##### Department of Mathematics,

University of California San Diego

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### Food For Thought Seminar

## Evangelos ``Vaki'' Nikitopoulos

#### UCSD

## Algebratizing Differential Geometry: Linear Differential Operators

##### Abstract:

It is frequently the case that certain objects in differential topology/geometry can be described in purely algebraic terms, where the algebraic structures involved are constructed using the smooth structure(s) of the underlying manifold(s). For example, a common equivalent characterization of a smooth vector field on a smooth manifold $M$ is a derivation of the $\mathbb{R}$-algebra of smooth real-valued functions on $M$. I shall discuss this example and describe how it led me to a considerably more involved one: linear differential operators on $M$. This talk should be of interest to anyone who likes differential topology/geometry, algebraic geometry, or algebra.

### November 6, 2018

### 12:00 PM

### AP&M 7321

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