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Explore the mathematical complexities and computational challenges involved in solving geometric flows and free boundary problems through this 49-minute conference talk from BIMSA's ICBS2025. Delve into advanced numerical analysis techniques and discover innovative computational methods specifically designed to address the unique difficulties that arise when working with geometric flows, where shapes evolve over time according to geometric properties, and free boundary problems, where the boundary of the domain is unknown and must be determined as part of the solution. Learn about the theoretical foundations underlying these mathematical phenomena, examine the numerical challenges that traditional methods face when applied to such problems, and understand how new computational approaches are being developed to overcome these limitations. Gain insights into the intersection of differential geometry, partial differential equations, and computational mathematics, while discovering how these advanced techniques are pushing the boundaries of what can be solved numerically in geometric analysis.
