HyperComplex Seminar Courses

GRACYASK: Graphs, Cycles, and Skyrmions in Discrete Trivial Fiber Bundles

Explore topological structures in higher dimensions, focusing on Skyrmions and Hopons. Gain insights into their potential applications in material science and biological processes, bridging theoretical physics with practical advancements.

• YouTube
• 13 minutes
• Self-Paced
• Free Video

Euler and Schrödinger Equations - Turning Points in Complex Mathematics and Physics

Explore the historical impact of Euler and Schrödinger on complex mathematics and quantum mechanics, from algebraic beginnings to modern applications in quantum chemistry.

• YouTube
• 43 minutes
• Self-Paced
• Free Video

Recovering Bicomplex Holomorphic Functions Without Cauchy-Riemann Equations

Explore advanced techniques for recovering bicomplex holomorphic functions without using Cauchy-Riemann equations, focusing on complex harmonic functions and their applications in hypercomplex analysis.

• YouTube
• 28 minutes
• Self-Paced
• Free Video

Engineering Resonant Metasurfaces for Photonic Applications

Explore engineering approaches for resonant metasurfaces in photonics. Learn about 2D nanostructures, their applications, and novel design methods for enhanced light-matter interactions and specific optical functionalities.

• YouTube
• 34 minutes
• Self-Paced
• Free Video

Chimera States for Coupled Pendula

Explore chimera states in coupled pendula systems with Prof. Tomasz Kapitaniak's insightful seminar on complex synchronization phenomena.

• YouTube
• 41 minutes
• Self-Paced
• Free Video

The Divergence Theorem for Vector Fields - Applications and Generalizations

Explore the divergence theorem's applications in PDEs, geometry, physics, and engineering, including proofs of Archimedean principle and multidimensional Pythagorean theorem.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

Pattern Explorer Tool for Testing CEP Patterns

Explore a tool for testing Complex Event Processing patterns through automata compilation and symbolic event sequence generation. Enhance pattern understanding and error detection in event streams.

• YouTube
• 44 minutes
• Self-Paced
• Free Video

On Convex Peano Curve, Connected Methods and Problem

Explore continuous surjections mapping intervals to convex sets in Cartesian space. Discover new convex analysis methods applicable to various function classes and related conjectures.

• YouTube
• 45 minutes
• Self-Paced
• Free Video

2WQC - Adding Postparation as Reversed State Preparation Process to Solve NP Problems

Explore analytical solutions for position-based charge qubits and N-interacting qubits in quantum dot networks. Examine Hadamard and phase-rotating gates, and the interface between superconducting and semiconductor qubits.

• YouTube
• 52 minutes
• Self-Paced
• Free Video

Quantum and Post-Quantum Cryptography - Opportunities, Controversies, and Path to Quantum Resistance

Explore quantum-resistant cryptography, including post-quantum algorithms and physical-layer approaches. Examine NIST's recent announcements and the potential of hybrid solutions for secure communication in the quantum era.

• YouTube
• 1 hour 8 minutes
• Self-Paced
• Free Video

On the Continuous Extension of the Logarithmic Double Layer Potential to Boundary of Domain

Explore continuous extension of logarithmic double layer potential to Ahlfors-regular curve boundaries. Learn necessary and sufficient conditions for extension and examine illustrative examples.

• YouTube
• 47 minutes
• Self-Paced
• Free Video

Geometric Properties of Quantum States Representing Directed Graphs on Quantum Computer

Explore geometric properties of multi-qubit states represented by directed graphs, examining curvature, torsion, and entanglement using quantum computers and simulators.

• YouTube
• 32 minutes
• Self-Paced
• Free Video

Low-energy High-performance Computing Based on Superconducting Technology

Explore superconducting computing's potential for energy-efficient, high-performance applications. Learn about SFQ logic, adiabatic logic, and innovative circuit technologies advancing post-CMOS computing.

• YouTube
• 1 hour 2 minutes
• Self-Paced
• Free Video

Application of Unsupervised Learning to AC Susceptibility Measurements of High-Temperature Superconductors

Explore unsupervised learning applications in analyzing AC susceptibility measurements of high-temperature superconductors, focusing on clustering techniques and data representation methods.

• YouTube
• 33 minutes
• Self-Paced
• Free Video

Application of Scattering Parameters to DPL Time-Lag Parameter Estimation Using MEMS Structures

Explore MEMS test structures for DPL model parameter estimation in nanoscale IC materials using scattering parameters and the 2-omega method.

• YouTube
• 28 minutes
• Self-Paced
• Free Video