BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Ellen Eischen (University of Oregon) DTSTART:20220407T160000Z DTEND:20220407T170000Z DTSTAMP:20260423T005849Z UID:UCDANT/25 DESCRIPTION:Title: Some congruences and consequences in number theory and beyond\nby Elle n Eischen (University of Oregon) as part of Dublin Algebra and Number Theo ry Seminar\n\n\nAbstract\nIn the mid-1800s\, Kummer observed some striking congruences between certain values of the Riemann zeta function\, which h ave important consequences in algebraic number theory\, in particular for unique factorization in certain rings. In spite of its potential\, this to pic lay mostly dormant for nearly a century until it was revived by Iwasaw a in the mid-1950s. Since then\, advances in arithmetic geometry and numbe r theory (in particular\, for modular forms\, certain analytic functions t hat play a central role in number theory) have enabled substantial extensi on to congruences in the context of other arithmetically significant data\ , and this has remained an active area of research. In this talk\, I will survey old and new tools for studying such congruences. I will conclude by introducing some unexpected challenges that arise when one tries to take what would seem like immediate next steps beyond the current state of the art.\n LOCATION:https://researchseminars.org/talk/UCDANT/25/ END:VEVENT END:VCALENDAR