination strata.
Gringotts Wizarding Bank is well known as the only financial institution in all of the Wizarding UK as documented in the works recounting the heroics of Harry Potter. The concentration of power and wealth in this single bank needs to be weighed against the financial stability of the entire Wizarding economy. This study…
The vector of periodic, compound returns of a typical investment portfolio is almost never a convex combination of the return vectors of the securities in the portfolio. As a result the ex post version of Harry Markowitz's "standard mean-variance portfolio selection model" does not apply to compound return data. We pro…
We describe a method for recursively calculating Gromov-Witten invariants of all blowups of the projective plane. This recursive formula is different from the recursive formulas due to Göttsche and Pandharipande in the zero genus case, and Caporaso and Harris in the case of no blowups. We use tropical curves and a recu…
New progress on frame flow ergodicity for nearly pinched manifolds.
Recent results on ergodic theory for Riemann surface laminations and foliations.
Formula connects foliated simplicial volume with group cost.
In this note we show that the Riemann moduli spaces equipped with the Weil--Petersson metric are quantum ergodic for . We also provide other examples of singular spaces with ergodic geodesic flow for which quantum ergodicity holds.
We extend to orbifolds classical results on quantum ergodicity due to Shnirelman, Colin de Verdière and Zelditch, proving that, for any positive, first-order self-adjoint elliptic pseudodifferential operator P on a compact orbifold X with positive principal symbol p, ergodicity of the Hamiltonian flow of p implies quan…
Strong stability of ergodic iterations proven without ergodic driving sequence.
The paper studies the ergodicity of frame flow on even-dimensional manifolds.
Non-ergodic measures found in horocycle flow on Abelian differentials.
Log-ergodic model improves velocity of money prediction.
'Ergodicity economics' is criticized as pseudoscience.
We construct an example of a uniquely ergodic measured foliation on a surface such that the associated translation flow on the orientation double cover is minimal but not uniquely ergodic. We then prove a geometric criterion for the horizontal foliation of a quadratic differential to be uniquely ergodic. The second the…
New method stabilizes quantum ergodicity for mixed quantization and partial hyperbolicity.
The study shows that ergodic measures are not generic on non-positively curved manifolds.
We show that Masur's logarithmic law of geodesics in the moduli space of translation surfaces does not imply unique ergodicity of the translation flow, but that a similar law involving the flat systole of a Teichmüller geodesic does imply unique ergodicity. It shows that the flat geometry has a better control on ergodi…
We relate ergodic-theoretic properties of a very small tree or lamination to the behavior of folding and unfolding paths in Outer space that approximate it, and we obtain a criterion for unique ergodicity in both cases. Our main result is that non-unique ergodicity gives rise to a transverse decomposition of the foldin…
The paper studies ergodicity of flows on subspaces, generalizing earlier work.
A smooth diffeomorphism is said to be distributionally uniquely ergodic (DUE for short) when it is uniquely ergodic and its unique invariant probability measure is the only invariant distribution (up to multiplication by a constant). Ergodic translations on tori are classical examples of DUE diffeomorphisms. In this ar…
A measured solenoid is a laminated space endowed with a tranversal measure invariant by holonomy, as defined in arXiv:0910.2836. A measured solenoid immersed in a smooth manifold produces a closed current (known as generalized Ruelle-Sullivan current). Uniquely ergodic solenoids are those for which there is a unique (u…
These are expository notes from the 2008 Srni Winter School. They have two purposes: (1) to give a quick introduction to exterior differential systems (EDS), which is a collection of techniques for determining local existence to systems of partial differential equations, and (2) to give an exposition of recent work (jo…
The paper connects function theory, dynamics, and ergodic theory via Thurston's theory.
The paper introduces a new method to create stable ergodic actions on higher-dimensional manifolds.
This work investigates a mixture of LMC and RMHMC with MMALA for geometric ergodicity.
Study shows non-wandering, partially hyperbolic systems are ergodic.
We introduce the concept of solenoid as an abstract laminated space. We do a thorough study of solenoids, leading to the notion of ergodic and uniquely ergodic solenoids. We define generalized currents associated with immersions of oriented solenoids with a transversal measure into smooth manifolds, generalizing Ruelle…
Study shows mapping class group action is ergodic on specific representations.
We study how resetting affects geometric Brownian motion, showing it becomes stationary but remains non-ergodic.
Proves Torelli group action is ergodic on Lie group character varieties.
The paper provides a link between ergodic theory and symplectic topology. A classical notion of ergodic theory is a skew product map associated with a loop in a group of transformations. We study skew products which come from loops in the group of Hamiltonian diffeomorphisms of a symplectic manifold. Our main question …
We review some developments on clustering stochastic processes and come with the conclusion that asymptotically consistent clustering algorithms can be obtained when the processes are ergodic and the dissimilarity measure satisfies the triangle inequality. Examples are provided when the processes are distribution ergod…