Math department seminar: Dr. Kira Adaricheva

Dr. Kira Adaricheva (Hofstra University) will be giving the math department's first seminar for Fall 2020 on Friday, September 4 at 3:30 p.m.

Title: Convex geometries representable by at most 5 circles on the plane

Abstract: In a unique project led by Adam Sheffer from Baruch College (NYC), 8 mathematicians from universities across the US worked with about 300 undergraduate students from around the world in 12 research projects in PolyMath style, during two months of summer 2020.

One of the projects guided by Kira Adaricheva (Hofstra University) and involving 20 students investigated the open question of whether there exists a convex geometry (a closure system with anti-exchange axiom) on a 5-element set that has convex dimension less than 6 and is not representable by circles on the plane, an open question from a publication in Discrete Mathematics in 2019.

The question was answered in the positive because several geometries that do not have representation were found with convex dimensions = 4 and 5. Moreover, all 672 geometries on a 5-element set were either represented by circles on the plane or classified into one of possible non-representable class.

It was also proved that one of these classes comprising 7 geometries was not representable due to the Triangle Property. The results of this project will appear on the arXiv in September.  

 

Please contact johanna.n.franklin@hofstra.edu for the zoom link.

Friday, September 04, 2020

Cost:

free

Categories:

Location:

Zoom
Zoom Link
Online, NY 00000


Contact:

Johanna Franklin

Phone: (516) 463-5739

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