June 23-25, 2026 · Almería, Spain
The International Workshop Advancing Applied Geometric Algebra in Academia and Industry combines invited research talks, informal discussion and social activities in Cabo de Gata. The academic sessions are planned for Tuesday and Thursday, with Wednesday reserved for local-holiday activities and informal exchange.
This is a preliminary public schedule. Pending abstracts will be updated as speakers confirm their final text.
For questions or to propose a contribution, contact pagilm@ual.es.
The workshop recordings are hosted on Internet Archive and organized below by presenter.
| Time | Speaker / Activity | Contribution |
|---|---|---|
| 09:30 - 10:00 | Welcome + Francisco G. Montoya | Stability in power electronic converters using Idem/Nilpotent bases |
| 10:00 - 10:30 | Radek Sláma | Volumetric precision using PGA |
| 10:30 - 11:00 | Jaroslav Hrdina | Efficient trajectory planning of a UR5e manipulator around a single spherical obstacle with the help of CGA |
| 11:00 - 11:30 | Aneeqa Mehrab | Robotic arm calibration based on quaternionic neural networks |
| 11:30 - 12:00 | Coffee break | Informal discussion |
| 12:00 - 12:30 | Aleš Návrat | Möbius transformations in conformal geometric algebra |
| 12:30 - 13:00 | Johanka Brdečková | Types of conformal transformations and representation of faulted signals |
| 13:00 - 13:30 | Sebastià Xambó | Morley Theorem using GA |
| 13:30 - 15:00 | Lunch | Group lunch nearby, details for confirmed participants |
| Evening | Noche de San Juan | Optional Mediterranean beach celebration |
| Time | Activity | Notes |
|---|---|---|
| All day | Cabo de Gata social day | Excursion to nearby beaches and coves, by bike or on foot depending on the group and weather |
| During the excursion | Beach, swimming and optional snorkelling | Participants are encouraged to bring swimwear, towel, sunscreen, water shoes or sandals, and snorkelling gear if they have it |
| Afternoon / evening | Informal cultural activity | Details will be shared directly with confirmed participants |
| Time | Speaker / Activity | Contribution |
|---|---|---|
| 09:30 - 10:00 | Eckhard Hitzer | Quaternion algebra family |
| 10:00 - 10:30 | Jian Wang | GA-Compiler: Compiling Natural Language into FPGA-Accelerated Geometric Algebra Programs |
| 10:30 - 11:00 | Jorge Ventura Gil | The Geometry of Faults in Inverter-Dominated Grids: A Geometric Algebra Classifier |
| 11:00 - 11:30 | Coffee break | Informal discussion |
| 11:30 - 12:00 | Santiago Sánchez-Acevedo | Power system stability based on Frenet-Serret model and GA |
| 12:00 - 12:30 | Francisco M. Arrabal | A Multivariable Geometric Laplace Transform and its Application to Fault Detection in Distributed-Converter DC Buses |
| 12:30 - 13:00 | Oliver Rettig | Robotics Kinematics with PGA and G6 - Identification of singularities of serial robot manipulators |
| 13:00 - 13:30 | Discussion / Closing remarks | Open discussion and next steps |
| 13:30 - 15:30 | Farewell lunch | Details for confirmed participants |
| Afternoon | Informal Almería city activity | Optional local food and conversation in the city center |
Manufacturing tolerances in industrial robot arms introduce small but systematic errors in the Denavit-Hartenberg kinematic parameters, leading to measurable end-effector positioning inaccuracies. This work proposes a Quaternionic Neural Network approach for identifying and compensating these errors in the UR5e robot arm. A BoundedQuaternionMLP with physics-informed output bounds is trained end-to-end through a differentiable Dual Quaternion forward kinematics chain, enabling simultaneous estimation of position and orientation errors. The method is validated on synthetic data with known injected errors and on real UR5e simulation trajectories, demonstrating its effectiveness for complete kinematic calibration.
In the context of volumetric precision, measuring errors across the entire working space of a CNC machine is time-consuming. Working in Projective Geometric Algebra (PGA) for 3D Euclidean space, this contribution interpolates a grid of error vectors from a significantly reduced set of measured edge values. The interpolation method demonstrates high precision along the edges and bounding planes of the workspace.
We introduce an idempotent-nilpotent decomposition in the complexified Clifford algebra and apply it to impedance-based stability analysis of grid-connected converters. The proposed basis decomposes every impedance matrix into terms with direct engineering meaning: common-mode/differential-mode impedances and inter-modal couplings in the dq frame. We show that this basis yields a positive-definite scalar product, a basis-invariant invertibility criterion, the geometric origin of recent decoupling transformations, and a generalized small-gain condition for closed-loop stability. The framework subsumes the Pauli decomposition and clarifies the algebraic structure underlying impedance-based stability analysis.
We investigate energy-efficient trajectory planning for a UR manipulator operating in the presence of a single spherical obstacle. The proposed approach focuses on minimizing the energy demands associated with obstacle avoidance while preserving smooth, collision-free manipulator motion. The obstacle is represented using a simplified spherical model, enabling efficient geometric computations and real-time applicability.
In complex analysis, Mobius transformations are defined as mappings of the extended complex plane by a rational function of two linear complex polynomials. They have wide-ranging applications in physics and computer science, as well as in electrical engineering, where they are also known as bilinear transformations. In the literature, however, this term is used for transformations of the so-called Möbius geometry of non-oriented spheres. This is no coincidence: they are, in fact, the same. This lecture aims to explain this connection using conformal geometric algebra.
This contribution discusses types of conformal transformations and how signals with faults can be represented using conformal transformations.
Singularities are angle configurations in which a robot loses the ability to move in at least one direction. Therefore, their detection is important in path planning. While the classical approach is based on the usual numerical calculation of the determinant of a 6 x n Jacobi matrix for an n-degrees-of-freedom robot, this work addresses methods based on twists, which can be modelled by geometric algebra. In concrete terms, a geometrical understanding of singularities, modelling direct kinematics with Cl(3,0,1), and singularity detection based on Cl(6,0,0) are shown. The implementation is done with GaalopScript. The approach leads to symbolic expressions which include a high number of trigonometric functions; specific symbolic simplifications are needed, requiring extensions beyond out-of-the-box Gaalop.
The aim of this talk is to present a proof of F. Morley's theorem concerning triangles in the Euclidean plane phrased in terms of its geometric algebra. This proof yields a result that is stronger than the known synthetic proofs and provides a systematic approach to the 27 equilateral triangles associated to any triangle and to their remarkable properties.
Quaternions of W. R. Hamilton have become essential in aerospace engineering, computer graphics, robotics and beyond, but they are far from alone. The wider family includes complex biquaternions, octonions, dual quaternions, split quaternions and commutative Segre quaternions. Clifford further built geometric algebras Cl(p,q) from tensor products of quaternions, and complex biquaternions are isomorphic to Cl(3,0). The talk also discusses dual quaternions in PGA and CGA, para-quaternions, para-octonions and Okubo-related algebraic structures.
Converter-interfaced generation can mask the current signatures used by conventional protection: fault currents are limited and shaped by control loops, reducing the sensitivity of impedance- and sequence-based relays. This talk reads faults from the geometry of measured voltage and current curves in G(ℝ³). In a balanced system, the voltage curve defines a reference circle in the Kirchhoff plane; during a ground fault, the mean voltage-curve bivector tilts away from that reference. A single geometric product between the reference and measured bivectors gives both detection and faulted-phase information, with fault resistance emerging as a by-product. The same family of curve invariants handles line-to-line and symmetric faults, requiring voltage-side evidence for each decision. On 922 electromagnetic-transient simulations of a converter-fed benchmark, the classifier achieves 100% accuracy in detection, type and faulted phase, generalizes to a second grid without retuning, and produces zero false operations on a synthetic security suite. The method is synchronization-free, inexpensive per sample and extends naturally to n-phase systems, demonstrated on six phases.
This analysis models three-phase power signals as 3D trajectories, using Geometric Algebra to define characteristics of current and voltage that are related to system stability. By applying Frenet-Serret frame theory, we treat the electrical signal as a curve in space. In ideal conditions, these GA characteristics remain constant, proving geometric invariance. However, harmonic distortion or transients, such as load shifts and phase imbalances, cause the system's geometry to change. We quantify these disturbances by monitoring the GA changes as a real-time diagnostic tool for detecting faults and power stability issues without needing traditional frequency-domain modelling.
We introduce a two-dimensional Geometric Laplace Transform that maps a space-time signal (t, x) to a pair of geometric frequency variables built on two commuting bivectors. The resulting algebra is the commutative algebra of bicomplex, or Segre, numbers, keeping temporal and spatial phases in separate readable planes. Applied to a DC distribution bus with distributed power converters, the transform yields a closed space-time dispersion relation and an admittance-shaping control law. A localized converter fault is represented as a space-time singularity whose transform factorizes into temporal and spatial signatures, enabling estimators that locate the fault from geometric spatial phase or modal weights and classify injection-loss, shunt, sensor and controller faults with a physical-consistency safeguard. A reproducible 100 m bus example shows stabilization and sub-meter localization. The advantage is intrinsically multivariable: in a single variable the construction reduces to the ordinary complex Laplace transform.
Geometric Algebra provides a unified mathematical representation for high-dimensional geometric objects, spatial transformations and geometric relation computation, making it well suited for describing complex geometric computing tasks. However, constructing, optimizing and implementing GA programs usually requires substantial expertise in algebraic modelling and low-level programming, while FPGA development adds hardware-description and synthesis constraints. This work proposes GeoGA-Compiler, a natural-language-driven framework that uses GAGPT to translate geometric computing tasks into GAALOPScript programs and then performs symbolic optimization and heterogeneous CPU/FPGA execution through the GAALOP compiler. Experimental results report a 90% compilation success rate and 90% functional accuracy in GAALOPScript generation tasks, with clear FPGA acceleration effects across multiple geometric computing tasks.