arXiv research

Generative models synthesize microstructures respecting physical invariances.

Machine learning knot invariants with physics applications.

INO learns physical models with momentum conservation laws.

GJMS operators connect geometry, analysis, and physics.

This is an overview article on finite type invariants, written for the Encyclopedia of Mathematical Physics

We propose localization techniques for computing Gromov-Witten invariants of maps from Riemann surfaces with boundaries into a Calabi-Yau, with the boundaries mapped to a Lagrangian submanifold. The computations can be expressed in terms of Gromov-Witten invariants of one-pointed maps. In genus zero, an equivariant ver…

Physics-informed neural networks improve by measuring effective dimensionality of constraints.

Based on Lie group method, potential symmetry and invariant solutions for generalized quasilinear hyperbolic equations are studied. To obtain the invariant solutions in explicit form, we focus on the physically interesting situations which admit potential symmetries. Then by using the partial Lagrangian approach, we fi…

A new method uses physics-informed neural networks to solve reliability analysis problems without simulations.

Polynomial invariants classify molecular chains based on their contact arrangements.

We continue our program initiated in [arXiv:0912.4261] to consider supersymmetric surface operators in a topologically-twisted N=2 pure SU(2) gauge theory, and apply them to the study of four-manifolds and related invariants. Elegant physical proofs of various seminal theorems in four-manifold theory obtained by Ozsvat…

Ray-Singer torsion is a mathematical concept with applications in physics.

IsoGCNs learn invariant and equivariant graph features for efficient simulations.

This is a survey article on finite type invariants of 3-manifolds written for the Encyclopedia of Mathematical Physics to be published by Elsevier.

MetaPhysiCa tackles robust physics-informed machine learning for OOD tasks.

The goal of this article is twofold. First, we find a natural home for the double affine Hecke algebras (DAHA) in the physics of BPS states. Second, we introduce new invariants of torus knots and links called "hyperpolynomials" that address the "problem of negative coefficients" often encountered in DAHA-based approach…

In their papers published in 1993 and 1994, by expressing certain physical quantity in two distinct ways, Bershadsky-Cecotti-Ooguri-Vafa discovered a remarkable equivalence between Ray-Singer analytic torsion and elliptic instanton numbers for Calabi-Yau threefolds. After their discovery, in a paper published in 2008, …

Equivariant flows generate symmetric distributions for complex systems.

Steerable E(3) Graph Neural Networks incorporate geometric and physical covariant information.

InvNet models data with known invariances efficiently.

3D models vulnerable to adversarial attacks, new method improves success rate and naturalness.

Paper introduces a method to generate physically feasible dynamics with physical priors.

Turaev transformed knot theory and 3-manifold invariants.

Paper calculates Donaldson-Thomas invariants for a specific category.

In this paper, we study the perturbative aspects of the half-twisted variant of Witten's topological A-model coupled to a non-dynamical gauge field with Kahler target space X being a G-manifold. Our main objective is to furnish a purely physical interpretation of the equivariant cohomology of the chiral de Rham complex…

New connections found between knot invariants and Rozansky-Witten theory.

We prove the ADO invariants are a q-holonomic family and establish recursion relations.

The paper develops GPR models for hyperelastic materials, improving accuracy and rotational invariance.

Gopakumar-Vafa large N duality is a correspondence between Chern-Simons invariants of a link in a 3-manifold and relative Gromov-Witten invariants of a 6-dimensional symplectic manifold relative to a Lagrangian submanifold. We address the correspondence between the Chern-Simons free energy of S^3 with no link and the G…

Quantum invariants of 3-manifolds and links reviewed, with connections to other topological invariants.

Two methods use simulation to improve anomaly detection in particle physics.

Develops tests for conditional symmetry under group actions.

New method identifies physical constants from video data alone.

The paper connects knot invariants to quiver representations via curve counting.

Geometric GNNs improve graph discrimination through GWL.

Deser and Nepomechie established a relationship between masslessness and rigid conformal invariance by coupling to a background metric and demanding local Weyl invariance, a method which applies neither to massive theories nor theories which rely upon gauge invariances for masslessness. We extend this method to describ…

We provide a physical definition of new homological invariants $\mathcal{H}_a (M_3)$ of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on $M_3$ times a 2-disk, $D^2$, whose Hilbert space of BPS states plays the role of a basic build…

Revisits Vafa-Witten theory, deriving new invariants and homologies.

Weaved helices form mechanically stable 3D structures.

Constructs 3D topological field theories from a specific quantum group, linking to physics invariants.

The paper studies minimal resistance dynamics in radial fields, finding unique solutions for incompressible flows.

One considers a special class of PDEs systems and one determines the associated symmetry group. Particulary, for the Blair system, one finds the symmetry group. A solutions of the Blair system gives a conformally flat contact metric structure and also it defines a "force-free" model of solar physics. By using the symme…

Let Z^{LMO} be the 3-manifold invariant of [LMO]. It is shown that Z^{LMO}(M)=1, if the first Betti number of M, b_{1}(M), is greater than 3. If b_{1}(M)=3, then Z^{LMO}(M) is completely determined by the cohomology ring of M. A relation of Z^{LMO} with the Rozansky-Witten invariants Z_{X}^{RW}[M] is established at a p…

Neumann's work connects 3-manifold invariants to quantum topology.

Efficient surrogate modeling for complex PDEs with physical laws.

We discuss normal forms and symplectic invariants of parabolic orbits and cuspidal tori in integrable Hamiltonian systems with two degrees of freedom. Such singularities appear in many integrable systems in geometry and mathematical physics and can be considered as the simplest example of degenerate singularities. We a…

We generalize the analysis by Moore and Witten in [arXiv:hep-th/9709193], and consider integration over the u-plane in Donaldson theory with surface operators on a smooth four-manifold X. Several novel aspects will be developed in the process; like a physical interpretation of the "ramified" Donaldson and Seiberg-Witte…

Defines observer-invariant time derivatives on moving surfaces.