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BEGIN:VEVENT
SUMMARY:Ling Long (Louisiana State University)
DTSTART;VALUE=DATE-TIME:20210629T140000Z
DTEND;VALUE=DATE-TIME:20210629T160000Z
DTSTAMP;VALUE=DATE-TIME:20230208T072311Z
UID:HypergeometricSeries/1
DESCRIPTION:Title: Hypergeometric Functions\, Character Sums and Applications\nby Ling Long (Louisiana State University) as part of A Lecture Series o
n Hypergeometric Series\n\n\nAbstract\nHypergeometric functions form a cla
ss of special functions satisfying a lot of symmetries. They are closely r
elated to the arithmetic of one-parameter families of algebraic varieties\
, such as the Legendre curves. $p$-adic hypergeometric functions were inve
stigated by Dwork leading to his fundamental unit root theory. Hypergeome
tric functions over finite fields were initiated by Katz and Greene\, furt
her developments were made in recent years by many authors.\n\nIn the prop
osed mini course\, we will explore hypergeometric functions over different
settings. Applications of the combined perspectives include obtaining cha
racter sum identities\, computing special L-values of modular forms\, fin
ding and proving supercongruences (influenced by important conjectures of
Buekers\, van Hamme\, Rodridguez-Villegas\, Roberts and Rodridguez-Villeg
as\, constructing decomposable Galois representations\, and computing ari
thmetic invariance of certain abelian varieties.\n\nThe mini-course will c
onsist of 4 lectures\, each 90-minute with a short break in the middle.\n
LOCATION:https://researchseminars.org/talk/HypergeometricSeries/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ling Long (Louisiana State University)
DTSTART;VALUE=DATE-TIME:20210630T140000Z
DTEND;VALUE=DATE-TIME:20210630T160000Z
DTSTAMP;VALUE=DATE-TIME:20230208T072311Z
UID:HypergeometricSeries/2
DESCRIPTION:Title: Hypergeometric Functions\, Character Sums and Applications\nby Ling Long (Louisiana State University) as part of A Lecture Series o
n Hypergeometric Series\n\n\nAbstract\nHypergeometric functions form a cla
ss of special functions satisfying a lot of symmetries. They are closely r
elated to the arithmetic of one-parameter families of algebraic varieties\
, such as the Legendre curves. $p$-adic hypergeometric functions were inve
stigated by Dwork leading to his fundamental unit root theory. Hypergeome
tric functions over finite fields were initiated by Katz and Greene\, furt
her developments were made in recent years by many authors.\n\nIn the prop
osed mini course\, we will explore hypergeometric functions over different
settings. Applications of the combined perspectives include obtaining cha
racter sum identities\, computing special L-values of modular forms\, fin
ding and proving supercongruences (influenced by important conjectures of
Buekers\, van Hamme\, Rodridguez-Villegas\, Roberts and Rodridguez-Villeg
as\, constructing decomposable Galois representations\, and computing ari
thmetic invariance of certain abelian varieties.\n\nThe mini-course will c
onsist of 4 lectures\, each 90-minute with a short break in the middle.\n
LOCATION:https://researchseminars.org/talk/HypergeometricSeries/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ling Long (Louisiana State University)
DTSTART;VALUE=DATE-TIME:20210701T140000Z
DTEND;VALUE=DATE-TIME:20210701T160000Z
DTSTAMP;VALUE=DATE-TIME:20230208T072311Z
UID:HypergeometricSeries/3
DESCRIPTION:Title: Hypergeometric Functions\, Character Sums and Applications\nby Ling Long (Louisiana State University) as part of A Lecture Series o
n Hypergeometric Series\n\n\nAbstract\nHypergeometric functions form a cla
ss of special functions satisfying a lot of symmetries. They are closely r
elated to the arithmetic of one-parameter families of algebraic varieties\
, such as the Legendre curves. $p$-adic hypergeometric functions were inve
stigated by Dwork leading to his fundamental unit root theory. Hypergeome
tric functions over finite fields were initiated by Katz and Greene\, furt
her developments were made in recent years by many authors.\n\nIn the prop
osed mini course\, we will explore hypergeometric functions over different
settings. Applications of the combined perspectives include obtaining cha
racter sum identities\, computing special L-values of modular forms\, fin
ding and proving supercongruences (influenced by important conjectures of
Buekers\, van Hamme\, Rodridguez-Villegas\, Roberts and Rodridguez-Villeg
as\, constructing decomposable Galois representations\, and computing ari
thmetic invariance of certain abelian varieties.\n\nThe mini-course will c
onsist of 4 lectures\, each 90-minute with a short break in the middle.\n
LOCATION:https://researchseminars.org/talk/HypergeometricSeries/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Ling Long (Louisiana State University)
DTSTART;VALUE=DATE-TIME:20210701T140000Z
DTEND;VALUE=DATE-TIME:20210701T160000Z
DTSTAMP;VALUE=DATE-TIME:20230208T072311Z
UID:HypergeometricSeries/4
DESCRIPTION:Title: Hypergeometric Functions\, Character Sums and Applications\nby Ling Long (Louisiana State University) as part of A Lecture Series o
n Hypergeometric Series\n\n\nAbstract\nHypergeometric functions form a cla
ss of special functions satisfying a lot of symmetries. They are closely r
elated to the arithmetic of one-parameter families of algebraic varieties\
, such as the Legendre curves. $p$-adic hypergeometric functions were inve
stigated by Dwork leading to his fundamental unit root theory. Hypergeome
tric functions over finite fields were initiated by Katz and Greene\, furt
her developments were made in recent years by many authors.\n\nIn the prop
osed mini course\, we will explore hypergeometric functions over different
settings. Applications of the combined perspectives include obtaining cha
racter sum identities\, computing special L-values of modular forms\, fin
ding and proving supercongruences (influenced by important conjectures of
Buekers\, van Hamme\, Rodridguez-Villegas\, Roberts and Rodridguez-Villeg
as\, constructing decomposable Galois representations\, and computing ari
thmetic invariance of certain abelian varieties.\n\nThe mini-course will c
onsist of 4 lectures\, each 90-minute with a short break in the middle.\n
LOCATION:https://researchseminars.org/talk/HypergeometricSeries/4/
END:VEVENT
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