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UID:59f5bdfa662fb6e829b21b67893a505f
CATEGORIES:Symmetric Functions & Probability Theory Seminar
CREATED:20250403T145432
SUMMARY:Differential Operators for Macdonald's Hypergeometric Functions
LOCATION:Hill 705
DESCRIPTION:<section id="h.6936e4438f6c6b5c_15" style="display: table; position: relati
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 dth: 100%; position: relative;"><span style="font-family: Lato, Arial; font
 -size: 11pt; font-variant: normal; font-weight: bold; vertical-align: basel
 ine;">Date</span><span style="font-size: 11pt; font-variant: normal; vertic
 al-align: baseline;">: 0</span><span style="font-size: 11pt; vertical-align
 : baseline;">4</span><span style="font-size: 11pt; font-variant: normal; ve
 rtical-align: baseline;">/0</span><span style="font-size: 11pt; vertical-al
 ign: baseline;">9</span><span style="font-size: 11pt; font-variant: normal;
  vertical-align: baseline;">/2025</span></div><p dir="ltr" style="margin: 1
 2px 0px 0px; outline: none; position: relative; text-decoration: inherit; c
 olor: #212121; font-size: 11pt; font-style: inherit; font-weight: 400; font
 -family: Lato, sans-serif; line-height: 1.6667;"><span style="font-family: 
 Lato, Arial; font-variant: normal; font-weight: bold;">Speaker</span><span 
 style="font-variant: normal;">:&nbsp;</span><a href="https://sites.math.rut
 gers.edu/~hc813/" target="_blank" rel="noopener" style="color: inherit; tex
 t-decoration: none;"><span style="color: #006580; text-decoration: underlin
 e;">Hong Chen</span></a><span style="font-variant: normal;">&nbsp;(Rutgers)
 </span></p><p dir="ltr" style="margin: 12px 0px 0px; outline: none; positio
 n: relative; text-decoration: inherit; color: #212121; font-size: 11pt; fon
 t-style: inherit; font-weight: 400; font-family: Lato, sans-serif; line-hei
 ght: 1.6667;"><span style="font-family: Lato, Arial; font-variant: normal; 
 font-weight: bold;">Title</span><span style="font-variant: normal;">:&nbsp;
 </span>Differential Operators for Macdonald's Hypergeometric Functions</p><
 p dir="ltr" style="margin: 12px 0px 0px; outline: none; position: relative;
  text-decoration: inherit; color: #212121; font-size: 11pt; font-style: inh
 erit; font-weight: 400; font-family: Lato, sans-serif; line-height: 1.6667;
  padding-bottom: 0px;"><span style="font-family: Lato, Arial; font-variant:
  normal; font-weight: bold;">Abstract</span><span style="font-variant: norm
 al;">:&nbsp;</span>In his widely circulated 1980s manuscript (now available
  as [<a href="https://arxiv.org/abs/1309.4568" target="_blank" rel="noopene
 r" style="color: inherit; text-decoration: none;"><span style="color: #0065
 80; text-decoration: underline;">arXiv:1309.4568</span></a>]), Macdonald in
 troduced hypergeometric functions with a parameter alpha (the Jack paramete
 r) and posed foundational questions about their properties. In this talk, I
  will present a general construction of differential operators pDq that cha
 racterize Macdonald’s hypergeometric functions pFq for arbitrary p and q. T
 hese operators generalize the ones studied by Constantine--Muirhead, Fujiko
 shi, and Macdonald.&nbsp;</p></div></div></div></div></div></div></div></di
 v></div></section><section id="h.6936e4438f6c6b5c_4" style="display: table;
  position: relative; table-layout: fixed; width: 1349.7px; padding-bottom: 
 0px; padding-top: 0px; color: #000000; font-family: sans-serif; font-size: 
 16px; font-style: normal; font-weight: 400; letter-spacing: normal; orphans
 : 2; text-align: start; text-indent: 0px; text-transform: none; widows: 2; 
 word-spacing: 0px; white-space: normal;"></section>
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 ve; table-layout: fixed; width: 1349.7px; padding-bottom: 1.5rem; padding-t
 op: 1.5rem; color: #000000; font-family: sans-serif; font-size: 16px; font-
 style: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-a
 lign: start; text-indent: 0px; text-transform: none; widows: 2; word-spacin
 g: 0px; white-space: normal;"><div style="display: table-cell; vertical-ali
 gn: middle; width: 1349.7px;"><div tabindex="-1" style="width: 1280px; marg
 in: 0px auto; max-width: 1280px; padding-left: 48px; padding-right: 48px; o
 utline: 0px;"><div style="display: inline-block; padding-left: 0px; padding
 -right: 0px; position: relative; vertical-align: top; width: 1184.02px;"><d
 iv style="padding-left: 14.7917px; padding-right: 14.7917px;"><div jscontro
 ller="sGwD4d" jsaction="https://math.rutgers.edu/zXBUYb:zTPCnb;zQF9Uc:Qxe3n
 d;" jsname="F57UId"><div style="width: 1154.43px; margin-top: 0px; margin-b
 ottom: 0px; max-width: 1280px;"><div id="h.6936e4438f6c6b5c_12" style="disp
 lay: inline-block; padding-left: 0px; padding-right: 0px; position: relativ
 e; vertical-align: top; width: 1154.43px;"><div style="width: 1154.43px;"><
 div style="position: relative; width: 1154.43px; padding: 8px;"><div jscont
 roller="Ae65rd" jsaction="https://math.rutgers.edu/touchstart:UrsOsc; click
 :KjsqPd; focusout:QZoaZ; mouseover:y0pDld; mouseout:dq0hvd;fv1Rjc:jbFSOd;Cr
 fLRd:SzACGe;" style="display: inline-block; max-width: 100%; position: rela
 tive;"><span style="font-family: Lato, Arial; font-size: 11pt; font-variant
 : normal; font-weight: bold; vertical-align: baseline;">Date</span><span st
 yle="font-size: 11pt; font-variant: normal; vertical-align: baseline;">: 0<
 /span><span style="font-size: 11pt; vertical-align: baseline;">4</span><spa
 n style="font-size: 11pt; font-variant: normal; vertical-align: baseline;">
 /0</span><span style="font-size: 11pt; vertical-align: baseline;">9</span><
 span style="font-size: 11pt; font-variant: normal; vertical-align: baseline
 ;">/2025</span></div><p dir="ltr" style="margin: 12px 0px 0px; outline: non
 e; position: relative; text-decoration: inherit; color: #212121; font-size:
  11pt; font-style: inherit; font-weight: 400; font-family: Lato, sans-serif
 ; line-height: 1.6667;"><span style="font-family: Lato, Arial; font-variant
 : normal; font-weight: bold;">Speaker</span><span style="font-variant: norm
 al;">:&nbsp;</span><a href="https://sites.math.rutgers.edu/~hc813/" target=
 "_blank" rel="noopener" style="color: inherit; text-decoration: none;"><spa
 n style="color: #006580; text-decoration: underline;">Hong Chen</span></a><
 span style="font-variant: normal;">&nbsp;(Rutgers)</span></p><p dir="ltr" s
 tyle="margin: 12px 0px 0px; outline: none; position: relative; text-decorat
 ion: inherit; color: #212121; font-size: 11pt; font-style: inherit; font-we
 ight: 400; font-family: Lato, sans-serif; line-height: 1.6667;"><span style
 ="font-family: Lato, Arial; font-variant: normal; font-weight: bold;">Title
 </span><span style="font-variant: normal;">:&nbsp;</span>Differential Opera
 tors for Macdonald's Hypergeometric Functions</p><p dir="ltr" style="margin
 : 12px 0px 0px; outline: none; position: relative; text-decoration: inherit
 ; color: #212121; font-size: 11pt; font-style: inherit; font-weight: 400; f
 ont-family: Lato, sans-serif; line-height: 1.6667; padding-bottom: 0px;"><s
 pan style="font-family: Lato, Arial; font-variant: normal; font-weight: bol
 d;">Abstract</span><span style="font-variant: normal;">:&nbsp;</span>In his
  widely circulated 1980s manuscript (now available as [<a href="https://arx
 iv.org/abs/1309.4568" target="_blank" rel="noopener" style="color: inherit;
  text-decoration: none;"><span style="color: #006580; text-decoration: unde
 rline;">arXiv:1309.4568</span></a>]), Macdonald introduced hypergeometric f
 unctions with a parameter alpha (the Jack parameter) and posed foundational
  questions about their properties. In this talk, I will present a general c
 onstruction of differential operators pDq that characterize Macdonald’s hyp
 ergeometric functions pFq for arbitrary p and q. These operators generalize
  the ones studied by Constantine--Muirhead, Fujikoshi, and Macdonald.&nbsp;
 </p></div></div></div></div></div></div></div></div></div></section><sectio
 n id="h.6936e4438f6c6b5c_4" style="display: table; position: relative; tabl
 e-layout: fixed; width: 1349.7px; padding-bottom: 0px; padding-top: 0px; co
 lor: #000000; font-family: sans-serif; font-size: 16px; font-style: normal;
  font-weight: 400; letter-spacing: normal; orphans: 2; text-align: start; t
 ext-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; white-
 space: normal;"></section>
CONTACT:Hong Chen
DTSTAMP:20260829T164804
DTSTART;TZID=America/New_York:20250409T104500
DTEND;TZID=America/New_York:20250409T234500
SEQUENCE:0
TRANSP:OPAQUE
END:VEVENT
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