##### Department of Mathematics,

University of California San Diego

****************************

### Department Colloquium

## Jeff Viaclovsky

#### UCI

## Gravitational instantons and algebraic surfaces

##### Abstract:

Geometers are interested in the problem of finding a "best"

metric on a manifold. In dimension 2, the best metric is usually one which possesses the most symmetries, such as the round metric on a sphere, or a flat metric on a torus. In higher dimensions, there are many more classes of geometrically interesting metrics. I will give a general overview of a certain class of Einstein metrics in dimension 4 which have special holonomy, and which are known as "gravitational instantons." I will then discuss certain aspects of their classification and connections with algebraic surfaces.Lei Ni

### October 13, 2022

### 4:00 PM

****************************