Related papers: On the complexity of evaluating highest weight vec…
This paper is concerned with the construction, analysis and realization of a numerical method to approximate the solution of high dimensional elliptic partial differential equations. We propose a new combination of an Adaptive Wavelet…
This note summarizes the talk by the author at the workshop "Geometry and Computer Science" held in Pescara in February 2017. We present how SageMath can help in research in Complex and Differential Geometry, with two simple applications,…
The Weak Gravity Conjecture (WGC) asserts a powerful consistency condition on gauge theories coupled to gravity, and it is widely believed that its proof will shed light on the quantum origin of gravitational interactions. Holography, and…
Let $G$ be a connected graph. A vertex $w$ strongly resolves a pair $u$, $v$ of vertices of $G$ if there exists some shortest $u-w$ path containing $v$ or some shortest $v-w$ path containing $u$. A set $W$ of vertices is a strong resolving…
We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…
Let $\widehat G \subseteq G$ be complex reductive algebraic groups. The branching problem that aims to study $G$-modules as $\widehat G$-modules is encoded by a collection of branching multiplicities parameterised by pairs of dominant…
Many theories of gravity are spoiled by strongly coupled modes: the high computational cost of Hamiltonian analysis can obstruct the identification of these modes. A computer algebra implementation of the Hamiltonian constraint algorithm…
Canonical analysis leading to formal quantisation of the higher derivative theories are considered. The first order formalism is adopted where all the configuration space variables along with their higher time derivatives are considered to…
Let $G$ be a simply connected semisimple algebraic group over $\mathbb{C}$ and let $\rho :G\rightarrow GL(V_\lambda)$ be an irreducible representation of highest weight $\lambda$. Suppose that $\rho$ has finite kernel. Springer defined…
We investigate the representations of a class of conformal Galilei algebras in one spatial dimension with central extension. This is done by explicitly constructing all singular vectors within the Verma modules, proving their completeness…
We introduce the framework of general probabilistic theories (GPTs for short). GPTs are a class of operational theories that generalize both finite-dimensional classical and quantum theory, but they also include other, more exotic theories,…
We analyse the connections between the Wheeler DeWitt approach for two dimensional quantum gravity and holography, focusing mainly in the case of Liouville theory coupled to $c=1$ matter. Our motivation is to understand whether some form of…
The general relativistic perturbations of scalar-tensor theories (STT) of gravity are studied in a manifestly gauge invariant Hamiltonian formalism. After the derivation of the Hamiltonian equations of motion in this framework, the gauge…
Metric space magnitude, an active field of research in algebraic topology, is a scalar quantity that summarizes the effective number of distinct points that live in a general metric space. The {\em weighting vector} is a closely-related…
The expressive power of Graph Neural Networks (GNNs) has been studied extensively through the Weisfeiler-Leman (WL) graph isomorphism test. However, standard GNNs and the WL framework are inapplicable for geometric graphs embedded in…
The Geometric Algebra Transformer (GATr) is a versatile architecture for geometric deep learning based on projective geometric algebra. We generalize this architecture into a blueprint that allows one to construct a scalable transformer…
Geometric realizations for the restrictions of GNS representations to unitary groups of $C^*$-algebras are constructed. These geometric realizations use an appropriate concept of reproducing kernels on vector bundles. To build such…
Many natural computational problems in computer science, mathematics, physics, and other sciences amount to deciding if two objects are equivalent. Often this equivalence is defined in terms of group actions. A natural question is to ask…
The GVW algorithm is a signature-based algorithm for computing Gr\"obner bases. If the input system is not homogeneous, some J-pairs with higher signatures but lower degrees are rejected by GVW's Syzygy Criterion, instead, GVW have to…
Gromov--Wasserstein optimal transport (GWOT) aligns metric measure spaces by matching their within-domain relational structures, but large-scale GWOT remains challenging because its objective is nonconvex and projection onto the transport…