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Watch a 48-minute lecture by J Maurice Rojas from Texas A&M University titled "Breaking Complexity Barriers in Real Algebraic Geometry" presented at IPAM's LatMath 2025 Workshop. Explore how real solutions to large nonlinear systems of equations are central to engineering applications and complexity theory, with recent work showing that counting solutions can lead to new separations of complexity classes related to the P vs. NP problem. Discover the connections between solving polynomial equations, algorithmic complexity, fewnomial theory, and combinatorics, including a recent link between the abc-Conjecture and accelerating equation solving over real numbers. No background in algebraic geometry is required to understand this presentation, which features joint research with Weixun Deng, Alperen Ergur, and Grigoris Paouris.
