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SUMMARY:The least perimeter partition of a disc - Wang Chen (Aberystwyth U
 niversity)
DTSTART:20230823T110000Z
DTEND:20230823T113000Z
UID:TALK204046@talks.cam.ac.uk
DESCRIPTION:We study the problem of partitioning a disc into N connected r
 egions with two different areas while minimizing the perimeter. This becom
 es progressively more challenging as N increases due to the combinatorial 
 increase in possible configurations. To address this issue\, we propose an
  approach based on minima of a system of particles interacting via a poten
 tial function. These act as seed points for a Voronoi diagram\, which give
 s appropriate topologies for the minimum perimeter\, which are then evalua
 ted using the Surface Evolver software. Our preliminary results indicate t
 hat this method accurately reproduces all existing conjectured candidates 
 for N &le\; 10\, while reducing computational resources. Moreover\, we ext
 end our findings by predicting potential candidate solutions for the least
  perimeter partition of a disc for N > 10.
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