题目： Frobenius manifolds and Frobenius-algebra valued integrable system
报告人：左达峰（教授，中国科学技术大学数学科学学院, 博导）
时间：2018年1月13日（周六）上午9:30-10:30
地点：闻理园A4-305室
摘要： The notion of integrability will often extend from systems with scalar-valued fields to systems with algebra-valued fields. In such extensions the properties of, and structures on, the algebra play a central role in ensuring integrability is preserved. In this talk based on a joint work with Ian strachan, a new theory of Frobenius algebra-valued integrable systems is developed. This is achieved for systems derived from Frobenius manifolds by utilizing the theory of tensor products for such manifolds, as developed by Kaufmann (Int Math Res Not 19:929–952, 1996), Kontsevich and Manin (Inv Math 124: 313–339, 1996). By specializing this construction, using a fixed Frobenius algebra A, one can arrive at such a theory. More generally, one can apply the same idea to construct an A-valued topological quantum field theory. The Hamiltonian properties of two classes of integrable evolution equations are then studied: dispersionless and dispersive evolution equations. Application of these ideas are discussed, and as an example, an A-valued modified Camassa–Holm equation is constructed.
报告人简介：
2003年中国科学技术大学理学博士，2003.8---2005.7 清华大学数学科学系博士后，2006.1—2008.12 韩国高等研究院访问学者, 2013年入选教育部新世纪优秀人才支持计划，2013.10—2014.8 英国格拉斯哥大学数学统计系访问学者. 主要研究方向：可积系统，Frobenius流形及其相关问题，在Advances in Mathematics, Inverse problems, Letters in Mathematical Physics, Journal of Mathematical Physics, Journal of Geometry and Physics等期刊杂志上发表论文20余篇。
