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:20260422T212926Z 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:20210630T140000Z DTEND:20210630T160000Z DTSTAMP:20260422T212926Z 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:20210701T140000Z DTEND:20210701T160000Z DTSTAMP:20260422T212926Z 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:20210701T140000Z DTEND:20210701T160000Z DTSTAMP:20260422T212926Z 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 END:VCALENDAR