The brain, which allows us to reflect on ourselves and the world, is a complex physical system. From complex subcellular biochemical processes, through nonlinear physics of neuronal membrane, complex cell morphology, communication in non-trivial networks, to behavior, every level of brain functioning is bringing different challenges.

In my lecture I will focus on three problems we have been working on. First, I will say a few words about the problem of information coding in the brain and the language used to describe the activity of the nervous system (I call it the kinematics of spike trains). Then, I will discuss the problem of the reference system in the brain, or brain atlases. Whenever we want to localize a phenomenon in the brain we must use some reference system. Given substantial inter-specimen variability this poses a challenge. I will discuss how we handle this.

Finally, I will discuss the problem of measurement, the relation between the activity of the cells and the measurement on the example of extracellular electric potential measurement. I will discuss the problems of inference from limited and imprecise measurements.

The lecture will be more popular than formal yet I will not shy away from mathematics. My main goal will be to inspire: show that biology in general and neuroscience in particular are great fields for a theoretician lending a wealth of interesting and difficult problems of practical and conceptual importance.