# An introduction to Lie groups, symmetries, and symplectic geometry. Gulbenkian Summer School in Differential Geometry. Gulbenkian Foundation, LISBON. July 23, 2018 - July 27, 2018

Instructional Course, Workshop, or Symposium

The notion of groups of motions and symmetries of objects is a fundamental one in mathematics, and it is nowhere more important than dealing with continuous motions and and problems in physics and geometry. I will start by discussing familiar objects, such as the group of rotations in space and higher dimensions, and move on to other groups, mainly groups of linear transformations, so that we can stay as concrete as possible. After developing the theory of continuous groups and seeing how these objects can be studied using multivariable calculus and linear algebra, we will then apply these concepts to study some mechanical systems and the surprising connection between symmetries and conservation laws that is so fundamental in modern mathematics and physics.

### Service Performed By

- Bryant, Robert Phillip Griffiths Professor of Mathematics

### Date

- July 23, 2018 - July 27, 2018

### Service or Event Name

- Gulbenkian Summer School in Differential Geometry

### Host Organization

- Gulbenkian Foundation, LISBON

### Location or Venue

- Lisbon, Portugal