## Q-Math Seminar

## About the Q-Math Seminar

The Q-Math Seminar is a series of seminars regularly held at the Mathematics department of the Carlos III University and the ICMAT. The topics discussed usually in the seminar are related with mathematical aspects of quantum theory and include:

- Differential Geometry
- Functional Analysis
- Operator Theory
- Quantum Information Theory

## Upcoming seminars

### María Barbero (UPM)

#### Geometric integrators of mechanical systems by lifting retraction maps

##### Monday the 10th of May, 2021, 12:30, Online Seminar: https://eu.bbcollab.com/guest/6da3b2acc1ad40b4b9588ce14d4f5c0e

The notion of retraction map is used in many research fields such as approximation of trajectories of differential equations, optimization theory, interpolation theory etc. In this talk we will review the concept of retraction map in differentiable manifolds to generalize it to obtain an extended retraction map from the tangent bundle of the configuration manifold to two copies of this manifold. We show this construction includes well-known numerical methods.

The property of being a retraction map is preserved when suitably lifting it to the tangent and cotangent bundle. We will show that some lifts of retraction maps define symplectic geometric integrators for mechanical systems. This is a joint work with David Martín de Diego.