Geometric Analysis in Mathematical General Relativity, PDE and Quantum Physics
Ente: GEOMETRIC ANALYSIS
Scadenza: 2029-08-31
Importo max: 300.000 EUR
Paese: US
Descrizione
This project investigates the mathematics of partial differential equations arising in general relativity - the physical theory describing gravitation, black holes, and the large-scale universe - and in quantum physics, the theory governing matter and energy at the smallest scales. Partial differential equations describe how physical quantities change in space and time, and they form the foundation of technological innovations as well as scientific models in areas ranging from the fundamental laws of nature to quantum computing and artificial intelligence (AI). General relativity underpins technologies such as the Global Positioning System (GPS), while quantum physics drives emerging quantum technologies. Remarkably, the physics of the large and the physics of the small share deep mathematical structures, and this project develops unifying methods to advance understanding in both domains. The results of this project connect directly to gravitational-wave observations by experiments such as LIGO/Virgo and NANOGrav, and the investigation of memory phenomena in quantum electrodynamics lays theoretical foundations for experiments in new directions with promise for future quantum technologies. The project strengthens scientific literacy and workforce development by training postdoctoral researchers, graduate students, and students at all levels. Public outreach - including accessible talks, online content, and public events - as well as talks at academic conferences communicate the research to broad audiences while fostering intellectual exchange within the scientific community. Research findings are disseminated through publications and online media to ensure broad visibility and accessibility for both researchers and the public.
The project establishes a mathematically rigorous comprehension of the dynamics and underlying structures of partial differential equations describing physical phenomena. It develops new methods in geometric analysis and nonlinear partial differential equations to study the Einstein equations - the core of general relativity linking the universe’s physical content to geometry - gravitational radiation, memory effects - permanent changes of the spacetime by gravitational waves - and singularity formation, including black holes, as well as related equations in quantum electrodynamics. The project investigates the Cauchy problem for the Einstein equations for various classes of physical spacetimes, the mathematical structures of gravitational radiation and memory in general relativity, and partial differential equations in other physical theories, including studies of memory analogs in quantum electrodynamics. The mathematical tools developed in this project apply to other structurally similar equations in mathematics and across the sciences. The investigation of electromagnetic analogs of memory in quantum electrodynamics advances the theoretical understanding needed for future experiments and potential applications in qua
Istituzione: Regents of the University of Michigan - Ann Arbor
Sede: ANN ARBOR, MI
PI: Lydia Bieri
Settori: Mathematical & Physical Sciences
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