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Explore advanced mathematical optimization techniques in this 24-minute keynote speech from the 3rd International Conference on Applied Physics and Mathematical Modeling. Learn about sharp minima theory and its applications to fair resource allocation problems from Dr. Bismark Singh of the University of Southampton. Discover how mathematical modeling approaches can address complex distribution challenges when resources are limited, examining the intersection of optimization theory and fairness principles. Gain insights into cutting-edge research that bridges applied mathematics and real-world resource management scenarios, understanding how sharp minima concepts contribute to developing equitable allocation strategies in constrained environments.