Our lab uses mathematical models of synapses, neurons and networks to explain aspects of perception and behaviour. We consider models for the cortical pyramidal neurons and micro-circuitries which are being experimentally investigated in vivo and in vitro at our Department (Enhanced dendritic activity in awake rats). A further interest is the neuronal substrate of learning and memory. One question we are addressing is how state-action sequences can be learned from an ongoing stream of synaptic inputs and a single delayed feedback signal (Dendritic encoding of sensory stimuli controlled by deep cortical interneurons). We also develop models of sensory processing and its interaction with cortical top-down signals. These explain experimental recordings from the visual cortex obtained while solving perceptual or classification tasks (Perceptual Learning via Modification of Cortical Top-Down Signals), (Modulating the granularity of category formation by global cortical states). Our models try to highlight some key mechanisms by which the interaction of synapses and neurons enables our brains to deal with everyday tasks.