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UID:5d421924efb89a82dbb42a03a404bfc1
CATEGORIES:Symmetric Functions & Probability Theory Seminar
CREATED:20250123T202027
SUMMARY:Hyperdeterminantal total positivity
LOCATION:Hill 705
DESCRIPTION:<p dir="ltr" style="margin: 12px 0px 0px; outline: none; position: relative
 ; color: #212121; font-size: 11pt; font-style: normal; font-weight: 400; fo
 nt-family: Lato, sans-serif; line-height: 1.6667; letter-spacing: normal; o
 rphans: 2; text-align: start; text-indent: 0px; text-transform: none; widow
 s: 2; word-spacing: 0px; white-space: normal;"><span style="font-family: La
 to, Arial; font-variant: normal; font-weight: bold;">Speaker</span><span st
 yle="font-variant: normal;">:&nbsp;</span><a href="https://science.psu.edu/
 stat/people/dsr11" target="_blank" rel="noopener" style="color: inherit; te
 xt-decoration: none;"><span style="color: #006580; font-variant: normal; te
 xt-decoration: underline;">Donald Richards</span></a><span style="font-vari
 ant: normal;">&nbsp;(Penn State)&nbsp;</span></p><p dir="ltr" style="margin
 : 12px 0px 0px; outline: none; position: relative; color: #212121; font-siz
 e: 11pt; font-style: normal; font-weight: 400; font-family: Lato, sans-seri
 f; line-height: 1.6667; letter-spacing: normal; orphans: 2; text-align: sta
 rt; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; w
 hite-space: normal;"><span style="font-family: Lato, Arial; font-variant: n
 ormal; font-weight: bold;">Title</span><span style="font-variant: normal;">
 : Hyperdeterminantal total positivity</span></p><p dir="ltr" style="margin:
  12px 0px 0px; outline: none; position: relative; color: #212121; font-size
 : 11pt; font-style: normal; font-weight: 400; font-family: Lato, sans-serif
 ; line-height: 1.6667; letter-spacing: normal; orphans: 2; text-align: star
 t; text-indent: 0px; text-transform: none; widows: 2; word-spacing: 0px; wh
 ite-space: normal;"><span style="font-family: Lato, Arial; font-variant: no
 rmal; font-weight: bold;">Abstract</span><span style="font-variant: normal;
 ">:&nbsp;</span><span style="color: #242424; font-variant: normal;">This ta
 lk will cover some recent joint research with K. W. Johnson.&nbsp;</span></
 p><p dir="ltr" style="margin: 12px 0px 0px; outline: none; position: relati
 ve; color: #212121; font-size: 11pt; font-style: normal; font-weight: 400; 
 font-family: Lato, sans-serif; line-height: 1.6667; letter-spacing: normal;
  orphans: 2; text-align: start; text-indent: 0px; text-transform: none; wid
 ows: 2; word-spacing: 0px; white-space: normal;"><span style="color: #24242
 4; font-variant: normal;">Let m be a positive integer, and let K be real-va
 lued function defined on 2m-dimensional Euclidean space.&nbsp; We define th
 e concept of&nbsp;</span><span style="color: #242424; font-style: italic; f
 ont-variant: normal;">hyperdeterminantal total positivity</span><span style
 ="color: #242424; font-variant: normal;">&nbsp;for the kernel K, thereby ge
 neralizing the classical concept of total positivity. We construct examples
  of hyperdeterminantal totally positive kernels, extending in particular th
 e fundamental classical example, K(x,y) = exp(xy), x,y ∈ ℝ, of a totally po
 sitive kernel.&nbsp; By applying a hyperdeterminantal Binet-Cauchy argument
 , a generalization of Karlin's Basic Composition Formula is derived and the
 n applied to construct numerous additional examples of hyperdeterminantal t
 otally positive kernels.&nbsp; Further generalizations of the concept of hy
 perdeterminantal total positivity by means of the theory of finite reflecti
 on groups are described, and some open problems are posed.</span><span styl
 e="color: #000000; font-variant: normal;"></span></p>
CONTACT:Donald Richards
DTSTAMP:20260828T123507
DTSTART;TZID=America/New_York:20250129T104500
DTEND;TZID=America/New_York:20250129T234500
SEQUENCE:0
TRANSP:OPAQUE
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