Topics

(I) Clifford algebras

Spinors, multilinear algebra and tensor products, quadratic spaces, K-theory, Witt groups, K-theory of rings, associative algebras, algebraic combinatorics including symmetric functions, combinatorial aspects of representation theory, group actions, group rings including twisted and skew group rings, non-commutative Groebner bases, Hopf algebras, algebroids, octonions …

(II) Geometric algebras

Geometric analysis, invariant differential operators, conformal and non-commutative geometry, geometric integral transforms, image processing, quaternion and Clifford Fourier and Wavelet transforms, robotics, structural dynamics, computer graphics, quaternion and hypercomplex neural networks, geographic information systems, optics, molecular chemistry …

(III) Global analysis, differential geometry, spin geometry

Dirac operators on manifolds, calculus on manifolds; nonlinear operators, spaces and manifolds of mappings, monogenic mappings, partial differential equations on manifolds, applications to physics, connections on bundles, gauge transformations, BRST formalism, infinite-dimensional Grassmann algebra with generators …

(IV) Clifford algebras and Clifford analysis in theoretical physics

Spectral triples and elementary particle physics, Dirac equation in electron physics, q-deformations and noncommutative spacetime, qantum field theory using Hopf algebras and other algebraic techniques, quantum gravity, quaternionic quantum mechanics and quantum fields,electrodynamics, non-associative structures, division algebras and their applications in physics, quaternions and Clifford algebra in crystallography, Clifford spaces …

(V) Clifford analysis, quaternionic analysis, applications

Dirac operators, relations to harmonic and Fourier analysis, singular integral operators, operator algebras, functional calculi, function spaces, partial differential equations, Radon transforms, scattering theory, inverse problems …

(VI) Discrete Clifford structures, numerical methods

Discrete Clifford algebras, discrete function theory, discrete potential theory, signal processing, discrete wavelet transforms, numerical methods for partial differential equations, dynamical systems, visualization …

(VII) History of Clifford algebras and Clifford analysis

Education, art, entertainment, interdisciplinary aspects, philosophical aspects, biographical studies, history of Grassmann algebra, history of quaternion algebra, reception and interpretation, psychology …

(VIII) Quaternionic and Clifford Fourier transforms and wavelets

Quaternion Fourier transform, Clifford Fourier transform, windowed Clifford Fourier transform, spacetime Fourier transform, geometric Fourier transform, Hilbert transform, Riesz transform, Clifford square roots of -1, Clifford Fourier kernel, Cauchy kernel, Poisson kernel, operator exponential, translation operator, Clifford convolution, hypercomplex signal, hyperanalytic signal, 2D+t analytic video signals, multidimensional complex signal, monogenic signal, conformal monogenic signal, improper non-stationary complex-valued signals, quaternionic time-frequency representation, quaternionic spectral analysis, multivector wave packet analysis, orthogonal planes split, multiquaternion Clifford algebras, monogenic curvature scale-space, demodulation, color image processing, visualization of flow fields, analysis of flow fields, Clifford wavelets, diffusive wavelets …

(IX) Ternary algebras and their applications

Ternary analogue of Grassmann algebra, ternary analogue of Clifford algebra, generalized Dirac equation, ternary generalization of supersymmetry, calculus of cubic matrices …