Hauptseminar Geometrie

Prof. Dr. Chris Wendl, Humboldt-Universität zu Berlin

Everyone knows that you can't have transversality and symmetry at the same time. This basic fact causes headaches in many areas of geometry that depend on global analysis: e.g. in symplectic topology, it complicates the definitions of enumerative invariants such as Gromov-Witten theory, because multiple covers can prevent moduli spaces of J-holomorphic curves from being smooth objects of the "correct" dimension. The finite-dimensional analogue of this problem is in itself nontrivial, and amounts to the observation that for smooth maps respecting a finite group action, Sard's theorem typically does not hold equivariantly. In this talk, I will explain a fairly general strategy for recognizing the obstructions to equivariant transversality (or whatever the next best thing may be), and proving that transversality holds generically whenever those obstructions vanish. I will briefly sketch three applications: (1) genericity of Morse functions on orbifolds, (2) period-doubling bifurcations of periodic orbits, (3) super-rigidity for holomorphic curves in Calabi-Yau 3-folds.

Dienstag, den 14. Januar 2020 um 13.00-14.30 Uhr, in Mathematikon, INF 205, SR C Dienstag, den 14. Januar 2020 at 13.00-14.30, in Mathematikon, INF 205, SR C

Der Vortrag folgt der Einladung von The lecture takes place at invitation by Prof. Peter Albers