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From Soliton Theory to Quantum Invariants of Manifolds

Student-Run Applied & Math Seminar

Speaker: Motohico Mulase, UC Davis
Location: 2112 MSB
Start time: Wed, Apr 13 2011, 12:10PM

Soliton theory has a long history that is deeply rooted in the core of applied mathematics. It has also supplied many mysteries to pure mathematics. Since the late 1970s we have come to the understanding that these nonlinear PDEs are a manifestation of rich geometric structures. In the 21st century, it is speculated that somehow miraculously these nonlinear dynamics govern yet hidden relations among quantum invariants of manifolds. In this expository talk, I will start with the historical origin of the KdV equation, and present an overview of the development to the current excitement on quantum invariants in topology and symplectic geometry.