**abstract:**
On a Riemannian manifold, two real-valued functions are conjugate if their gradients are everywhere orthogonal and of the same length. One may ask the question as to whether there are a set of equations that a function must satisfy in order that it admit a conjugate. In dimension 2 the answer is well-known: it is necessary and sufficient that the function be harmonic. In joint work with M. G. Eastwood, we explore this question in dimension 3. The solution turns out to be far from obvious and involves various conformally invariant differential conditions.

Tue 21 Feb, 9:00 - 10:00, Aula Dini

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