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On the continuity of the Loewner Map

Date: Tuesday, November 20, 2018 15:30 - 16:30
Speaker: Atul Shekhar (KTH)
Location: Uni Wien BZ 2, 2. OG., OMP 1
Series: Mathematics and CS Seminar
Host: M. Beiglböck, N. Berestycki, L. Erdös, J. Maas
Contact: Uni Wien

One of the central problem in the theory of Loewner chains is to give a complete understanding of the existence of trace and continuity of the Loewner map which maps the driving function to its trace.  We will present some new results dealing with finite energy drivers, bounded variation drivers and 1/2-Holder drivers. In the random case, we will show a smoothing effect of the presence of noise on the boundary behaviour of the associated conformal maps. These results are motivated by rough path theory and we will make a connection of the trace problem to the well understood continuity of the Ito-Lyons map.

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