##### Department of Mathematics,

University of California San Diego

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### Center for Computational Mathematics Seminar

## Joris Vankerschaver

#### University of California San Diego

## The Symplectic Geometry of Fish

##### Abstract:

Fish, or in general any mechanical object moving in an inviscid fluid, can be described by means of a number of interesting differential-geometric structures, amongst other bundles and connections, groups of diffeomorphisms, and symplectic reduction. I will describe some of these structures and outline their role in fluid dynamics. Along the way, a number of parallels will appear with other dynamical systems: time permitting, we will describe a Kaluza-Klein description of fluid-structure interactions (making the link with magnetic particles), and we will see how the flux homomorphism from symplectic geometry makes an appearance through an old construction of Kelvin.

### November 2, 2010

### 11:00 AM

### AP&M 2402

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