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:20260404T100027Z UID:numbertheoryinbangalore/1 DESCRIPTION:Title: Asymptotics and codimensions of modules over Iwasaw a algebras\nby Sujatha Ramdorai (University of British Columbia) as pa rt of IISc Number Theory seminar\n\n\nAbstract\nLet $R$be the Iwasawa alge bra over 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 finitely generated $R$-module. In the late 1970’s \, Harris studied t he asymptotic growth of the ranks of certain coinvariants of \n$M$ arising from the action of open subgroups of $G$ and related them to the codimens ion of $M$. In this talk\, we explain how Harris’ proofs can be simplifi ed and improved upon\, with possible applications to studying some natural subquotients of the Galois groups of number fields.\n LOCATION:https://stable.researchseminars.org/talk/numbertheoryinbangalore/ 1/ END:VEVENT BEGIN:VEVENT SUMMARY:Gabor Wiese (University of Luxembourg) DTSTART:20220211T093000Z DTEND:20220211T103000Z DTSTAMP:20260404T100027Z UID:numbertheoryinbangalore/2 DESCRIPTION:Title: Galois Families of Modular Forms\nby Gabor Wies e (University of Luxembourg) as part of IISc Number Theory seminar\n\n\nAb stract\nFollowing a joint work with Sara Arias-de-Reyna and François Legr and\, we present a new kind of families of modular forms. They come from r epresentations of the absolute Galois group of rational function fields ov er $\\Q$. As a motivation and illustration\, we discuss in some details on e example: an infinite Galois family of Katz modular forms of weight one i n characteristic 7\, all members of which are non-liftable. This may be su rprising because non-liftability is a feature that one might expect to occ ur only occasionally.\n LOCATION:https://stable.researchseminars.org/talk/numbertheoryinbangalore/ 2/ END:VEVENT BEGIN:VEVENT SUMMARY:Jaclyn Lang (Temple University) DTSTART:20220225T123000Z DTEND:20220225T133000Z DTSTAMP:20260404T100027Z 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 Herbrand’s theorem\, Ribet used Eisenstein-cuspidal congruences to prod uce unramified degree- $p$ extensions of the $p$ -th cyclotomic field whe n $p$ is an odd prime. After reviewing Ribet’s strategy\, we will disc uss recent 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 prime that is congruent to $− 1 \\mod p $. This answers a quest ion posted on Frank Calegari’s blog.\n LOCATION:https://stable.researchseminars.org/talk/numbertheoryinbangalore/ 3/ END:VEVENT BEGIN:VEVENT SUMMARY:Jungwon Lee (Mathematics Institute\, Warwick) DTSTART:20220304T123000Z DTEND:20220304T133000Z DTSTAMP:20260404T100027Z UID:numbertheoryinbangalore/4 DESCRIPTION:Title: Another view of Ferrero--Washington Theorem\nby Jungwon Lee (Mathematics Institute\, Warwick) as part of IISc Number Theo ry seminar\n\n\nAbstract\nWe reprove the main equidistribution instance in the Ferrero–Washington proof of the vanishing of cyclotomic Iwasawa $\\ mu$-invariant\, based on the ergodicity of a certain $p$-adic skew extensi on dynamical system that can be identified with Bernoulli shift (joint wit h Bharathwaj Palvannan).\n LOCATION:https://stable.researchseminars.org/talk/numbertheoryinbangalore/ 4/ END:VEVENT BEGIN:VEVENT SUMMARY:Nobuo Sato (National Taiwan University) DTSTART:20220311T093000Z DTEND:20220311T103000Z DTSTAMP:20260404T100027Z UID:numbertheoryinbangalore/5 DESCRIPTION:Title: On Eulerian multiple zeta values and the block shuf fle relations\nby Nobuo Sato (National Taiwan University) as part of I ISc Number Theory seminar\n\n\nAbstract\nEuler solved the famous Basel pro blem and discovered that Riemann zeta functions at positive even integers are rational multiples of powers of π. Multiple zeta values (MSVs) are a multi-dimensional generalization of the Riemann zeta values\, and MZVs whi ch are rational multiples of powers of π is called Eulerian MZVs. In 1996 \, Borwein-Bradley-Broadhurst discovered a series of conjecturally Euleria n MZVs which together with the known Eulerian family seems to exhaust all Eulerian MZVs at least numerically. A few years later\, Borwein-Bradley-Br oadhurst-Lisonek discovered two families of interesting conjectural relati ons among MZVs generalizing the previous conjecture of Eulerian MZVs\, whi ch were later extended further by Charlton in light of alternating block s tructure. In this talk\, I would like to present my recent joint work with Minoru Hirose concerning block shuffle relations that simultaneously reso lve and generalize the conjectures of Charlton.\n LOCATION:https://stable.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:20260404T100027Z UID:numbertheoryinbangalore/6 DESCRIPTION:Title: Dimensions of admissible representations of reduct ive p-adic groups\nby Marie-France Vigneras (Institut de Mathematiques de Jussieu\, Paris\, France) as part of IISc Number Theory seminar\n\n\nA bstract\nI will answer some questions (admissibility\, dimensions of inva riants by Moy-Prasad groups)\non representations of reductive p-adic group s and on Hecke algebras modules raised in my paper for the 2022-I.C.M. Noe ther lecture.\n LOCATION:https://stable.researchseminars.org/talk/numbertheoryinbangalore/ 6/ END:VEVENT END:VCALENDAR