Tiltrædelsesforelæsning ved professor Henrik Pedersen
15.12.2022 kl. 14.00 - 15.00
About Exhuming a Mathematician after Twenty Years as Dean
In this talk I will explain where in mathematics I come from and where I want to go. The talk will not be very technical but is rather meant for a broad audience of mathematicians.
I shall begin by discussing how one can encode elements of differential geometry into holomorphic form and then rely on geometry and the constrains of the Cauchy-Riemann equations to solve problems in the intersection of differential geometry and mathematical physics.
I shall touch upon minimal surfaces, the Einstein equations in Riemann geometry and Einstein Weyl geometry. Guided by holomorphic geometry I shall present how any self-dual Einstein metric with nonzero scalar curvature and two symmetries can be given by a solution to a linear equation on the upper half plane.
Introducing a hyperkähler manifold, which also solves the Einstein equation, leads me to discuss geometric quantization, which is what I want to study in the coming years. Indeed, a hyperkähler manifold has a symplectic form which is the first step in the quantization scheme. In fact, there is a whole family of symplectic forms parametrized by a sphere. Picking one automatically gives a complex polarization due to the Kähler condition and thus we get a second ingredient for quantization. Come December 15, I may still be struggling to understand what happens next.
Department of Mathematical Sciences
Skjernvej 4A room 5.034