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UID:0a74b4657727025943a0742fe2a0c2bf
CATEGORIES:Topology/Geometry Seminar
CREATED:20240913T152930
SUMMARY:Solving the word problem in the mapping class group in quasi-linear time
LOCATION:Hill 705
DESCRIPTION:<p style="margin: 15px 0px 0px; outline: none; position: relative; color: #
 3d3d3d; font-size: 13pt; font-weight: 400; font-family: 'Open Sans'; line-h
 eight: 1.6; letter-spacing: normal; orphans: 2; text-align: start; text-ind
 ent: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-space: 
 normal;">Abstract:&nbsp;Mapping class groups of surfaces are of fundamental
  importance in dynamics, geometric group theory, and low-dimensional topolo
 gy.&nbsp; The word problem for groups in general, the definition of the map
 ping class group, its finite generation by twists, and the solution to its 
 word problem were all set out by Dehn [1911, 1922, 1938].&nbsp; Some of thi
 s material was rediscovered by Lickorish [1960's] and then by Thurston [197
 0-80's] -- they gave important applications of the mapping class group to t
 he topology and geometry of three-manifolds.&nbsp; In the past fifty years,
  various mathematicians (including Penner, Mosher, Hamidi-Tehrani, Dylan Th
 urston, Dynnikov) have given solutions to the word problem in the mapping c
 lass group, using a variety of techniques.&nbsp; All of these algorithms ar
 e quadratic-time.</p><p style="margin: 15px 0px 0px; outline: none; positio
 n: relative; color: #3d3d3d; font-size: 13pt; font-weight: 400; font-family
 : 'Open Sans'; line-height: 1.6; letter-spacing: normal; orphans: 2; text-a
 lign: start; text-indent: 0px; text-transform: none; widows: 2; word-spacin
 g: 0px; white-space: normal;">We give an algorithm requiring only $O(n log^
 3(n))$ time. We do this by combining Dynnikov's approach to curves on surfa
 ces, M"oller's version of the half-GCD algorithm, and a delicate error anal
 ysis in interval arithmetic.</p><p style="margin: 15px 0px 0px; outline: no
 ne; position: relative; color: #3d3d3d; font-size: 13pt; font-weight: 400; 
 font-family: 'Open Sans'; line-height: 1.6; letter-spacing: normal; orphans
 : 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; 
 word-spacing: 0px; white-space: normal;">This is joint work with Mark Bell.
 </p>
CONTACT:Saul Schleimer, University of Warwick
DTSTAMP:20260827T103136
DTSTART;TZID=America/New_York:20240917T160000
DTEND;TZID=America/New_York:20240917T170000
SEQUENCE:0
TRANSP:OPAQUE
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