BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Junior Geometry Seminar
SUMMARY:On Banachâ€™s isometric subspaces problem - Daniil M
amaev\, PDMI RAS and LSGNT
DTSTART;TZID=Europe/London:20230524T160000
DTEND;TZID=Europe/London:20230524T170000
UID:TALK201628AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/201628
DESCRIPTION:Is a normed vector space V whose n-dimensional lin
ear subspaces are all isometric\, for a fixed 2 <=
n < dim V\, necessarily Euclidean? This question
was asked in 1932 by S. Banach and in the known ca
ses the answer is always affirmative. In a joint w
ork with S. Ivanov and A. Nordskova we handle `the
smallest' previously unresolved case n = 3\, but
the problem remains open for n + 1 = dim V = 4k >=
8 and n + 1= dim V = 134. \n\nI will start by for
mulating the problem in a couple equivalent ways\,
then give an overview of previous partial results
\, and proceed by sketching the proof in the case
n = 3. If time permits\, I will also discuss the l
ocal (stronger) version of the problem and its app
lication to Finsler geometry.
LOCATION:MR13
CONTACT:
END:VEVENT
END:VCALENDAR