Conference sessions
The conference will host the following session:
- AI approaches to Geometry
Organisers: Edward Hirst (University of London, UK), Yang-Hui He (University of Oxford, UK), Henrique N. Sá Earp (University of Campinas, Brazil)
Geometric transformations play a central role in the architectures and training of modern AI methods. Whilst geometrically-inspired insights often lead to improved AI techniques, the converse application allows AI methods to provide new means of building, approximating, and examining important geometries. Clifford algebras further provide an algebraic framework to study many important geometric transformations, potentially offering novel compact and coordinate-free architecture modifications. This session explores this intersection, bringing together the array of AI techniques most suited to geometric problems and the geometric-objects most amenable to data representation and machine learning. - Clifford algebra and the fundamental forces of nature (CAFFN)
Organisers: Gene McClellan (Applied Research Associates, USA), Anthony Lasenby (Cambridge University, UK)
Of interest for this session are applications of Clifford algebra, geometric calculus, and octonions to the physics of strong, electromagnetic, weak, and gravitational fields. Topics could include geometric and Clifford algebra approaches to understanding fundamental physical interactions, and current research connecting octonions to Standard Model symmetries and beyond. Applications to topics within gravitational theory such as dark matter and dark energy are also welcome. - Generalizations of complex analysis: Clifford, hypercomplex analysis and beyond
Organisers: Swanhild Bernstein (TU Bergakademie Freiberg, Germany), Paula Cerejeiras (Universidade de Aveiro, Portugal), Fabrizio Colombo (Politecnico di Milano, Italy), Irene Sabadini (Politecnico di Milano, Italy)
Clifford analysis and more in general hypercomplex analysis can be regarded as an extension of complex analysis to higher dimensions. The field has attracted attention in several areas, as it provides an elegant way of dealing with problems of mathematical physics in higher dimensions, in operator theory, analysis of PDEs, spectral theory based on the S-spectrum, reproducing kernel methods and Schur analysis, among others. This session aims to present recent advances in the field, mostly for functions with values in associative algebras, as well as its various applications in related areas. - Differential invariants and geometric complexes
Organizers: Vladimir Soucek (Charles University, Czechia), Roman Lavicka (Charles University, Czechia), Jan Slovak (Masaryk University, Czechia)
This session explores recent progress at the intersection of Clifford analysis, representation theory, and differential geometry. Modern Clifford analysis offers a local function theory for invariant first-order systems of PDEs and reveals rich structures such as Howe duality and geometric complexes of invariant differential operators. Symmetries of invariant operators appear in a broad scale of incarnations. - Geometric Algebra for Modern Signal Processing: Foundations and Frontiers
Organisers: Anna Kit Ian Kou (University of Macau, China), Eckhard Hitzer (International Christian University, Japan)
This session highlights cutting-edge research where Geometric Algebra (GA), including quaternions as well as related algebras like octonions and Okubo algebra, etc., provide a unifying mathematical framework for advanced signal processing. We will explore foundational advances that transcend traditional methods, focusing on novel GA-based integral transforms (including a.o. Fourier transforms, linear canonical transforms, wavelets, etc.), hypercomplex tensor decompositions, and generalized convolution theorems. A key theme is the application of these theoretical tools to solve complex, multidimensional problems in areas such as vector-sensor processing, image analysis, and geometric deep learning. The session aims to bridge theoretical mathematics and practical implementation, demonstrating how GA leads to more efficient, coherent, and intuitively derived solutions. We invite contributions on both the theoretical development of these tools and their application to demonstrate the potent synergy between abstract algebra and practical computation. - Fractional integro-differential operators in Clifford analysis
Organisers: Milton Ferreira (Polytechnical University of Leiria, Portugal), Nelson Vieira (Universidade de Aveiro, Portugal)
This session explores fractional integro-differential operator theory within Clifford algebras, focusing on nonlocal, multiscale methods for multivector-valued functions and fields. Core themes include fractional Dirac-type operators and their powers, fractional Clifford–Fourier transforms, semigroup and spectral constructions, and uncertainty principles for fractional Clifford transforms. Topics include, but are not limited to: Foundations of fractional Riemann–Liouville/Caputo/Riesz operators in Clifford settings; Fractional powers of Dirac, d-bar, and radial operators; Two-sided fractional Clifford–Fourier frameworks and kernel representations; Fractional pseudodifferential and Hankel–Clifford operator calculi; Fischer/CK extensions and functional calculi for nonlocal operators; Inversion, Plancherel, and mapping properties on Sobolev/Besov-type Clifford spaces; Discrete and semidiscrete fractional Dirac operators; Applications to nonlocal PDEs, imaging and inverse problems, time–frequency analysis, space-time modelling in mathematical physics, and artificial intelligence. - Function theories in Cayley-Dickson algebras
Organisers: Sören Kraußhar (Universität Erfurt, Germany), Helmuth R. Malonek (Universidade de Aveiro, Portugal), Guangbin Ren (University of Science and Technology of China)
This session highlights recent developments in function theories over Cayley–Dickson algebras, with an emphasis on non-associative structures. These include octonions, split-octonions, complex octonions, sedenions, general alternative and twisted $\mathbb{Z}_2$-graded algebras, the Okubo algebra, and related systems. Topics include—but are not limited to—Fourier transforms and wavelet theory in this context, non-associative analysis and geometry, octonionic functional analysis, and their specific applications to physics and non-commutative geometry. - Harmonic analysis
Organisers: Uwe Kähler (Universidade de Aveiro, Portugal), Jens Wirth (Universität Stuttgart, Germany)
Harmonic Analysis has always played a key role in developing new methods and topics in both complex and hypercomplex analysis as well as in the broader application of Clifford algebras. This session is dedicated to recent advances in harmonic analysis in both two and higher-dimensional settings, with a particular focus on the interplay of algebraic, analytic and geometric methods. Topics will include, but are not limited to, Fourier transforms and related integral transforms over topological groups, symbolic calculi, applications to spectral theory, and functional and integral inequalities. Special emphasize will also be given to time-frequency analysis and its applications in signal and image processing. Contributions on the application of methods from harmonic analysis in machine and deep learning are also welcome. - Mathematical physics
Organisers: Tat Gosh (National Taiwan University), Heikki Orelma (University of Tampere, Finland), Pramod Padmanabhan (Indian Institute of Technology Bhubaneswar), Adrian Vajiac (Chapman University, US)
