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SUMMARY:Dr. Nobuo Sato (National Taiwan University)
DTSTART:20240508T060000Z
DTEND:20240508T070000Z
DTSTAMP:20260423T052955Z
UID:MAC8028/30
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAC8028/30/"
 >Iterated beta integrals</a>\nby Dr. Nobuo Sato (National Taiwan Universit
 y) as part of Trends in Mathematical Research\n\nLecture held in NTNU Gong
 guan S101.\n\nAbstract\nI will explain my recent work on iterated beta int
 egrals with Minoru Hirose at Nagoya University. Iterated beta integrals ar
 e a type of iterated integrals on branched universal abelian coverings of 
 the projective line\, which commonly generalize hyperlogarithms and beta i
 ntegrals. In addition to the properties that generalize those of hyperloga
 rithms and beta integrals\, iterated beta integrals enjoy a new property t
 hat we call translation invariance. The translation invariance yields equa
 lities between iterated integrals on translation-equivalent coverings of t
 he projective line\, and especially for genus-zero pair of translation-equ
 ivalent coverings\, it yields non-trivial equalities between special value
 s of hyperlogarithms. Such equalities include the famous 2-3-2 formula for
  multiple zeta values proved by Zagier\, its analog for multiple t-values\
 , the 2-1 formula for multiple zeta star values\, and various other formul
 as of a similar kind. By classifying all genus-zero pairs\, some new inter
 esting cases popped up\, one of which resolves a conjecture by Charlton co
 ncerning the area of a family of Lawson surfaces.\n
LOCATION:https://researchseminars.org/talk/MAC8028/30/
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