The next geometry seminar will be given by Sonja Hohloch (Antwerp). The talk will take place at 1.30pm on 30th May, in the Salle de Profs on the 9th floor of building NO. Sonja’s title is *“Hyperkähler Floer homology”* and her abstract is below.

Classical Floer homology was devised in order to estimate the number of nondegenerate 1-periodic Hamiltonian solutions on compact manifolds. The construction relies heavily on the analysis of so-called pseudo-holomorphic curves, solutions of a generalized Cauchy-Riemann equation.

Hyperkähler Floer homology estimates the number of nondegenerate solutions of a certain `triholomorphic’ equation. Hereby the L^2 gradient flow is simulated by the so-called Cauchy-Riemann-Fueter equation. Hyperkähler Floer homology was developed by myself together with G. Noetzel and D. Salamon.

We will sketch the construction of hyperkähler Floer homology, prove the so-called hyperkähler Arnold conjecture on flat compact hyperkähler manifolds, and explain (if there is time left) how one can reformulate the triholomorphic equation as a Hamiltonian system on the iterated loop space.