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Chun-Hung Liu (劉俊宏), Asymptotic dimension of minor-closed families and beyond

October 22 Thursday @ 10:10 AM - 11:10 AM KST

Zoom ID:95464969835 (356260)

The asymptotic dimension of metric spaces is an important notion in  geometric group theory. The metric spaces considered in this talk are  the ones whose underlying spaces are the vertex-sets of (edge-)weighted  graphs and whose metrics are the distance functions in weighted graphs.  A standard compactness argument shows that it suffices to consider the  asymptotic dimension of classes of finite weighted graphs. We prove that  the asymptotic dimension of any minor-closed family of weighted graphs,  any class of weighted graphs of bounded tree-width, and any class of  graphs of bounded layered tree-width are at most 2, 1, and 2,  respectively. The first result solves a question of Fujiwara and  Papasoglu; the second and third results solve a number of questions of  Bonamy, Bousquet, Esperet, Groenland, Pirot and Scott. These bounds for  asymptotic dimension are optimal and generalize and improve some results  in the literature, including results for Riemannian surfaces and Cayley  graphs of groups with a forbidden minor.

Details

Date:
October 22 Thursday
Time:
10:10 AM - 11:10 AM KST
Event Category:
Event Tags:

Venue

Zoom ID:95464969835 (356260)

Organizer

O-joung Kwon (권오정)
IBS 이산수학그룹 Discrete Mathematics Group
기초과학연구원 수리및계산과학연구단 이산수학그룹
대전 유성구 엑스포로 55 (우) 34126
IBS Discrete Mathematics Group (DIMAG)
Institute for Basic Science (IBS)
55 Expo-ro Yuseong-gu Daejeon 34126 South Korea
E-mail: dimag@ibs.re.kr, Fax: +82-42-878-9209
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