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DTSTART:20260308T070000
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DTSTART:20251102T060000
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DTSTART;TZID=America/Toronto:20260505T143000
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URL:https://uwaterloo.ca/combinatorics-and-optimization/events/algebraic-an
 d-enumerative-combinatorics-seminar-siddhartha
SUMMARY:Algebraic and Enumerative combinatorics seminar - Siddhartha\nSahi-
 Hypergeometric functions of matrix argument
CLASS:PUBLIC
DESCRIPTION:SPEAKER:\n Siddhartha Sahi\n\nAFFILIATION:\n Rutgers University
 \n\nLOCATION:\n MC 6029\n\nABSTRACT:In a widely circulated manuscript from
  the 1990s\, I.G.\nMacdonald introduced certain higher-rank analogs of the
  classical\nhypergeometric functions $_pF_q$\, which are expressed as expl
 icit\nseries in Jack and Macdonald polynomials in one and two sets of\nvar
 iables. For special choices of parameters\, these series reduce to\nthe hy
 pergeometric functions of matrix argument introduced earlier by\nC. Herz a
 nd A.T. James\, which have numerous applications in number\ntheory\, multi
 variate statistics\, signal processing\, and random matrix\ntheory.\n\nThe
  classical hypergeometric functions are solutions to the\nhypergeometric d
 ifferential equation. Macdonald raised the problem of\nproviding an analog
 ous characterization for higher-rank functions by\nmeans of differential e
 quations. Over the years\, this problem was\nsolved for a small number of 
 cases where p and q are at most 3.\nHowever\, as the operators become incr
 easingly complicated\, the general\nproblem remained open for 40 years. In
  this talk\, we will present a\ncomplete solution. This is joint work with
  Hong Chen.\n\nTHERE WILL BE A PRE-SEMINAR AT 1:30PM IN MC 6029 IN A FLIPP
 ED\nCLASSROOM FORMAT BASED ON MACDONALD’S MANUSCRIPT ON HYPERGEOMETRIC\n
 FUNCTIONS (HTTPS://ARXIV.ORG/ABS/1309.4568\n[https://arxiv.org/abs/1309.45
 68]). PARTICIPANTS ARE EXPECTED TO READ\nTHE MANUSCRIPT IN ADVANCE\, AND T
 HE SESSION WILL FOCUS ON QUESTIONS AND\nDISCUSSION LED BY THE SPEAKER.
DTSTAMP:20260604T125446Z
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