arXiv research

Born-Infeld solitons linked to maximal surfaces via Ramanujan's identities.

The tail of the colored Jones polynomial of an alternating link is a $q$-series invariant whose first $n$ terms coincide with the first $n$ terms of the $n$-th colored Jones polynomial. Recently, it has been shown that the tail of the colored Jones polynomial of torus knots give rise to Ramanujan type identities. In th…

The article extends a knot polynomial algorithm for singular knots.

Researchers found a $q$-series identity for a specific knot using $\mathfrak{sl}_3$ representations.

The height function of various surfaces decomposes into finite sums of scaled and translated versions of itself.

The paper shows how Scherk-type surfaces can be decomposed into helicoids.

Derive new Euler-Ramanujan-type identities and infinite decompositions for zero mean curvature graphs in various spaces.

We conjecture that the stable Khovanov homology of torus knots can be described as the Koszul homology of an explicit non-regular sequence of quadratic polynomials. The corresponding Poincare series turns out to be related to the Rogers-Ramanujan identity.

The paper connects dilogarithm identities to Pell's equation solutions via continued fractions.

We study the head and tail of the colored Jones polynomial while focusing mainly on alternating links. Various ways to compute the colored Jones polynomial for a given link give rise to combinatorial identities for those power series. We further show that the head and tail functions only depend on the reduced checkerbo…

New explicit constructions of unbalanced Ramanujan bipartite graphs.

New bounds on diameters and generators for specific lattices and graphs.

We develop the Ercolani-Sinha construction of SU(2) monopoles and make this effective for (a five parameter family of centred) charge 3 monopoles. In particular we show how to solve the transcendental constraints arising on the spectral curve. For a class of symmetric curves the transcendental constraints become a numb…

The tail of a sequence $\{P_n(q)\}_{n \in \mathbb{N}}$ of formal power series in $\mathbb{Z}[[q]]$ is the formal power series whose first $n$ coefficients agree up to a common sign with the first $n$ coefficients of $P_n$. This paper studies the tail of a sequence of admissible trivalent graphs with edges colored $n$ o…

Counterexamples to Wise's theorem found using triangle groups and Ramanujan graphs.

The paper classifies affine minimal translation surfaces and finds their properties.

Develops mixed quantization for graph vector bundles.

This paper presents a deterministic method for matrix completion using Ramanujan graphs.

Maximal surfaces in $\mathbb{L}^3$ correspond to timelike minimal surfaces.

Quantum invariants of three-manifolds linked to mock theta functions.

Proposes RBGP framework for efficient block sparse neural networks.

New conjectures link SU(r) Vafa-Witten invariants to Ramanujan's continued fractions.

New volume functions for random hyperbolic surfaces link to spectral gaps.

Expander graphs have been a focus of attention in computer science in the last four decades. In recent years a high dimensional theory of expanders is emerging. There are several possible generalizations of the theory of expansion to simplicial complexes, among them stand out coboundary expansion and topological expand…

Expander graphs have been intensively studied in the last four decades. In recent years a high dimensional theory of expanders has emerged, and several variants have been studied. Among them stand out coboundary expansion and topological expansion. It is known that for every $d$ there are unbounded degree simplicial co…

In this work we present a new local to global criterion for proving a form of high dimensional expansion, which we term cosystolic expansion. Applying this criterion on Ramanujan complexes, yields for every dimension, an infinite family of bounded degree complexes with the topological overlapping property. This answer …

New resurgent analysis reveals dual $q$-series for Chern-Simons theory crossing natural boundaries.

The study explores autonomous systems and their connections to contact geometry and Frobenius manifolds.

Erdős-Kac theorem applied to geodesics on modular surface.

New cutoff phenomenon found for geodesic paths on hyperbolic manifolds.

Randomly initialized networks contain subnetworks that perform similarly to target networks.

We compute the Moore-Witten regularized u-plane integral on CP^2, and we confirm their conjecture that it is the generating function for the SO(3)-Donaldson invariants of CP^2. We prove this conjecture using the theory of mock theta functions and harmonic Maass forms. We also derive further such generating functions fo…

New spectral conditions ensure graph rigidity and global rigidity in the Euclidean plane.

A new method to prune neural networks with iterative randomization improves efficiency.

Explicitly constructed 3XOR instances hard for Sum-of-Squares hierarchy.

This paper discovers new identities linking geodesic and orthogeodesic lengths on hyperbolic surfaces.

Establishes a correspondence between two mathematical identities.

The paper examines distances and random walks on hyperbolic surfaces.

Quandle homology was defined from rack homology as the quotient by a subcomplex corresponding to the idempotency, for invariance under the type I Reidemeister move. Similar subcomplexes have been considered for various identities of racks and moves on diagrams. We observe common aspects of these identities and subcompl…

Einstein's philosophy uses differential identities to derive GR field equations.

The paper derives curvature identities for 5D and 6D Einstein manifolds.

Global Pestov identity proved on frame bundle and related fibrations.

RLINK uses deep reinforcement learning to improve user identity linkage across social networks.

Proves Bochner's identity on graphs using a new auxiliary graph.

Doodles link to commutator identities in a 2-sphere.

This work connects Higgs bundles to Calabi-Yau manifolds via mirror symmetry.

The paper studies harmonic identity maps on Riemannian manifolds.

Paper learns identity-sensitive word embeddings from text corpora.