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Christian Pauly University Nice Sophia-Antipolis, France

„ Symmetry: a journey from the golden ratio to quantum field theories“

The guiding theme of this colloquium talk is the notion of symmetry in mathematics. Starting from elementary considerations of the Ancient Greeks, I will continue with a quick introduction to some enumerative problems in modern mathematics, mainly of geometrical nature, and show how ideas from physics, mainly quantum field theories, have lead to surprising solutions. I focus on two particular examples reflecting the fruitful interaction between geometry and physics : Kontsevich's formula for counting rational plane curves and the Verlinde formula computing topological invariants of moduli spaces. I will make special efforts to unravel the mathematical complexity of these notions. The talk is intended for a broad audience including non-mathematicians.