Research Interests

I am interested in geometric analysis, specifically in the use of Cauchy-Riemann type equations to study 3 and 4 manifolds. Previously I have shown how to define well behaved moduli spaces of J-holomorphic maps into folded symplectic 4-manifolds with circle invariant folds. This extends the tool of J-holomorphic curves beyond the category of symplectic manifolds and includes cases of manifolds that are not even pre-symplectic. In examples I have shown that these moduli spaces are compact, and I am currently working on a general compactness statement for the moduli space in order to obtain folded symplectic invariants.

Parts of this program have considerable overlap with Symplectic Field Theory, Contact Homology, and recent efforts to prove the Weinstein conjecture. This is still a rapidly developing field with many interesting questions and applications.

Selected Publications

• von Bergmann, Jens, Pseudoholomorphic maps into folded symplectic four-manifolds, Geometry & Topology, 11, 2007, 1--45.
• von Bergmann, Jens and von Bergmann, HsingChi, Foucault pendulum through basic geometry, American Journal of Physics, 2007, 75, 10, 888-892.