Driven by the growing use of quantum technology, our mission is to push the boundary of our understanding of the fundamental structure of quantum systems. In an attempt to resolve these foundational questions, one is naturally led to the intersection of non-commutative geometry, operator algebras, and quantum field theory, which represents one of the most promising frontiers for understanding the true nature of quantum spacetime. However, while various disciplines explore these identical questions, they often rely on distinct mathematical frameworks—creating a significant barrier to unified development. Motivated by these challenges, this workshop aims
- To gather prominent scholars from the international and the Asia-Pacific communities to exchange ideas and advance this research frontier with contributions coming from several different approaches to ``quantum geometry''.
- To foster deep cross-fertilization between international quantum geometry communities and the rapidly developing Southeast Asian mathematical and theoretical physics landscape.
- Shift the focus from routine computational problem-solving toward designing \textbf{conceptually rigorous, sophisticated, and inspiring mathematical problems} that challenge current conceptual boundaries.
- Formulate open problems in non-commutative geometry and quantum gravity that require nuanced physical insight and synthetic mathematical reasoning beyond current automated AI capabilities.
- Train the next generation of graduate students and researchers to leverage AI as a computational engine while cultivating the mathematical depth and creativity necessary to ask the right fundamental questions.
This workshop will provide students and early-career researchers in Thailand and the Asia-Pacific region with direct exposure to various techniques and mathematical tools used in the following fields:
- Non-commutative and Lorentzian Spectral Geometry: spectral triples, gauge theory formulations, quantum spacetime causality, and Lorentzian signatures.
- Generalized and Higher Geometries: generalized complex geometry, higher gauge theories, Lie algebroids, exceptional geometry, double field theory.
- Quantum Symmetries and Groups: deformation quantization, Hopf algebras and quantum group symmetries in quantum spacetime.
- Modular Theory and Operator Algebras: algebraic quantum field theory (AQFT), Tomita-Takesaki modular theory, and quantum information in field theory and gravity.
- Applications to Cosmology, Quantum Gravity, High Energy, Condensed Matter: quantum spacetime in quantum gravity, non-commutative and mirror CPT cosmologies, black hole entropy and holography, inflationary models in non-commutative spacetime, spectral description of the standard model of fundamental interactions, topologically ordered phases and non-commutative solid-state physics.
