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Explore the fundamentals of Gröbner bases in this 20-minute conference talk presented at FSE 2025 and chaired by Willi Meier. Delve into the mathematical foundations and applications of Gröbner bases, a powerful computational tool in algebraic geometry and commutative algebra that plays a crucial role in solving systems of polynomial equations. Learn about the theoretical underpinnings and practical implementations of these algebraic structures, which are essential for cryptographic applications and computational algebra. This presentation serves as the first part of a comprehensive two-part series on Gröbner bases, providing foundational knowledge that will be built upon in the subsequent talk. Access additional resources including research papers and presentation slides through the FSE 2025 program website to enhance your understanding of this advanced mathematical topic.
