The Southeast Geometry Seminar (SGS) is a semiannual series of one day event sponsored by:
This year we will have two new features:
Abstract: I will talk on some recent results in collaboration with I. Rodnianski. The results simplify and generalize the recent breakthrough of D. Christodoulou concerning the formation of trapped surfaces in general relativity.
Abstract: We consider a system of three surfaces, graphs over a bounded domain in ℝ2 , intersecting along a time-dependent curve and moving by mean curvature while preserving the pairwise angles at the curve of intersection (equal to 2π/3.) This deffines a two-dimensional parabolic free boundary problem, for which we prove short-time existence of classical solutions (for sufficiently regular initial data satisfying a compatibility condition). For the corresponding symmetric problem (a graph over a time-dependent domain intersecting ℝn at a constant angle and moving by mean curvature) there are also results on long-time behavior.
Abstract: We consider a spatially homogeneous and isotropic system of Dirac particles coupled to classical gravity. We find a mechanism where quantum oscillations of the Dirac wave functions can prevent the formation of the big bang or big crunch singularity.