»ã±¨±êÌâ (Title)£ºBorsuk¡¯s Partition Problem, Hadwiger¡¯s Covering Conjecutre, and the Boltyanski-Gohberg Conjecture

ÖÐÎıêÌ⣺Borsuk µÄ·ÖÇøÎÊÌâ¡¢Hadwiger µÄ¸²¸Ç²Â²â ºÍ Boltyanski-Gohberg ²Â²â

»ã±¨ÈË (Speaker)£º×Ú´«Ã÷£¨Ìì½ò´óѧ£©

»ã±¨¹¦·ò (Time)£º2023Äê12ÔÂ15ÈÕ(ÖÜÎå) 10:00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿GJ303

Ô¼ÇëÈË(Inviter)£ºÏ¯¶«ÃË¡¢Àî½ú¡¢Õŵ¿­

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»ã±¨ÌáÒª£ºIn 1933, K. Borsuk proposed the following problem: Can every bounded set in the n-dimensional Euclidean space be divided into n + 1 subsets of smaller diameters? In 1957, H. Hadwiger made the following conjecture: Every n-dimensional convex body K can be covered by 2 n translates of its interior int(K). In 1965, V. G. Boltyanski and I. T.Gohberg made the following conjecture: Every bounded set in an n-dimensional normed space can be divided into 2 n subsets of smaller diameters. These problems are closely related. Up to now, all of them are far away from being completely solved. In this talk, we will introduce a computer approach to these problems. In particular, we will show an asymptotic solution to the Boltyanski-Gohberg conjecture.