Classification of solutions to the Toda system for a general simple Lie algebra
Speaker: Zhaohu Nie, Utah State
Abstract: Toda systems are generalizations of the Liouville equation to other simple Lie algebras. They are examples of integral systems and have various applications in geometry and physics. For Lie algebras of type A, Lin, Wei and Ye classified their solutions with finite integrals and singular sources at the origin. The speaker generalized their classification to Lie algebras of types B and C. In this talk, we will generalize the classification of solutions to Toda systems for all types of simple Lie algebras using a unified Lie-theoretic approach. The method relies heavily on the structure theories of the local solutions and of the W-invariants for the Toda system. The solution space is shown to be parametrized by a subgroup of the corresponding Lie group. We will also show the quantization result for the corresponding integrals. This is a joint work with C.-S. Lin and J. Wei.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:35pm - 3:30pm