Surjective Submersions in Technology
Integrating topology, sheaf theory, and mathematics to research and create wellness-focused and artificial intelligence, community based solutions.
Enterprise Solutions
Research in Immersive Topology
Research Timeline
2011-2018
Initial, deep, collegiate learning in topological signal processing, acoustics, pure mathematics, statistics, computer science, non-profit, educational, tecnhology entrepreneurship artistic, athletic, and cultural experiences.
2018-2027
Establishing foundations of Immersive Topology through theoretical development and practical applications in wellness technology. Intuitive solutions are derived, explored, analyzed, and synthesized with personal Nature immersion, physical embodiment, Ayurveda studies, community involvement, and mathematical meditation and more Types. Dynamically grew knowledge, talent, and skill based with Navy high-fidelity, real-time, underwater sonar modeling and simulation, fluid modeling and analysis, model validation, data analysis, software engineering and systems engineering.
2027-2030
PhD research integrating Navy mathematics with Golden Enterprises solutions, focusing on advanced applications of sheaf and category theory and finalizing rigorous, pure mathematical proofs.
2030-2040
Long-term development of Immersive Topology and its applications across multiple domains, envisioning harmonious, balanced, golden knowledge, technology, communities, practices, and collective dreams.
Mathematical Framework
Topological Analysis
Mathematical investigations in:
- Signal and Phase Space Analysis
- CW Complex, Manifold Based Sampling
- Principal Component Analysis
- Peristent Homology and Surjective Submersion Theorems
- Euler-Bessel Transforms
Category Theory Construction
Utilizing categorical frameworks for sheaf and topology integration, focusing on:
- Sheaves sampled on n-Spheres and deformations
- Multiple Sheaves Integration
- Liftings and Representations
- Category C₁ = ShvPA(X,T)
- Functor and Natural Transformation Analysis
Current Research Focus
Immersive Research Blog
Fundamental explorations and original experiences in Immersive Topology and its applications.
Active Papers
Currently developing 6 papers exploring various aspects of Immersive Topology and its applications.
Solution Integration
Research supporting the development and integration of Golden Enterprise solutions.
Research Connections
Publications
Research Papers
Books
Immersive Topolgoy
A comprehensive exploration of topology in signal processing applications, focusing on innovative approaches to data analysis and processing.
Technical Reports
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July 2022
"Geodesic Validation"
US Navy Technical Report
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May 2022
"Fluid Modeling"
US Navy Technical Report
Journey in Mathematics
Mathematical Heritage
Einstein to Turing
Foundations of theoretical physics and modern computation
Social Progress & Scientific Revolution
Integration of social change with mathematical advancement
Fractals to Internet
Algorithmic and recursive digititzation and expansion
Professional Background
Navy Mathematician
Current role and contributions in mathematical research and applications
View CV →Academic Research
Focus on topological signal processing and sheaf theory applications
Fields of Study
Topology, Fourier Analysis, Number Theory, Computer Science Artificial Intelligence, Complex Algebraic Geomtry, Lie Groups, Complex Analysis, Corporate Social Responsiblity, Business Law, Non-Profit Entrepreneurship, Information Technology, Finance, Accouting.
Enterprise Development
Founding and evolution of Golden Enterprises
Mathematical Evolution
Acoustics Modeling, Nature Immersion
Real-World Applications and local journeys
Topological Signal Processing
Modern applications in wellness and technology
Category Theory
Framework for integrated mathematical solutions
Sheaf Theory Applications
Bridging theoretical and practical domains
Mathematical Genealogy
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Bertram KostantAdvisor (1976)
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Michael RobinsonAmerican University
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Brian DiZioGolden Enterprises
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The Golden Enterprises Story
From New England's rich mathematical heritage to modern technological innovation, Golden Enterprises represents a convergence of theoretical mathematics and practical applications. Our journey relates to the evolution of modern mathematics itself, from classical theory to advanced wellness solutions.
Mathematical Foundations
Current Innovation
Ongoing Evolution
Our Impact
Golden Enterprise Solutions is making a difference in communities through the integration of mathematical theory and practical applications.
Users experiencing mathematical wellness
Local communities engaged
Research papers in development