Oberseminar Geometrie, Topologie und Analysis

H. Geiges, G. Marinescu, S. Sabatini, D. V. Vu

Sommersemester 2023

Freitag, 10:30-11:30, Seminarraum 2 (Raum 204)

14./15.4.23 Geometric Dynamics Days in Dortmund

28.4.23 Joint Seminar on Complex Algebraic Geometry and Complex Analysis in Bochum

5.5.23 Niels Martin Møller (Kopenhagen)
Uniqueness theorems for collapsed simply connected translating solitons

Abstract: We consider self-translating solitons for the mean curvature flow of complete embedded 2-surfaces of finite genus and finite entropy. Under a natural collapsedness condition - amounting to the confinement into slabs of 3-space - we will discuss a couple of recent uniqueness/rigidity theorems. Firstly, in joint work with E.S. Gama and F. Martín, we recently used Morse theory for minimal surfaces a la Radó to obtain classifications of simply connected translating solitons of low entropy. Then, in very recent joint work with D. Impera and M. Rimoldi, we characterize the grim reaper cylinder as unique within the class of all width pi translaters which are bounded from below, with no further assumptions on topology or curvature.
12.5.23 Steven Sivek (Imperial College, z.Zt. MPI Bonn)
Floer homology and non-fibered knot detection

Abstract: Floer homology can tell whether a knot is fibered, and this has led to proofs that both knot Floer homology and Khovanov homology can positively identify a small handful of knots, including the unknot, the trefoils and the figure eight, and the cinquefoil. In this talk, I'll discuss recent work with John Baldwin in which we show for the first time that both invariants can also detect non-fibered knots, including 52, and that HOMFLY homology detects infinitely many knots. The key input is a classification of genus-1 knots which are "nearly fibered" from the perspective of knot Floer homology.
16.6.23 BACH Seminar in Bochum

H. Geiges, 23.2.23