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