报告题目：On reflections to set-theoretic solutions of the Yang-Baxter equation
报 告 人：Paola Stefanelli
所在单位：University of Salento
报告时间：April 10, 2025, 21:00-23:00
报告地点：Zoom Id: 904 645 6677，Password: 2024
会议链接：
https://zoom.us/j/9046456677?pwd=Y2ZoRUhrdWUvR0w0YmVydGY1TVNwQT09&omn=89697485456
报告摘要: The Yang-Baxter equation (YBE) is a fundamental equation of mathematical physics that has been extensively studied in the last few years. Alongside it, the reflection equation serves as a significant tool in the theory of quantum groups and integrable systems, which was first investigated in 1984 by Cherednik. In 2013, Caudrelier, Crampé, and Zhang formulated the set-theoretic version of the YBE, and, later on, some new results were obtained, mainly concerning involutive and non-degenerate solutions
This talk aims to present a strategy for determining reflections to left non-degenerate set-theoretic solutions (X, r) of the YBE as provided in a joint work with A. Albano and M. Mazzotta, and obtained by examining the behavior of these solutions with their derived solutions or, equivalently, with (left) self-distributive structures associated with them. Our approach is strongly motivated by a recent description of left non-degenerate solutions (X, r) in terms of Drinfel’d twist, namely, a family of automorphisms of the shelf associated with (X, r), which is obtained in a joint paper with A. Doikou and B. Rybołowicz.
报告人简介：Paola Stefanelli is currently a Tenured Assistant Professor at the University of Salento, where she earned her PhD in 2015 under the supervision of Prof. Francesco Catino. Her research focuses on the interaction between set-theoretical solutions to the Yang-Baxter equation and various algebraic structures, such as skew braces, cycle sets, racks, and their generalizations. She pays particular attention to the constructive aspects of these solutions and, more recently, to their associated reflections. Additionally, she is interested in studying set-theoretical solutions to the pentagon equation for specific classes of semigroups. Another area of her research involves describing the regular subgroups of the affine group of a vector space.
