BEGIN:VCALENDAR VERSION:2.0 PRODID:researchseminars.org CALSCALE:GREGORIAN X-WR-CALNAME:researchseminars.org BEGIN:VEVENT SUMMARY:Vaidehee Thatte (King's College London) DTSTART:20241004T070000Z DTEND:20241004T080000Z DTSTAMP:20260423T022830Z UID:KyuDaiSem/5 DESCRIPTION:Title: Ramification Theory for Henselian Valued Fields\nby Vaidehee Thatte (King's College London) as part of Kyushu University Algebra Seminar\n\nLe cture held in Room C-513 in the West No. 1 Bldg. of Ito Campus.\n\nAbstrac t\nRamification theory serves the dual purpose of a diagnostic tool and tr eatment by helping us locate\, measure\, and treat the anomalous behavior of mathematical objects. In the classical setup\, the degree of a finite G alois extension of "nice" fields splits up neatly into the product of two well-understood numbers (ramification index and inertia degree) that encod e how the base field changes. In the general case\, however\, a third fact or called the defect (or ramification deficiency) can pop up. The defect i s a mysterious phenomenon and the main obstruction to several long-standin g open problems\, such as obtaining resolution of singularities. The prima ry reason is\, roughly speaking\, that the classical strategy of "objects become nicer after finitely many adjustments" fails when the defect is non -trivial. I will discuss my previous and ongoing work in ramification theo ry that allows us to understand and treat the defect.\n LOCATION:https://researchseminars.org/talk/KyuDaiSem/5/ END:VEVENT END:VCALENDAR