Lezing

# This Week’s Discoveries | 31 October 2017

- Matthew Weaver
- Nils Bruin

- Datum
- 31 oktober 2017
- Tijd
- Locatie
- Oort Building

Niels Bohrweg 2

2333 CA Leiden - Zaal
- De Sitterzaal

### First lecture

**Title**

Coupling two Different Mechanical Resonators with Light in an Optical Cavity

**Speaker **

Matthew Weaver (LION)

Matthew is a PhD student in the group of Dirk Bouwmeester at UC Santa Barbara. He is a regular guest in the Quantum Optics group at LION.

**Abstract**

Single mechanical resonators are relatively simple and well understood. However, coupled resonators exhibit interesting possibilities such as synchronization and energy or information storage. Usually mechanical resonators only interact if they have similar frequency and a direct mechanical connection. I will discuss how we can use lasers to generate a mechanical interaction between resonators which are separated in both frequency and space, using a process analogous to energy level transitions in atoms or molecules. We use an optical cavity to enhance the interaction and provide an absolute frequency reference. This enables us to generate a network of mechanical states which we hope to use for quantum information storage and tests of fundamental quantum physics in large systems.

### Second lecture

**Title**

Most hyperelliptic curves are pointless

**Speaker**

Nils Bruin (Simon Fraser University, Canada)

Nils Bruin is Professor of Mathematics at Simon Fraser University, Vancouver, Canada. He specializes in arithmetic geometry, and in particular in explicit and computational methods for solving diophantine equations. He completed his degree at Universiteit Leiden (UL) in 1999 on the topic of generalized Fermat equations. He is currently visiting the Mathematical Institute at UL.

**Abstract**

A central problem in arithmetic geometry is to determine if an equation has any solutions in rational numbers. Heuristic arguments suggest that many equations describing curves should have rather few such solutions, but proving precise statements about them turns out to be surprisingly hard.

Manjul Bhargava proved in 2013 that a large proportion of hyperelliptic curves (measured in a very precise way) have no rational solutions: they are pointless, so to say. Partly for this result he was awarded the Fields Medal, often called the Nobel Prize for mathematics, in 2014.

I will explain the problem, indicate why it is hard, and sketch some of the ingredients Bhargava introduced to prove his results.