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UID:20250716T154926EDT-3488NNFTV7@132.216.98.100
DTSTAMP:20250716T194926Z
DESCRIPTION:Macdonald polynomials\, diffusivity\, and Kerov conjecture.\n\n
 Pioneers of the study of totally positive (all minors non-negative) matric
 es\, Krein\, Schoenberg\, Karlin\, were motivated by analytic questions\, 
 but the topic has later percolated to the domain of representation theory 
 and algebraic combinatorics. This talk is about one story illustrating thi
 s interplay of algebra and analysis. In 1952 Edrei et al. used Nevanlinna 
 theory to prove the classification of the totally positive infinite upper 
 triangular Toeplitz matrices. In 1960s-1980s this problem was connected to
  the representation theory of the infinite symmetric group by Thoma\, Vers
 hik\, Kerov. In 1992 Kerov has conjectured a generalization of this theore
 m based on the notion of Macdonald polynomials. Over the years several spe
 cial cases related to different representation-theoretic settings were pro
 ved. I will talk about a recent proof of the general case\, that required 
 a new approach. One of the key difficulties was to find a replacement of t
 he Nevanlinna theory argument. The new argument is based on certain diffus
 ivity on the branching graph of Macdonald polynomials.\n
DTSTART:20180223T190000Z
DTEND:20180223T200000Z
LOCATION:Room VCH-3830\, CA\, Université Laval
SUMMARY:Konstantin Matveev\, Brandeis University
URL:/mathstat/channels/event/konstantin-matveev-brande
 is-university-285190
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