arXiv research

The study uses machine learning to model semantic drift in digital content.

We describe a project, called the "Discretization in Geometry and Dynamics Gallery", or DGD Gallery for short, whose goal is to store geometric data and to make it publicly available. The DGD Gallery offers an online web service for the storage, sharing, and publication of digital research data.

Study on knots formed by Coxeter galleries, finding bounds and symmetric trefoils.

Machine learning accurately distinguishes Sato-Tate groups for hyperelliptic curves.

For a Liouville domain $W$ satisfying $c_1(W)=0$, we propose in this note two versions of symplectic Tate homology $\underrightarrow{H}\underleftarrow{T}(W)$ and $\underleftarrow{H}\underrightarrow{T}(W)$ which are related by a canonical map $κ\colon \underrightarrow{H}\underleftarrow{T}(W) \to \underleftarrow{H}\under…

New spectral sequence connects to topological Hochschild homology.

Machine learning predicts Shafarevich-Tate group orders of elliptic curves.

The Koszul-Tate resolution is described in the context of the geometry of jet spaces and differential equations. The application due to Barnich, Brandt, and Henneaux of this resolution to computing the horizontal cohomology is analyzed. Relations with the Vinogradov spectral sequence are discussed.

The paper connects Chern-Simons invariants to mixed Tate motives in hyperbolic 3-manifolds.

Constructs a new graded variety from algebraic data.

From an operad C with an action of a group G, we construct new operads using the homotopy fixed point and orbit spectra. These new operads are shown to be equivalent when the generalized G-Tate cohomology of C is trivial. Applying this theory to the little disk operad C_2 (which is an S^1 operad) we obtain variations o…

Study shows spectral action coefficients are periods in specific spacetimes.

Study heat kernel coefficients in Bianchi IX gravity models.

Normal forms for Q-structures on graded manifolds explained.

The paper shows that certain geometric structures remain unchanged under specific twists.

The paper defines slant submanifolds in Norden manifolds.

If $G_1$ and $G_2$ are finite groups with periodic Tate cohomology, then $G_1\times G_2$ acts freely and smoothly on some product $S^n \times S^n$.

Cyclification of orbifolds explained in cohesive higher topos theory.

Paper studies Iwasawa invariants for 3-manifolds, proving a formula similar to Kida's.

Open geometry puzzles keep the author engaged.

New method designs joint initial noises for diffusion models to improve diversity and alignment.

Constructs a topological cover of real line's multiplicative group.

Given a generic Lagrangian system, its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. This construction is generalized to arbitrary differential operators on a smooth fiber bundle. Namely, if a certain necessary and sufficient condi…

Period domains, the classifying spaces for (pure, polarized) Hodge structures, and more generally Mumford-Tate domains, arise as open $G_{\mathbb{R}}$--orbits in flag varieties $G/P$. We investigate Hodge--theoretic aspects of the geometry and representation theory associated with these flag varieties. In particular, w…

We determine the equilibria of a rigid loop in the plane, subject to the constraints of fixed length and fixed enclosed area. Rigidity is characterized by an energy functional quadratic in the curvature of the loop. We find that the area constraint gives rise to equilibria with remarkable geometrical properties: not on…

A generic degenerate Lagrangian system of even and odd variables on an arbitrary smooth manifold is examined in terms of the Grassmann-graded variational bicomplex. Its Euler-Lagrange operator obeys Noether identities which need not be independent, but satisfy first-stage Noether identities, and so on. However, non-tri…

We refine the intersection product in homology to an equivariant setting, which unifies several known constructions. As an application, we give a common generalisation of the Chas-Sullivan string product on a manifold and the Chataur-Menichi string product on the classifying space by defining a string product on the Bo…

The paper generalizes convex and star-shaped concepts to symplectic spaces and studies variational problems.

Constructs spectral sequences for Morava E-theory of configuration spaces.

The paper studies deformations of Lagrangian fibrations on symplectic manifolds.

We consider the moduli space $\mathcal{R}_n$ of pairs of monic, degree $n$ polynomials whose resultant equals $1$. We relate the topology of these algebraic varieties to their geometry and arithmetic. In particular, we compute their étale cohomology, the associated eigenvalues of Frobenius, and the cardinality of their…

New instanton homology theories for 3-manifolds and bundles.

System learns user preferences to synthesize materials quickly.

A new method for cross-view classification using divide-and-conquer.

Data science reveals patterns in elliptic curve ranks and coefficients.

FORBES learns flexible belief states for POMDPs using normalizing flows.

Traditional nearest points methods use all the samples in an image set to construct a single convex or affine hull model for classification. However, strong artificial features and noisy data may be generated from combinations of training samples when significant intra-class variations and/or noise occur in the image s…

Unified theory of orbifolds and cohomology.

Advances data-driven coarse-graining for complex systems.

A new system combines vision and language for person re-identification.

NFT art market shows strong preferential ties among sellers and buyers.

WARPd method solves inverse problems with approximate sharpness conditions.

This is a prejudiced survey on the Ahlfors (extremal) function and the weaker {\it circle maps} (Garabedian-Schiffer's translation of "Kreisabbildung"), i.e. those (branched) maps effecting the conformal representation upon the disc of a {\it compact bordered Riemann surface}. The theory in question has some well-known…

Study explores how dataset breadth and depth affect Siamese Neural Network performance.

Paper proposes a deep learning method for person re-identification using set to set distance.