Events
04. December 2025, 16:00 until 18:00
VSO Seminar: Polar Convexity in Finite Dimensional Euclidean Spaces (Part 1)
Seminar
Let ˆRn be the one point compactification of Rn obtained by adding a point at infinity. We say that a subset A ⊆ ˆRn is u-convex if for every pair of points z1, z2 ∈ A, the arc ofthe unique circle through u, z1 and z2, from z1 to z2 and not containing u, is contained in A. In this case, we call u a pole of A. When the pole u approaches infinity, u-convex sets become convex in the classical sense.
The notion of polar convexity in the complex plane has been used to analyze the behavior of critical points of polynomials.
In this talk, we extend the notion to finite dimensional Euclidean spaces. The goal of this work is to start building the theory of polar convexity and to show that the introduction of a pole creates a richer theory. For example, polar convexity enjoys a beautiful duality that does not exist in classical convexity. We formulate polar analogues of several classical results of the alternatives, such as Gordon and Farkas lemmas. Finally, we give a full description of the convex hull of finitely many points with respect to finitely many poles.
This is a joint work with Shubhankar Bhatt from the Department of Mathematics, The University of Western Ontario, Canada
Event details
- Event location
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Sem. R. DB gelb 04
1040 Wien
Wiedner Hauptstraße 8 E105-4 - Organiser
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VADOR
vador@tuwien.ac.at - Public
- No
- Entrance fee
- No
- Registration required
- No