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Miruna-Stefana Sorea, Max-Planck-Institut für Mathematik in den Naturwissenschaften, The shapes of level curves of real polynomials near strict local minima

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September 16 | 2:00 pm - 3:00 pm EDT

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We consider a real bivariate polynomial function vanishing at the origin and exhibiting a strict local minimum at this point. We work in a neighbourhood of the origin in which the non-zero level curves of this function are smooth Jordan curves. Whenever the origin is a Morse critical point, the sufficiently small levels become boundaries of convex disks. Otherwise, these level curves may fail to be convex. The aim of this talk is two-fold. Firstly, to study a combinatorial object measuring this non-convexity; it is a planar rooted tree. And secondly, we want to characterise all possible topological types of these objects. To this end, we construct a family of polynomial functions with non-Morse strict local minima realising a large class of such trees.
Host: Irina Kogan iakogan@math.ncsu.edu
Instructions to join: Zoom invitation is sent to the geometry and topology seminar list. If you are not on the list, please, contact the host to get the link.



September 16

2:00 pm - 3:00 pm
Event Category: