BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Sujatha Ramdorai (University of British Columbia) DTSTART:20220204T093000Z DTEND:20220204T103000Z DTSTAMP:20260422T213046Z UID:numbertheoryinbangalore/1 DESCRIPTION:Title: Asymptotics and codimensions of modules over Iwasawa algeb ras\nby Sujatha Ramdorai (University of British Columbia) as part of I ISc Number Theory seminar\n\n\nAbstract\nLet $R$be the Iwasawa algebra ove r a compact\, $p$-adic\, pro-$p$ group $G$\, where $G$ arises as a Galois group of number fields from Galois representations. Suppose $M$ is a fini tely generated $R$-module. In the late 1970’s \, Harris studied the asym ptotic growth of the ranks of certain coinvariants of \n$M$ arising from t he action of open subgroups of $G$ and related them to the codimension of $M$. In this talk\, we explain how Harris’ proofs can be simplified and improved upon\, with possible applications to studying some natural subquo tients of the Galois groups of number fields.\n LOCATION:https://researchseminars.org/talk/numbertheoryinbangalore/1/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabor Wiese (University of Luxembourg) DTSTART:20220211T093000Z DTEND:20220211T103000Z DTSTAMP:20260422T213046Z UID:numbertheoryinbangalore/2 DESCRIPTION:Title: Galois Families of Modular Forms\nby Gabor Wiese (Univ ersity of Luxembourg) as part of IISc Number Theory seminar\n\n\nAbstract\ nFollowing a joint work with Sara Arias-de-Reyna and François Legrand\, w e present a new kind of families of modular forms. They come from represen tations of the absolute Galois group of rational function fields over $\\Q $. As a motivation and illustration\, we discuss in some details one examp le: an infinite Galois family of Katz modular forms of weight one in chara cteristic 7\, all members of which are non-liftable. This may be surprisin g because non-liftability is a feature that one might expect to occur only occasionally.\n LOCATION:https://researchseminars.org/talk/numbertheoryinbangalore/2/ END:VEVENT BEGIN:VEVENT SUMMARY:Jaclyn Lang (Temple University) DTSTART:20220225T123000Z DTEND:20220225T133000Z DTSTAMP:20260422T213046Z UID:numbertheoryinbangalore/3 DESCRIPTION:Title: A modular construction of unramified $p$-extensions of $\\ Q(N^{1/p})$\nby Jaclyn Lang (Temple University) as part of IISc Number Theory seminar\n\n\nAbstract\nIn his 1976 proof of the converse to Herbra nd’s theorem\, Ribet used Eisenstein-cuspidal congruences to produce unr amified degree- $p$ extensions of the $p$ -th cyclotomic field when $p$ is an odd prime. After reviewing Ribet’s strategy\, we will discuss rec ent work with Preston Wake in which we apply similar techniques to produce unramified degree-$p$ extensions of $\\Q(N^{1 / p})$ when $N$ is a p rime that is congruent to $− 1 \\mod p $. This answers a question pos ted on Frank Calegari’s blog.\n LOCATION:https://researchseminars.org/talk/numbertheoryinbangalore/3/ END:VEVENT BEGIN:VEVENT SUMMARY:Jungwon Lee (Mathematics Institute\, Warwick) DTSTART:20220304T123000Z DTEND:20220304T133000Z DTSTAMP:20260422T213046Z UID:numbertheoryinbangalore/4 DESCRIPTION:Title: Another view of Ferrero--Washington Theorem\nby Jungwo n Lee (Mathematics Institute\, Warwick) as part of IISc Number Theory semi nar\n\n\nAbstract\nWe reprove the main equidistribution instance in the Fe rrero–Washington proof of the vanishing of cyclotomic Iwasawa $\\mu$-inv ariant\, based on the ergodicity of a certain $p$-adic skew extension dyna mical system that can be identified with Bernoulli shift (joint with Bhara thwaj Palvannan).\n LOCATION:https://researchseminars.org/talk/numbertheoryinbangalore/4/ END:VEVENT BEGIN:VEVENT SUMMARY:Nobuo Sato (National Taiwan University) DTSTART:20220311T093000Z DTEND:20220311T103000Z DTSTAMP:20260422T213046Z UID:numbertheoryinbangalore/5 DESCRIPTION:Title: On Eulerian multiple zeta values and the block shuffle rel ations\nby Nobuo Sato (National Taiwan University) as part of IISc Num ber Theory seminar\n\n\nAbstract\nEuler solved the famous Basel problem an d discovered that Riemann zeta functions at positive even integers are rat ional multiples of powers of π. Multiple zeta values (MSVs) are a multi-d imensional generalization of the Riemann zeta values\, and MZVs which are rational multiples of powers of π is called Eulerian MZVs. In 1996\, Borw ein-Bradley-Broadhurst discovered a series of conjecturally Eulerian MZVs which together with the known Eulerian family seems to exhaust all Euleria n MZVs at least numerically. A few years later\, Borwein-Bradley-Broadhurs t-Lisonek discovered two families of interesting conjectural relations amo ng MZVs generalizing the previous conjecture of Eulerian MZVs\, which were later extended further by Charlton in light of alternating block structur e. In this talk\, I would like to present my recent joint work with Minoru Hirose concerning block shuffle relations that simultaneously resolve and generalize the conjectures of Charlton.\n LOCATION:https://researchseminars.org/talk/numbertheoryinbangalore/5/ END:VEVENT BEGIN:VEVENT SUMMARY:Marie-France Vigneras (Institut de Mathematiques de Jussieu\, Pari s\, France) DTSTART:20221019T113000Z DTEND:20221019T123000Z DTSTAMP:20260422T213046Z UID:numbertheoryinbangalore/6 DESCRIPTION:Title: Dimensions of admissible representations of reductive p-a dic groups\nby Marie-France Vigneras (Institut de Mathematiques de Jus sieu\, Paris\, France) as part of IISc Number Theory seminar\n\n\nAbstract \nI will answer some questions (admissibility\, dimensions of invariants by Moy-Prasad groups)\non representations of reductive p-adic groups and o n Hecke algebras modules raised in my paper for the 2022-I.C.M. Noether le cture.\n LOCATION:https://researchseminars.org/talk/numbertheoryinbangalore/6/ END:VEVENT END:VCALENDAR