arXiv research

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

New criterion proves high dimensional expansion in bounded degree complexes.

New explicit constructions of unbalanced Ramanujan bipartite graphs.

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

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

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…

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

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…

Develops mixed quantization for graph vector bundles.

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

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

The study of pretzel knots' colored Jones polynomials yields new q-series identities.

The article extends a knot polynomial algorithm for singular knots.

Proposes RBGP framework for efficient block sparse neural networks.

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

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…

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

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

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

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.

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

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

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…

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.

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

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

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

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

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…

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.

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

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

The paper examines distances and random walks on hyperbolic surfaces.

The paper investigates the distribution of systoles on arithmetic Riemann surfaces.

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

New method finds compact strong lottery tickets in partially frozen networks.

Study compares two methods to extend $\widehat{Z}$ invariants, finding incompatibility for Brieskorn spheres.

We analyze the spectrum of a non-backtracking matrix in a degree-corrected stochastic block model.

Study on pricing options tied to stock tick complexity.

New condition prevents hyperbolic spaces from matching curve complexes.

Study on complex line fields on almost-complex manifolds, proving existence conditions.

Study complex deformations of compact complex surfaces in Calabi-Yau four-folds.

Homotopy types of curve and arc complexes are studied.

This research explores complex-valued neural networks and their implementation.

Paper introduces fat CW complexes including all closed manifolds.