From Ancient Greeks to Cluster Algebras: A Tale of Factorizations and Geometry
主 讲 人 ：Mara Pompili 博士
活动时间：06月11日15时00分
地 点 ：理科群1号楼D203室（ZOOM会议链接：https://us06web.zoom.us/j/86448715796?pwd=OQiVjx9OdqhfKY7wmauIYf8C9X9xAd.1；会议号: 86448715796密码: 584663）
讲座内容：
Around 100 AD, the Greek mathematician Ptolemy demonstrated that the product of the lengths of the diagonals of a cyclic quadrilater equals the sum of the products of the lengths of its opposite sides.
Nearly two thousand years later, Russian mathematicians Fomin and Zelevinsky drew inspiration from Ptolemy’s formula to introduce a new class of commutative rings, known as cluster algebras. These algebras originated in the context of representation theory and have found applications in various fields of mathematics, including Lie theory, combinatorics, algebraic geometry, and mathematical physics.
We will explore the definition and basic properties of cluster algebras, along with their surprising connection to Ptolemy’s theorem. We will then delve into the intriguing question first posed by Euclid in the context of integers: under what conditions do the elements of a cluster algebra factor into prime elements?
主讲人介绍：
Mara Pompili is a PhD student at the University of Graz (Austria) within the Discrete Mathematics Consortium of the Doctoral Academy. Her primary research interests include cluster algebras and non-unique factorization. Additionally, she is interested in skew braces and the Yang-Baxter equation, a topic she explored extensively during her Master’s at the University of Padova(Italy). Recently, she spent some time at the University of Oklahoma (USA) as a guest of Prof. Greg Muller.
