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SUMMARY:Embedding structures with distortion - Dr András Zsak
DTSTART:20220310T180000Z
DTEND:20220310T190000Z
UID:TALK171512@talks.cam.ac.uk
CONTACT:Gesa Dünnweber
DESCRIPTION:There is a wide variety of structures that are equipped with a
  distance.  A familiar example from school mathematics is three-dimensiona
 l Euclidean space: here the distance is the length of the straight line se
 gment joining two points which can be computed using Pythagoras's theorem.
  One might also be interested in the distance between fingerprints: a poli
 ce investigation might look for fingerprints whose distance is small to a 
 given one thereby narrowing down the list of potential suspects. In Biolog
 y one might wish to measure evolutionary distance between species.\n\nSome
  of these structures have additional features. For example in Euclidean sp
 ace there is vector addition and scalar multiplication. There is a recent\
 , very active and beautiful area of mathematics that at its core is concer
 ned with the following question. Given an arbitrary structure with a dista
 nce\, can we embed this in some way into another structure with a distance
  which has an additional vector structure like Euclidean space. Positive s
 olutions to such questions have consequences for large data\, algorithms\,
  compressed sensing\, etc. From a pure mathematics point of view what is p
 articularly attractive about this field is the meeting and interaction of 
 many different branches of mathematics: analysis\, probability\, geometry\
 , combinatorics\, etc.\n\nIn this talk we will explore the mathematics and
  some of the applications of this field. We will also cover some specific 
 problems and even give some proofs. Much of this should be accessible to P
 art IA students.
LOCATION:CMS Meeting Room 2
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