STP Statutory Public Lecture: 23 May 2019 – Prof Don Zagier
Speaker: Prof Don Zagier (Max Planck Institute, Bonn)
Title: Numbers, Knots, & Quantum Theory
Abstract: One of the most exciting developments in mathematics during the last 25 years has been the amazing strengthening of its ties with theoretical physics, with each domain inspiring the other with new insights and new problems. Particularly striking is that even on the mathematical side seemingly unrelated areas can turn out to have unexpected points in common that somehow arise from the underlying physics. In the lecture I will try to give a feeling for one or two of these connections, in particular a surprisingly deep result of number theory (a new construction of “algebraic units”) that was discovered and proved on the basis of purely experimental properties of certain quantum invariants of knots and that in its turn gave a proof of a conjecture of Werner Nahm that also related two apparently distant fields of pure mathematics and that itself was inspired from models in quantum field theory. If time permits, I will also discuss the resolution of the enigma of the famous “mock theta functions” of Ramanujan (described by him in a letter just before his death in 1920, but not defined properly until 2002) that turned out to be the key for understanding a quite different enigma in the string theory of black holes. These themes have recently turned out to be related to one another and are leading to a very exciting new direction in the theory of knots and 3-manifolds.
Date: Thursday 23 May 2019, 6pm.
Venue: Robert Emmet Theatre, Trinity College, Dublin.