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SUMMARY:Notions of entropy in ergodic theory and representation theory - T
 im Austin (Warwick)
DTSTART:20250501T150000Z
DTEND:20250501T160000Z
UID:TALK223906@talks.cam.ac.uk
CONTACT:HoD Secretary\, DPMMS
DESCRIPTION:Entropy has its origins in thermodynamics and statistical mech
 anics.  It was explored with mathematical rigour in Shannon's work on the 
 foundations of information theory\, and quickly found striking application
 s to ergodic theory in work of Kolmogorov and Sinai. Many variants and oth
 er applications have appeared in pure mathematics since\, connecting proba
 bility\, combinatorics\, dynamics and other areas.\n\n \n\nI will survey a
  few recent developments in this story\, with an emphasis on some of the b
 asic ideas that they have in common.  I will focus mostly on (i) Lewis Bow
 en's "sofic entropy"\, which helps us to study the dynamics of "large" gro
 ups such as free groups\, and (ii) a cousin of sofic entropy in the world 
 of unitary representations\, which leads to new large deviations principle
 s for tuples of random matrices.\n\nA wine reception in the Central Core w
 ill follow the lecture. 
LOCATION:MR2\, CMS
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