**May 07, 2018 at 10:45**

**Speaker(s):**
**Martin Bridson and Asgeir Tomasgard**

**Center(s): **University of Oxford and NTNU

**Martin Bridson: Chasing finite shadows of infinite groups through geometry **
There are many situations in geometry and group theory where it is natural or convenient to explore infinite groups via their actions on finite objects -- ie via their finite quotients. But how hard is it find finite quotients, and to what extent do they determine the group?

In this lecture, I'll outline the great advances of recent years in this area. I'll describe pairs of distinct groups that have the same finite quotients and I'll sketch the proof of some "profinite rigidity results", ie theorems showing that in certain circumstances one can identify an infinite group if one knows its set of finite quotients.

I'll emphasize how an enhanced understanding of spaces of non-positive curvature has underpinned progress on key algebraic questions, and pay particular attention to 3-dimensional manifolds, where a remarkable mingling of arithmetic and geometry leads to profinite rigidity theorems.

**Asgeir Tomasgard: Using stochastic programming to analyse demand response in European electricity markets**
Due to technological developments and political goals related to renewable energy and energy efficiency, the electricity system is undergoing significant changes. One of the main consequences is an active demand side where consumers take a more active role. We model several classes of shiftable and curtailable loads in residential, commercial and industrial sectors. The benefits of demand response consist of a reduction in peak load consumption, which leads to a reduction in capacity investments, production and consumption savings, reduced congestion phases, reliable integration of intermittent renewable resources and supply and demand flexibility.

We first present a model for the scheduling of energy flexibility in buildings. Next, we propose short-term decision-support models for aggregators that sell electricity to prosumers and buy back surplus electricity. The key element is that the aggregator can control flexible energy units at the prosumers. We demonstrate the approach in a generalized market design that is flexible enough to capture today’s market structure and still relevant in the next generation market design, both at wholesale and local level: an options market where flexibility is reserved for later use, a spot market for energy day-ahead or shorter, and a flexibility market where flexibility units are dispatched near real- time.

Finally, we look at the European level and analyse to what extent the demand response potential can facilitate an optimal transition to an European low emission power system. The results show that demand response decreases system operational costs and increases the capacity factors of IRES (Intermittent Renewable Sources). Results show that demand response capacity reduces investments in peak load plants and their capacity factors, from which follows lower CO2 emissions.

**Click to see the poster and the event program**