BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ling Long (Louisiana State University) DTSTART:20210629T140000Z DTEND:20210629T160000Z DTSTAMP:20260404T094546Z UID:HypergeometricSeries/1 DESCRIPTION:Title: Hypergeometric Functions\, Character Sums and Applicat ions\nby Ling Long (Louisiana State University) as part of A Lecture S eries on Hypergeometric Series\n\n\nAbstract\nHypergeometric functions for m a class of special functions satisfying a lot of symmetries. They are cl osely related to the arithmetic of one-parameter families of algebraic var ieties\, such as the Legendre curves. $p$-adic hypergeometric functions we re investigated by Dwork leading to his fundamental unit root theory. Hyp ergeometric functions over finite fields were initiated by Katz and Greene \, further developments were made in recent years by many authors.\n\nIn t he proposed mini course\, we will explore hypergeometric functions over di fferent settings. Applications of the combined perspectives include obtain ing character sum identities\, computing special L-values of modular forms \, finding and proving supercongruences (influenced by important conjectu res of Buekers\, van Hamme\, Rodridguez-Villegas\, Roberts and Rodridguez -Villegas\, constructing decomposable Galois representations\, and comput ing arithmetic invariance of certain abelian varieties.\n\nThe mini-course will consist of 4 lectures\, each 90-minute with a short break in the mid dle.\n LOCATION:https://stable.researchseminars.org/talk/HypergeometricSeries/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Ling Long (Louisiana State University) DTSTART:20210630T140000Z DTEND:20210630T160000Z DTSTAMP:20260404T094546Z UID:HypergeometricSeries/2 DESCRIPTION:Title: Hypergeometric Functions\, Character Sums and Applicat ions\nby Ling Long (Louisiana State University) as part of A Lecture S eries on Hypergeometric Series\n\n\nAbstract\nHypergeometric functions for m a class of special functions satisfying a lot of symmetries. They are cl osely related to the arithmetic of one-parameter families of algebraic var ieties\, such as the Legendre curves. $p$-adic hypergeometric functions we re investigated by Dwork leading to his fundamental unit root theory. Hyp ergeometric functions over finite fields were initiated by Katz and Greene \, further developments were made in recent years by many authors.\n\nIn t he proposed mini course\, we will explore hypergeometric functions over di fferent settings. Applications of the combined perspectives include obtain ing character sum identities\, computing special L-values of modular forms \, finding and proving supercongruences (influenced by important conjectu res of Buekers\, van Hamme\, Rodridguez-Villegas\, Roberts and Rodridguez -Villegas\, constructing decomposable Galois representations\, and comput ing arithmetic invariance of certain abelian varieties.\n\nThe mini-course will consist of 4 lectures\, each 90-minute with a short break in the mid dle.\n LOCATION:https://stable.researchseminars.org/talk/HypergeometricSeries/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Ling Long (Louisiana State University) DTSTART:20210701T140000Z DTEND:20210701T160000Z DTSTAMP:20260404T094546Z UID:HypergeometricSeries/3 DESCRIPTION:Title: Hypergeometric Functions\, Character Sums and Applicat ions\nby Ling Long (Louisiana State University) as part of A Lecture S eries on Hypergeometric Series\n\n\nAbstract\nHypergeometric functions for m a class of special functions satisfying a lot of symmetries. They are cl osely related to the arithmetic of one-parameter families of algebraic var ieties\, such as the Legendre curves. $p$-adic hypergeometric functions we re investigated by Dwork leading to his fundamental unit root theory. Hyp ergeometric functions over finite fields were initiated by Katz and Greene \, further developments were made in recent years by many authors.\n\nIn t he proposed mini course\, we will explore hypergeometric functions over di fferent settings. Applications of the combined perspectives include obtain ing character sum identities\, computing special L-values of modular forms \, finding and proving supercongruences (influenced by important conjectu res of Buekers\, van Hamme\, Rodridguez-Villegas\, Roberts and Rodridguez -Villegas\, constructing decomposable Galois representations\, and comput ing arithmetic invariance of certain abelian varieties.\n\nThe mini-course will consist of 4 lectures\, each 90-minute with a short break in the mid dle.\n LOCATION:https://stable.researchseminars.org/talk/HypergeometricSeries/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Ling Long (Louisiana State University) DTSTART:20210701T140000Z DTEND:20210701T160000Z DTSTAMP:20260404T094546Z UID:HypergeometricSeries/4 DESCRIPTION:Title: Hypergeometric Functions\, Character Sums and Applicat ions\nby Ling Long (Louisiana State University) as part of A Lecture S eries on Hypergeometric Series\n\n\nAbstract\nHypergeometric functions for m a class of special functions satisfying a lot of symmetries. They are cl osely related to the arithmetic of one-parameter families of algebraic var ieties\, such as the Legendre curves. $p$-adic hypergeometric functions we re investigated by Dwork leading to his fundamental unit root theory. Hyp ergeometric functions over finite fields were initiated by Katz and Greene \, further developments were made in recent years by many authors.\n\nIn t he proposed mini course\, we will explore hypergeometric functions over di fferent settings. Applications of the combined perspectives include obtain ing character sum identities\, computing special L-values of modular forms \, finding and proving supercongruences (influenced by important conjectu res of Buekers\, van Hamme\, Rodridguez-Villegas\, Roberts and Rodridguez -Villegas\, constructing decomposable Galois representations\, and comput ing arithmetic invariance of certain abelian varieties.\n\nThe mini-course will consist of 4 lectures\, each 90-minute with a short break in the mid dle.\n LOCATION:https://stable.researchseminars.org/talk/HypergeometricSeries/4/ END:VEVENT END:VCALENDAR