##### Department of Mathematics,

University of California San Diego

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### CSME Seminar

## Ari Stern

#### UCSD

## Geometric aspects of ODEs and PDEs

##### Abstract:

In this talk, I plan to discuss how differential geometry can provide useful insights into the study of ordinary and partial differential equations. In particular, I will focus on the role of symplectic geometry in classical Lagrangian and Hamiltonian mechanics, as well as its generalization to the multisymplectic geometry of classical field theory. Finally, I will talk about how this perspective has paved the way for the development of ``geometric'' numerical integrators, which exactly preserve important structures, symmetries, and invariants.

### April 9, 2009

### 12:00 PM

### AP&M 2402

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