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DESCRIPTION:Todd Kemp (UCSD)\n\nTitle: Random Matrices\, Heat Flow\, and Li
 e Groups\n\n\nAbstract: Random matrix theory studies the behavior of the ei
 genvalues and eigenvectors of random matrices as the dimension grows.   In 
 the age of data science\, it has become one of the hottest fields in probab
 ility theory and many parts of applied science\, from material deposition t
 o wireless communication. Initiated by Wigner in the 1950s (with some key r
 esults going back further to Wishart and other statisticians in the 1920s)\
 , there is now a rich and well-developed theory of the universal behavior o
 f random spectral statistics in models that are natural generalizations of 
 the Gaussian case. \n\nIn this talk\, I will discuss a generalization of th
 ese kinds of results in a new direction. A Gaussian random matrix can be th
 ought of as an instance of Brownian motion on a Lie algebra\; this opens th
 e door to studying the eigenvalues of Brownian motion on Lie groups. I will
  present recent progress understanding the asymptotic spectral distribution
  of Brownian motion on unitary groups and general linear groups.  The tools
  needed include probability theory\, functional analysis\, combinatorics\, 
 and representation theory.  No technical background is required\; only an i
 nterest in trying to understand some cool and mysterious pictures.
DTEND:20180427T213000Z
DTSTAMP:20260411T015355Z
DTSTART:20180427T203000Z
GEO:41.92421;-87.654991
LOCATION:Levan Center\, 201
SEQUENCE:0
SUMMARY:Math Department Colloquium
UID:tag:localist.com\,2008:EventInstance_3490585
URL:https://events.depaul.edu/event/math_department_colloquium_2476
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