This special ICTP QLS Colloquium will be given by Prof. Tatyana Sharpee. The talk on Hyperbolic geometry and symmetry breaking in neural circuits will take place in the Euler Lecture Hall, on Friday 1 March 2019 at 11.00 hrs and will be followed by light refreshments. Prof. Sharpee received her MSc degree in Theoretical Physics from Ukraine National University, Kiev, Ukraine and a Ph.D. in Theoretical Physics form Michigan State University. She turned from Condensed Matter physics to neuroscience early on in her career, first at UC San Francisco, then at UC San Diego and lately at Salk Institute where she is Associate Professor. Prof. Sharpee has been elected Fellow of the American Physical Society for "advancing our understanding of how neurons represent sensory signals and make decisions". Sharpee's work aims to develop a unifying theory of how biological systems process information. Specifically, she is uncovering how animals sense and adapt to their environment, as well as make predictions and decisions. To do this, she applies methods from physics, mathematics and information theory to chart the principles by which the brain's billions of neurons exchange energy and information. Abstract: A long standing idea in neuroscience is that the brain is adapted to the statistics of signals from the natural environment, and in some cases, as in the sense of smell, the brain and the natural environment have co-evolved together. I will first discuss how hyperbolic geometry can help provide coordinates for natural odors that offers insights into how we perceive smells. Then, I will briefly summarize our progress in mapping the hierarchy of transformations for visual signals in the brain. Finally, I will discuss how symmetry breaking and ideas from the theory of phase transitions can help systematize complexity of cell types that together provide accurate analogue representations of incoming signals using binary outputs. I will conclude with applications of these ideas to biological problems outside of neuroscience.