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.
AI helps build particle physics theories more efficiently.
Dualities in deformed N=2 SCFTs from link monodromy on D3-brane states.
CNN improves neutrino event reconstruction in IceCube DeepCore.
Connects 4-manifold topology to topological modular forms.
Refined 3D index uses surgery and gradings to distinguish 3-manifolds.
New geometric approach realizes 5D bulk theories with 4D edge modes.
We demonstrate the agreement between the Higgs branches of two N=2 theories proposed by Argyres and Seiberg to be S-dual, namely the SU(3) gauge theory with six quarks, and the SU(2) gauge theory with one pair of quarks coupled to the superconformal theory with E_6 flavor symmetry. In mathematical terms, we demonstrate…
Researchers create a partial resolution of Coulomb branches for gauge theories.
Link homology compared with geometric link invariants using Bott-Samelson varieties.
We construct a graph TQFT for the minus flavor of Heegaard Floer homology. Our graph TQFT extends Ozsváth and Szabó's TQFT for closed and connected 3-manifolds, and allows for cobordisms with disconnected ends. As an application, we give an explicit formula for the chain homotopy type of the -action on Heegaard Fl…
We study singularities of algebraic curves associated with 3d N=2 theories that have at least one global flavor symmetry. Of particular interest is a class of theories T_K labeled by knots, whose partition functions package Poincare polynomials of the S^r-colored HOMFLY homologies. We derive the defining equation, call…
Grapevine clusters wine reviews for personalized recommendations.
Veronese webs are rich geometric structures with deep relationships to various domains of mathematics. The PDEs which determine the Veronese web are overdetermined if dim >3, but in the case dim =3 they reduce to a special flavor of a non-linear wave equation. The symmetries embedded in the definition of a Veronese web…
DeepJet improves jet flavor classification and quark-gluon tagging.
New construction reveals SU(2)-flavor fields in heterotic M5-brane model.
We define a new homology theory we call symbol homology by using decorated moduli spaces of Whitney polygons. By decorating different types of moduli spaces we obtain different flavors of this homology theory together with morphisms between them. Each of these flavors encodes the properties of a different type of Heega…
Study of IR phases in 3D class R theories linked to non-hyperbolic 3-manifolds.
We make a detailed study of the moduli space of winding number two (k=2) axially symmetric vortices (or equivalently, of co-axial composite of two fundamental vortices), occurring in U(2) gauge theory with two flavors in the Higgs phase, recently discussed by Hashimoto-Tong (hep-th/0506022) and Auzzi-Shifman-Yung (hep-…
Study electric-magnetic duality in M-theory compactifications.
We give a complete calculation of the infinity flavor of Heegaard Floer homology with mod 2 coefficients for all three-manifolds and torsion Spin^c structures. The computation agrees with the conjectured calculation of Ozsvath and Szabo. This therefore establishes an isomorphism with Mark's cup homology mod 2.
Many procedures in science, engineering and medicine produce data in the form of geometric shapes. Mathematically, a shape can be modeled as an un-parameterized immersed sub-manifold, which is the notion of shape used here. Endowing shape space with a Riemannian metric opens up the world of Riemannian differential geom…
Given a three-manifold with b_1=1 and a nontorsion spin^c structure, we use finite dimensional approximation to construct from the Seiberg-Witten equations two invariants in the form of a periodic pro-spectra. Various functors applied to these invariants give different flavors of Seiberg-Witten Floer homology. We also …
The Alexander polynomial of a knot has been generalized in three different ways to give twisted invariants. The resulting invariants are usually referred to as twisted Alexander polynomials, higher-order Alexander polynomials and -Alexander invariants of knots. We quickly recall the definitions and we summarize an…
It is a classical theorem of Loewner that the systole of a Riemannian torus can be bounded in terms of its area. We answer a question of a similar flavor of Robert Young showing that if is a Riemannian 2-torus with boundary in , such that the boundary curve is a standard unit circle, then the length o…
We consider -dimensional integer rectifiable currents which are almost area minimizing and show that their tangent cones are everywhere unique. Our argument unifies a few uniqueness theorems of the same flavor, which are all obtained by a suitable modification of White's original theorem for area minimizing currents…
We give a combinatorial treatment of transverse homology, a new invariant of transverse knots that is an extension of knot contact homology. The theory comes in several flavors, including one that is an invariant of topological knots and produces a three-variable knot polynomial related to the A-polynomial. We provide …
We construct an algorithm that lists all closed essential surfaces in the complement of a knot that lies on the fiber of a trefoil or figure eight knot. Such knots are Berge knots and hence admit lens space surgeries. Furthermore they may have arbitrarily large hyperbolic volume. Using this algorithm we concoct large v…
Clarifies structures in link homology theories using Frobenius extensions.
This paper is devoted to the bipartite ranking problem, a classical statistical learning task, in a high dimensional setting. We propose a scoring and ranking strategy based on the PAC-Bayesian approach. We consider nonlinear additive scoring functions, and we derive non-asymptotic risk bounds under a sparsity assumpti…
New nonparametric tests for high-dimensional k-sample comparisons.
This book is made of two parts. The first is concerned with the differential form spectrum of congruence hyperbolic manifolds. We prove Selberg type theorems on the first eigenvalue of the laplacian on differential forms. The method of proof is representation theoritic, we hope the different chapters may as well serve …
When faced with high frequency streams of data, clustering raises theoretical and algorithmic pitfalls. We introduce a new and adaptive online clustering algorithm relying on a quasi-Bayesian approach, with a dynamic (i.e., time-dependent) estimation of the (unknown and changing) number of clusters. We prove that our a…
Enhanced matrix completion with nonconvex penalties for better predictive performance.
We establish three rank inequalities for the reduced flavor of Heegaard Floer homology of Seifert fibered integral homology spheres. Combining these inequalities with the known classifications of non-zero degree maps between Seifert fibered spaces, we prove that a map f from Y' to Y between Seifert homology spheres yie…
These are the notes of the three lectures I delivered at the mini-workshop "Knot Theory and Number Theory around the A-Polynomial" at the Instituto Superior Tecnico (IST) in Lisbon in January 2014. The goal of the lectures was to familiarize, both the author and, the audience with the A-polynomials and the connection b…
Improved equation learning accuracy via comprehensive R²-elimination and Bayesian model selection.
INFERS PDEs from data samples using learned context.
The purpose of the present paper is to introduce and explore two surprises that arise when we apply a standard procedure to study the number of finite type invariants of 3-manifolds introduced independently by M. Goussarov and K. Habiro based on surgery on claspers, Y-graphs or clovers, \cite{Gu,Ha,GGP}. One surprise i…
Extends Khimshiashvili's degree formula to non-isolated singularities.
Ozsvath and Szabo construct a spectral sequence with E_2 term Λ^*(H^1(Y;Z))\otimes Z[U,U^{-1}] converging to HF^\infty(Y,s) for a torsion Spin^c structure s. They conjecture that the differentials are completely determined by the integral triple cup product form via a proposed formula. In this paper, we prove that HF^\…
GROUSE (Grassmannian Rank-One Update Subspace Estimation) is an incremental algorithm for identifying a subspace of Rn from a sequence of vectors in this subspace, where only a subset of components of each vector is revealed at each iteration. Recent analysis has shown that GROUSE converges locally at an expected linea…
Paper proves flexibility of specific relations using convex integration.
Optimal transport distances, otherwise known as Wasserstein distances, have recently drawn ample attention in computer vision and machine learning as a powerful discrepancy measure for probability distributions. The recent developments on alternative formulations of the optimal transport have allowed for faster solutio…
Study shows how steepest descent algorithms' geometric margin increases during training.
Unified tau invariants in instanton and monopole Floer theories.
New racks defined; properties of rack representations explored.
We describe the asymptotic behavior of minimal area submanifolds in product spacetimes of an asymptotically hyperbolic space times a compact internal manifold. In particular, we find that unlike the case of a minimal area submanifold just in an asymptotically hyperbolic space, the internal part of the boundary submanif…
A geometric structure (FAP-structure), having both absolute parallelism and Finsler properties, is constructed. The building blocks of this structures are assumed to be functions of position and direction. A non-linear connection emerges naturally and is defined in terms of the building blocks of the structure. Two lin…