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BIMSA Member Seminar
BIMSA Member Seminar
What can we do with computational algebraic geometry?
What can we do with computational algebraic geometry?
演讲者
时间
2026年04月20日 14:35 至 15:15
地点
A6-101
线上
Zoom 388 528 9728
(BIMSA)
摘要
At its heart, algebraic geometry is the study of solutions to systems of polynomial equations. But what happens when the equations become too complicated to solve by hand? This is where computational algebraic geometry comes in.
This talk will provide an overview of the core ideas and tools in computational algebraic geometry, aimed at a general mathematical audience. We will begin with the classical problem of solving a system of polynomial equations. Such a system appears in all kinds of problems, like robotics, chemical reaction, computer vision, cryptanalysis, etc. We will explain briefly how algebraic geometry, homological algebra, combinatorics and symbolic computation help in such a problem. The critical leap to computation is made possible by Groebner bases, which is the workhorse in this subject.
Finally, I will introduce several projects I have worked/been working on to touch upon some modern applications of these computational techniques on fields such as computer-aided geometric design, tensor decomposition, and string theory, demonstrating that computational algebraic geometry is not just a sub-discipline, but a valuable lens for a wide range of scientific inquiry.
This talk will provide an overview of the core ideas and tools in computational algebraic geometry, aimed at a general mathematical audience. We will begin with the classical problem of solving a system of polynomial equations. Such a system appears in all kinds of problems, like robotics, chemical reaction, computer vision, cryptanalysis, etc. We will explain briefly how algebraic geometry, homological algebra, combinatorics and symbolic computation help in such a problem. The critical leap to computation is made possible by Groebner bases, which is the workhorse in this subject.
Finally, I will introduce several projects I have worked/been working on to touch upon some modern applications of these computational techniques on fields such as computer-aided geometric design, tensor decomposition, and string theory, demonstrating that computational algebraic geometry is not just a sub-discipline, but a valuable lens for a wide range of scientific inquiry.
演讲者介绍
Beihui Yuan gained her Ph.D. degree from Cornell University in 2021. She has joined BIMSA in 2023. Her current research interests include application of commutative algebra in pure and applied mathematics problems.